dynamic channel slot allocation scheme and performance...

Research ArticleDynamic Channel Slot Allocation Scheme and PerformanceAnalysis of Cyclic Quorum Multichannel MAC Protocol

Xing Hu1 LinhuaMa1 Shaocheng Huang2 Tianyu Huang1 and Shiping Liu1

1School of Aeronautics and Astronautics Engineering Air Force Engineering University Xirsquoan Shaanxi 710038 China2School of Electrical Engineering Royal Institute of Technology Stockholm Sweden

Correspondence should be addressed to Xing Hu hustartyahoocom

Received 4 November 2016 Accepted 27 June 2017 Published 28 September 2017

Academic Editor Ibrahim Zeid

Copyright copy 2017 Xing Hu et alThis is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In high diversity node situation multichannel MAC protocol can improve the frequency efficiency owing to fewer collisions com-paredwith single-channelMACprotocol And the performance of cyclic quorum-basedmultichannel (CQM)MACprotocol is out-standing Based on cyclic quorum system and channel slot allocation it can avoid the bottleneck that others suffered fromand can beeasily realized with only one transceiver To obtain the accurate performance of CQMMACprotocol aMarkov chainmodel whichcombines the channel-hopping strategy of CQM protocol and IEEE 80211 distributed coordination function (DCF) is proposedThe results of numerical analysis show that the optimal performance of CQM protocol can be obtained in saturation bound situa-tion And thenwe obtain the saturation bound of CQMsystemby bird swarm algorithm In addition to improve the performance ofCQMprotocol in unsaturation situation a dynamic channel slot allocation ofCQM(DCQM)protocol is proposed based onwaveletneural network Finally the performance of CQM protocol and DCQM protocol is simulated by Qualnet platform And the simu-lation results show that the analytic and simulation results match very well the DCQM performs better in unsaturation situation

1 Introduction

IEEE 80211DistributedCoordination Function (DCF) [1] hasbeen widely used in mobile ad hoc networks However inhigh diversity node situation the IEEE 80211 DCF suffersfrom many collisions resulting in low frequency utilization[2]

Multichannel MAC protocol can help to share the trafficloads among different channels Hence the collisions single-channel MAC protocols suffered from can be alleviated Infact IEEE 80211b and IEEE 80211a can support 3 and 13nonoverlapping channels respectively [2] This means thatdesigning a multichannel MAC (MMAC) protocol is feasibleand desirable in IEEE 80211-based mobile ad hoc networks

Thegreat challenge of designingMMAC is how to allocatechannels to node for transmitting information And solutionsto this problem can be classified into two patterns

(a) Channel negotiating pattern channels allocated bynegotiating through dedicated control slot or channel

(b) Channel-hopping pattern nodes switch channels in afixed pattern or random mechanism

There are many protocols ([3ndash15]) that belong to thechannel negotiating pattern In these protocols some areequipped with at least two transceivers such as protocols[3 7 11ndash14] For these protocols one transceiver is turned toa common control channel that is dedicated for negotiatingthe channel to be used next Once the channel is selected theother transceiver(s) will switch to the negotiated channel fordata transmissionThese protocols are referred to as the mul-titransceiver channel negotiating solutions An undesirablefeature of these protocols is high hardware cost In addition atone moment at most one transmission pair can be handledand the dedicated control transceiver is a bottleneck of thethroughput of network To solve these problems some areequipped with only one transceiver such as [4ndash6 8ndash10 15]Among them protocols [5 6 9 15] use a dedicated controlchannel for control message exchange In such methodsthe dedicated control channel will be either overloaded orunderutilized if the capacity of the dedicated control channeland the data channels is not properly distributed Someother proposals [4 8 10] use a common control periodwhich is similar to the ATIM window concept in IEEE

HindawiMathematical Problems in EngineeringVolume 2017 Article ID 8580913 16 pageshttpsdoiorg10115520178580913

2 Mathematical Problems in Engineering

80211 power-saving mode (PSM) for nodes to negotiate thedata channels Using either a dedicated control channel or acommon control period these protocols are referred to as thesingle-transceiver channel negotiating solutions Howeverthe bottleneck still exists and no concurrent handshaking isallowed

Different from the channel negotiating pattern someother solutions utilize the channel-hopping concept to switchamong data channels to achieve concurrent handshakingSimilarly some of channel-hopping pattern protocols areequippedwith at least two transceivers such as protocols [16ndash18] However owing to the high hardware cost and difficultyto be realized in current equipment we only discuss thesingle-transceiver protocols in the rest of paperThe protocols[19ndash21] are equipped with only one transceiver In theseprotocols different nodes have different channel-hoppingsequences and each pair of nodes is able to communicatewith each other when they switch to the same channel atthe same time slot In [19] a multichannel protocol calledmultichannel MAC protocol (McMAC) uses a commonlinear congruential generator to build each nodersquos channel-hopping sequence An asynchronous efficient multichannelMAC protocol (EM-MAC) also adopts the pseudorandomchannel-hopping mechanism in [20] In the slotted seededchannel-hopping protocol (SSCH) [21] a channel-hoppingmechanism is proposed such that any two nodes are guaran-teed to have a rendezvous once in one cycle A flaw of thesechannel-hopping protocols is that they may suffer from themissing receiver problem This problem frequently occursparticularly in a heavy-loaded environment [5] In [2]Chao and Tsai propose a cyclic quorum-based multichannel(CQM) MAC protocol According to channel-hopping strat-egy of CQM protocol based on cyclic quorum system everychannel has the same chance to be accessed Hence it canovercome the bottleneck of channel negotiating pattern andthe missing receiver problem of channel-hopping pattern

However as is known to us the most optimal per-formance of CQM protocol is not analyzed theoretically

yet And in unsaturation situation the performance of thefixed channel slot allocation scheme cannot be optimalHence to obtain the optimal performance we analyze theperformance of CQMprotocol theoretically based onMarkovchain model And a traffic prediction based dynamic channelslot allocation scheme of CQM protocol is proposed

The rest of this paper is organized as follows Thecyclic quorum system and CQM protocol are introduced inSection 2TheMarkov chainmodel and performance analysisof CQMprotocol are given in Section 3The saturation boundis obtained by bird swarm optimal algorithm in Section 4The traffic prediction based dynamic channel slot allocationscheme of CQM protocol is introduced in Section 5 Inaddition the theoretical performance analysis CQMprotocolis verified and the performance comparison between CQMand DCQM protocols is also given in Section 6 The paper isconcluded in Section 7

2 Introduction of CQM Protocol

21 Cyclic Quorum System Quorum systems have beenwidely used forMACprotocol designing inwireless networks[22 23] And a quorum system can be defined as follows

Given a universal set119880 = 0 119899 minus 1 a quorum system119876 under 119880 is a collection of nonempty subsets of 119880 eachcalled a quorum which satisfies the intersection property

119866 cap 119867 = 120601 forall119866119867 isin 119876 (1)

There are many quorum systems such as the cyclicquorum system the grid quorum system and the torusquorum system The cyclic quorum system has the elegantfeature of rotation closure property and it can provide equalopportunity for a node to transmit and to receive Therotation closure property is as follows

119866 cap rotate (119867 119894) = forall119866119867 isin 119876 119894 isin 0 119899 minus 1 where rotate (119867 119894) = (119895 + 119894) mod 119899 | 119895 isin 119867 (2)

A cyclic quorum system can be constructed from adifference set The definitions of a difference set and a cyclicquorum system are as follows

Given a set 119863 = 1198891 119889119896 119889119896 isin 119885119899 the set 119863 can be adifference set if forall (119890 = 0) mod 119899

exist (119889119894 minus 119889119895) = 119890 mod 119899 where 119889119894 119889119895 isin 119863 (3)

Given a difference set 119863 = 1198891 119889119896 119889119896 isin 119885119899 a cyclicquorum 119876 can be defined as follows119876 = 1198760 119876119899minus1

where 119876119894 = 1198891 + 119894 119889119896 + 119894 mod 119899 119894 = 1 119899 (4)

22 CQM Protocol Based on cyclic quorum system Chaoand Tsai propose a cyclic quorum-based multichannel(CQM)MAC protocol [2] The CQM protocol does not needchannel negotiating so the bottleneck of channel negotiatingmechanism can be avoided In CQM protocol nodes cancommunicate with others when they meet at the samechannel and same channel slot And it can provide equalopportunity for nodes to transmit and to receive through thecyclic quorum system

In CQM protocol time is divided into a series of cyclesEach cycle consists of default channel slots and switchingchannel slots numbered from 0 to 119911 minus 1 The value of 119911is determined by the integer set from which the adopteddifference set is derived According to [2] CQM system

Mathematical Problems in Engineering 3

0 1 1

1 2 3 4 5 1 2 3 4 5

1 1 1 10 0 00 0

10

0 0

0 0 0 0 01 111 1

Cycle t Cycle t

Default slot

Switching slot

Idle

Look up tableY

1

N

1

q

10 0 0 0 0 01 111 1

hellip

sucient

Transmission

Y

1

N

1

Channelslot T

Node 0

Node 1

Node N

＄A = 0＄SA = 0 1 3

＄B = 1

＄N = 1

＄SB = 1 2 4

＄３N = 1 2 4

７ＣＮ1

７ＣＮ2ij

７ＣＮ3i0

1 minus q

７i = 0

1 minus Pt_sucient Pt_sucient

TＬＧＣＨＣＨＡ is

７i

middot middot middot



+ 1

P_trac

Figure 1 The protocol processing of CQM protocol with two channels

performs better under 1198856 In this paper 1198856 is adopted in theanalysis of CQM system

Let 119879 denote the channel slot length to separate withsystem time slot 120590 We assume that the length of channelslot 119879 is long enough to transmit at least one data packetAt default channel slots a node stays at its default channelwaiting for transmission requests At switching channel slotsa node may switch to its intended receiverrsquos default channelWe use a cyclic quorum 119866119894 under 119885119899 to identify a nodersquosdefault slots Specifically for any node 119894 isin 119881 where119881 is the setof nodes in the network 119894th nodersquos default channel (denotedas DC119894) and default slots (denoted as DS119894) are chosen asfollows

DC119894 = node ID119894 (mod ℎ)DS119894 = 119866119895 119895 = node ID119894 (mod 119911) where 119894 isin 119881 (5)

where node ID119894 is the ID of 119894th nodeFigure 1 is an example of CQM operation under 1198856 with

two channels (numbered from 0 to 1) Nodes 0 1 and 119873with IDs 0 1 and 119873 respectively are within each otherrsquostransmission range Each nodersquos default channel and default

slots are shown in Figure 1 supposing that we choose thedifference set 0 1 3 under 1198856 as 1198660 The marked time slotsare default channel slots The number in each channel slot isthe channel that should be switched to

As is shown in Figure 1 when a packet arrives at a randomtime slot the packet should wait in queue until all precedingpackets are transmitted And then the node looks up itschannel-hopping table and checks whether it can meet itsdestination node at the current channel slot If theymeet eachother at the current channel slot the node can turn into theback-off stage Otherwise the node will turn into Wait1 stateto wait for the next channel slot available During back-offstage the back-off timer of a node is set to a random timeaccording to 80211 DCF scheme In this paper according toCQM protocol when the channel is occupied by the othernodes or the current channel slot is empty the back-offtimer is assumed to be held to wait for the next channelslot available And then the channel slot remaining will bechecked when back-off timer reaches zero If the channel slotremaining is long enough for one packet transmission thepacket will be transmitted Otherwise the node should turninto Wait31198940 state to wait for the next channel slot available


Table 1 Average channel slots analysis of node 0

Quorum combinationsWaiting channel slots between two

meetingsChannel slots in onecycle

Meetingstate

Waitingstate

Meetingslots

Waitingslots1198660 + 1198660 1ℎ 43ℎ 3ℎ (6ℎ minus 3)ℎ1198660 + 1198661 2 74 2 41198660 + 1198662 2 2 2 41198660 + 1198663 6 3 1 51198660 + 1198664 3 52 2 41198660 + 1198665 2 32 2 4

Results E(W meeting) E(W waiting) E(M slots) E(W slots)(15ℎ + 1) 6ℎ (129ℎ + 16) 12ℎ (3ℎ + 1) 2ℎ (9ℎ minus 1) 2ℎ

Finally after each successful transmission or after havingreached the maximum number of the retransmissions 119898 ifthere is a packet to be transmitted in queue the node entersinto checking processing again Otherwise the node entersinto the idle state 119902 denotes the probability of having anempty queue

Take Node 0 for example Table 1 shows average channelslots needed between twice meeting in one cycle in thesituation that the node is at meeting state and waiting stateAnd the average meeting slots and waiting slots in one cycleare also shown in Table 1

3 Performance Analysis of CQM Protocol

31 Markov Model of CQM Protocol Combined with thechannel-hopping strategy of CQM protocol and 80211 DCFthe Markov chain model of CQM protocol is proposed as isshown in Figure 2 We consider the following assumptionsfor modeling network (1) The network consists of 119899 nodesmoving in the range of transmission distance and packets aretransmitted from sources to destinations directly (2) A totalof ℎ channels are available for every node and all of themhave the same bandwidth (3) Every node knows the IDs ofits one-hop neighbors and every node is equipped with one-half-duplex transceiver which is able to switch to any channeldynamically (4) Every node is time synchronized and usesthe IEEE 80211 DCF (RTSCTS mode) as MAC protocol (5)Packets arrive to a node according to a Poisson process withrate 120582 packetss (6) The channel is assumed to be error-freePacket transmission is considered to be successful if there areno other packets transmissions at the same time

According to CQM protocol each node has the samechance to transmit packet through different channels So wecan take one selected channel of a node into consideration tomodel the CQM protocol scheme at MAC layer And then weassume that there are 1198991015840 = 119899ℎ nodes with packets rate 120582 tocontent in one selected channel in a random time slot Themodel consists of states that a node can reside in The points1198620 1198621 1198622 11986210158400 1198621015840119898 represent connection points which arenot states

During queuing stage the arriving packet will wait inbuffer if there are other packets to be transmitted And ifthere is no packet in buff the node will turn into idle state

If the packet is eligible to be transmitted the nodeenters into checking stageThe channel-hopping table will bechecked firstly The node can meet its destination node withprobability 119875meeting and turns into Wait1 state to wait for nextchannel slot available with probability 1 minus 119875meeting

During back-off stage we use the tuple (119894 119896) to representthe different states 119894 denotes the 119894th back-off stage andnumber 119894 = 0 1 1198981015840 119898 and 119896 denotes the value ofback-off timer in the range [0119882119894 minus 1] [24]119882119894 is the size ofthe CW at stage 119894 which can be expressed as follow

119882119894 = 2119894 lowast1198820 if 119894 le 119898101584021198981015840 lowast1198820 if 119894 gt 1198981015840 (6)

where 119898 denotes the maximum number of packet retrans-missions before the packet is dropped According to [25] thedefault value for1198981015840 is 5 and it is 7 for119898

When time slot 120590 is idle and the current channel slotremaining is sufficient for once back-off timer decrease thestate (119894 119896) will turn into (119894 119896 minus 1) with probability 1198751015840119905 sufficientOtherwise the back-off timer will be held and the node willwait for next channel slot available According to 80211 DCFthe packet will be transmitted when node turns into (119894 0)states Different from that in this model only if channelslot remaining is long enough for one packet transmissionthe packet will be transmitted at (119894 0) states Otherwise thenode will enter into Wait31198940 state to wait for next channel slotavailable 119875119894119896 denotes the probability of state (119894 119896) 119875119905 successdenotes the probability that a node transmits successfully ina random time slot and one selected channel We use 119875119862119894 todenote the probability that the node arrives at point 119862119894

In order to obtain the expression of state-steady probabil-ities of a node firstly we need to express 119875119894119896 in terms of 11987500According to Figure 2 during back-off stage we can obtainthe following relations


0 0

m 0

0 1

m 11

Idle

1

Queuing stage

Checkingstage

Back-ostage

11

1

1

1 1

11

C0

C1

C2

q

1 minus q

1 minus PＮrac

Ｎrac

1 minus Pmeeting

1 minus Pt_sucient

Pt_sucient

Pt_sucient

1 minus Pt_sucient

Pmeeting

P

７ＣＮ1

1W0

Pt_sucient

Pt_sucientP

t_sucient Pt_sucient

Pt_sucient

Pt_sucientPt_succss Pt_sucientP

t_sucient

Pt_sucient

1 minusPt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus P t_sucient

m 1m 0

Cm

７ＣＮ3m0

７ＣＮ2m1

C0

(1 minus Pt_sＯ＝＝ＭＭ)Wm


(1 minus Pt_sＯ＝＝ss )W1







７ＣＮ2mWminus1

７ＣＮ300

Pt_Ｍucient

７ＣＮ201

Cm

0W0 minus 1

Pt_succss

７ＣＮ20W0minus1

７ＣＮ3m 0

７ＣＮ2m 1 ７ＣＮ2

m Wminus1(1 minus Pt_sＯ＝＝ＭＭ)Wm+1

1

mWm minus 1

mWm minus 1

Figure 2 Markov chain model of CQM protocol

1198751198621015840119894= 1198751198940 lowast 119875119905 sufficient + 119875Wait3

1198940= 1198751198940 lowast 119875119905 sufficient + 1198751198940 lowast (1 minus 119875119905 sufficient) = 1198751198940 0 le 119894 le 119898

119875119894119896 = 119875119894119896+1 lowast 1198751015840119905 sufficient + 119875Wait2119894119896= 119875119894119896+1 lowast 1198751015840119905 sufficient + 119875119894119896+1 lowast (1 minus 1198751015840119905 sufficient) = 119875119894119896+1 0 le 119895 le 119882119894 minus 1

1198751198940 =

119908119894minus1sum119906=0

1198751198621015840119894minus1lowast 1 minus 119875119905 success119908119894 = (1 minus 119875119905 success)119894 lowast 11987500 1 le 119894 le 119898

1199080minus1sum119906=0

1198751198622 lowast 11199080 = 1198751198622 119894 = 0


119875119894119896 =

119908119894minus119896minus1sum119906=0

1198751198621015840119894minus1lowast 1 minus 119875119905 success119908119894 = 119908119894 minus 119896119908119894 lowast (1 minus 119875119905 success)119894 lowast 11987500 1 le 119894 le 119898

1199080minus119896minus1sum119906=0

1198751198622 lowast 11199080 = 1199080 minus 1198961199080 lowast 1198751198622 = 1199080 minus 1198961199080 lowast 11987500 119894 = 0(7)

where 119875119905 sufficient and 1198751015840119905 sufficient denote the probability that theremaining channel time is enough for one packet transmis-sion and once back-off timer decrease respectively They canbe expressed as follows

119875119905 sufficient = 119879 minus 119879119904119879 1198751015840119905 sufficient = 119879 minus 120590119879 (8)

Let 119875119904119903 denote the probability that only 119904 nodes out of 119903nodes transmit packets in a random time slot and one selectedchannel Hence 119875119905 success can be expressed as follows

119875119905 success = 11987501198991015840minus1 = 11986201198991015840minus1 (120591)0 (1 minus 120591)1198991015840minus1 = (1 minus 120591)1198991015840minus1 (9)

where 120591 denotes the probability that a node transmits onepacket in a random time slot and one selected channel 120591 canbe expressed as follows

120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0

(1 minus 119875119905 success)119894 lowast 11987500 = 120572 lowast 11987500where 120572 = 1 minus (1 minus 119875119905 success)119898+1119875119905 success (10)

Combining (9) with (10) 11987500 can be expressed with119875119905 success11987500 = 1 minus 119875119905 success1(1198991015840minus1)120572 (11)

And then the 119875119862119894 can be obtained as follows

1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0

(1 minus 119875119905 success)119894 lowast 11987500 lowast 119875119905 success+ (1 minus 119875119905 success)119898 lowast 11987500 = 11987500

(12)

119875Idle = 1198751198620 lowast 119902119875traffic= 119902119875traffic

11987500 (13)

1198751198621 = 1198751198620 lowast (1 minus 119902) + 119875Idle lowast 119875traffic = 1198751198620 = 11987500 (14)

1198751198622 = 1198751198621 lowast 119875meeting + 119875Wait1

= 1198751198621 lowast 119875meeting + 1198751198621 lowast (1 minus 119875meeting) = 1198751198621= 11987500(15)

where 119875meeting denotes the probability that a pair of nodes canmeet each other in a randomchannel slot and a selected chan-nel According to analysis above 119875meeting can be expressed asfollows

119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)

Let 119875Wait1 119875Wait2119894119896 and 119875Wait3

1198940denote the probability of

Wait1 Wait2119894119896 and Wait31198940 states respectively 119879Wait1 119879Wait2119894119896

and 119879Wait31198940denote the time cost at Wait1 Wait2119894119896 and Wait31198940

states According to Figure 2 they can be expressed as follows

119875Wait1 = 1198751198621 lowast (1 minus 119875meeting) = 9ℎ minus 112ℎ lowast 11987500119879Wait1 = 119864 (119882 waiting) lowast 119879 = 129ℎ + 1612ℎ lowast 119879119875Wait2

119894119896= (119882119894 minus 119896) lowast (1 minus 119875119905 success)119894 lowast 120590 lowast 11987500119882119894119879

119879Wait2119894119896= 119864 (119882 meeting) lowast 119879 = (15ℎ + 1) lowast 1198796ℎ

119875Wait31198940= (1 minus 119875119905 success)119894 lowast 11987500 lowast 119879119904119879

119879Wait31198940= 1198791199042 + 119864 (119882 meeting) lowast 119879= (15ℎ + 1) lowast 119879 + 3ℎ1198791199046ℎ

(17)

where 119875traffic = 1 minus 119890minus120582120590 denotes the probability of havingpacket to be transmitted in a random time slot 120590 when thenode is at Idle state 119902 denotes the probability that thereis no packet in the queue of a node after each successfultransmission or after having reached the maximum numberof the retransmissions119898 119902 can be expressed as follows

119902 = 119890minus120582lowast119864[119878119887] (18)

And then (13) can be rewritten as follows

119875Idle = 119902119875traffic11987500 = 1199021 minus 119890minus12058212059011987500 (19)

where 119864[119878119887] denotes the average service time of one packettransmission (from the packet leaving theMAC buffer until itis successfully transmitted or reaches the retry limit) Accord-ing to Figure 2 119864[119878119887] includes two section the first one is the


average time cost in checking stage (119864[119879Wait1]) and the otheris the average time cost in back-off stage(119864[119879backoff ])119864 [119878119887] = 119864 [119879Wait1] + 119864 [119879backoff ] (20)

According to Figure 2 119864[119879Wait1] can be expressed asfollows119864 [119879Wait1] = 119879Wait1 lowast 119875Wait1

= (9ℎ minus 1) lowast (129ℎ + 16) lowast 119879144ℎ2 lowast 11987500 (21)

To get the value of all states in Figure 2 the average timecost 119864[119879backoff ] in back-off stage should be obtained firstlyAccording to Figure 2 119864[119879backoff ] can be expressed as follows119864 [119879backoff ] = 120590 119898sum

119894=0

(1 minus 119875119905 success)119894 119882119894 minus 12 + 119898sum119894=0

(119879119878+ 119879Wait3

1198940lowast (1 minus 119875119905 succicient)) (1 minus 119875119905 success)119894

sdot 119875119905 success + 119898sum119894=1

(119879119862 + 119879Wait31198940lowast (1 minus 119875119905 succicient))

lowast ((1 minus 119875119905 success)119894 119875119905 success119894+ (119898 + 1) (1 minus 119875119905 success)119898+1)

(22)

Combining (6) with (22) 119864[119879backoff ] can be expressedwith 119875119905 success119864 [119879backoff ] = 1205902 ((1 minus (2 (1 minus 119875119905 success))

1198981015840+1)11988201 minus 2 (1 minus 119875119905 success)+ 21198981015840 (1 minus 119875119905 success)1198981015840+11198820 (1 minus (1 minus 119875119905 success)119898minus1198981015840)119875119905 successminus 120572) + (119879119878 + (15ℎ + 1) lowast 119879 lowast 119879119878 + 3ℎ11987911987826ℎ119879 )120572lowast 119875119905 success + (119879119862 + (15ℎ + 1) lowast 119879 lowast 119879119878 + 3ℎ11987911987826ℎ119879 )lowast (1 minus 119875119905 success) lowast 120572

(23)

Assume

120573 = (1 minus (2 (1 minus 119875119905 success))1198981015840+1)11988201 minus 2 (1 minus 119875119905 success)+ 21198981015840 (1 minus 119875119905 success)1198981015840+11198820 (1 minus (1 minus 119875119905 success)119898minus1198981015840)119875119905 success

120574 = (15ℎ + 1) lowast 119879 lowast 119879119878 + 3ℎ11987911987826ℎ119879 (24)

and then (23) can be rewritten as follows

119864 [119879backoff ] = 1205902 lowast (120573 minus 120572) + (119879119878 + 120574) lowast 120572 lowast 119875119905 success+ (119879119862 + 120574) lowast (1 minus 119875119905 success) lowast 120572 (25)

where 120590 denotes the average time between successive counterdecrements in back-off stage The time needed for successivecounter decrements includes situations only one time slot1205901015840 is needed when all the other nodes have no packet to betransmitted 119879119904 + 1205901015840 needed when a packet is transmittedsuccessfully by the other nodes and 119879119888 + 1205901015840 needed whena transmission collision occurs in the other nodes Let 1198751205901015840 119875119879119904+1205901015840 and 119875119879119888+1205901015840 denote probabilities of these situationsrespectively Where 1205901015840 denotes the average time cost for onceback-off timer decrease when the channel is idle 1205901015840 can beexpressed as follows

1205901015840 = 120590 lowast 1198751015840119905 sufficient + 119879Wait2119894119896lowast (1 minus 1198751015840119905 sufficient)

= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get

1198751205901015840 = 11987501198991015840minus1 = (1 minus 120591)1198991015840minus1 119875119879119904+1205901015840 = 11987511198991015840minus1 = 11986211198991015840minus1120591 (1 minus 120591)1198991015840minus2

= (1198991015840 minus 1) 120591 (1 minus 120591)1198991015840minus2 119875119879119888+1205901015840 = 1 minus 1198751205901015840 minus 119875119879119904+1205901015840

= 1 minus (1 minus 120591)1198991015840minus1 minus (1198991015840 minus 1) 120591 (1 minus 120591)1198991015840minus2 (27)

120590 can be expressed as follows

120590 = 1205901015840 lowast 1198751205901015840 + (119879119904 + 1205901015840) lowast 119875119879119904+1205901015840 + (119879119888 + 1205901015840)lowast 119875119879119888+1205901015840 (28)

where 119879119904 is the time cost for a successful transmission and 119879119888is the average time the channel is sensed busy by each stationduring a collision Let119867 = PHYℎ119889119903 +MACℎ119889119903 be the packetheader and let 120575 be the propagation delay119879119904 and119879119888 are equalto

119879119904 = DIFS + RTS + CTS + 119867 + 119864 [119875] + ACK+ 3SIFS + 4120575119879119888 = DIFS + RTS + CTS + SIFS + 120575 (29)


Based on this analysis the value of 119902 and 119875119905 success shouldbe obtained before all the state-steady probabilities of a nodecan be got Firstly the relation between themcan be expressedbased on (18) and (20)

119902 = 119890minus1205821015840lowast119864[119878119887] = 119890minus1205821015840lowast(119864[119879Wait1 ]+119864[119879backoff ]) (30)

In addition the relation between 119902 and 119875119905 success also canbe obtained by using the normalization condition

119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1

(1 + 120590119879) lowast 120573 minus 1205722 lowast 11987500 + 9ℎ minus 112ℎ lowast 11987500 + 1199021 minus 119890minus120582120590lowast 11987500 + 120572 lowast 119879119904119879 lowast 11987500 = 1

11987500 lowast ((1 + 120590119879) lowast 120573 minus 1205722 + 9ℎ minus 112ℎ + 1199021 minus 119890minus120582120590+ 120572 lowast 119879119904119879 ) = 1

(31)

The equation can be expressed as follows

11987500 = 1(1 + 120590119879) lowast (120573 minus 120572) 2 + (9ℎ minus 1) 12ℎ + 119902 (1 minus 119890minus120582120590) + (120572 lowast 119879119904) 119879 (32)

Equations (30) and (32) are nonlinear and nonconvexThe equation set can be solved using arithmetic solution Andthen all the probabilities of 119875119894119896 119875119862119894 119875Idle 119875Wait1 119875Wait2

119894119896 and119875Wait3

1198940can be got too

32 Throughput Analysis Now we will analyze the through-put of CQM protocol Let 119878 denote the throughput of CQMsystem In this paper we assume the total of ℎ channels isavailable and all of them have the same bandwidth Hencethe throughput of CQMprotocol can be expressed as follows

119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)

where 119864[119897] denotes the average payload size per virtual slot inone selected channel 119864[119897] can be expressed as follows

119864 [119897] = 1198751119899 lowast 119897 = 11986211198991015840120591 (1 minus 120591)1198991015840minus1 lowast 119897= 1198991015840120591 (1 minus 120591)1198991015840minus1 lowast 119897 (34)

And 119864[slot] denotes the virtual slot duration It containsthe duration of an empty slot time 120590 the time duration119879119878 dueto a successful transmission and the time duration 119879119862 due toa collision respectively And then the average slot duration119864[119904lot] can be obtained

119864 [slot] = 1198750119899 lowast 120590 + 1198751119899 lowast 119879119878 + (1 minus 1198750119899 minus 1198751119899 ) lowast 119879119862 (35)

Finally the normalized throughput of CQM protocol canbe obtained

119878 = 119878ℎ lowast 119862= 1198751119899 lowast 119897(1198750119899 lowast 120590 + 1198751119899 lowast 119879119878 + (1 minus 1198750119899 minus 1198751119899 ) lowast 119879119862) lowast 119862

(36)

33 Average Packet Transmission Delay Analysis In thissection we will analyze the expected packet transmissiondelay at the MAC layer of CQM protocol Our analysisconsiders the delay 119864[119863tr] for a successfully transmittedpacket in the case of saturation 119864[119863tr] is defined as the timewhen a packet becomes eligible to be transmitted until itis transmitted successfully So 119864[119863tr] is equal to the back-off service time (119864[119878119887]) excluding the term corresponding todropping a packet (119864[119879drop])119864 [119863tr] = 119864 [119878119887] minus 119864 [119879drop]

= 119864 [119879Wait1] + 119864 [119879backoff ] minus (1 minus 119875119905 success)119898+1lowast ((119898 + 1) lowast (119879119888 + 120574) + 120590 lowast 119898sum

119894=0

119882119894 minus 12 ) (37)

34 Numerical Analysis of CQM Protocol To show theinfluence of parameters (119899 120582 119879 and ℎ) to the performance(119864[119863tr] and 119878) of CQM system obviously we now present therelationship between them by numerical analysis when ℎ isset to 3 A summary of parameters is shown in Table 2

The throughput versus node number and packet rate isshown in Figure 3 when the channel slot length is set to100ms

As is shown in Figure 3(a) the throughput increasesgradually with the increased node number with a certainpacket rate and it approaches a constant in the end In anetwork with the node number increases more packets canbe transmitted successfully so the throughput of networkincreases However with the network size become muchbigger more andmore nodes transmit packets in one channelwith a certain bandwidth more and more collisions willoccur In the end the network will reach a balance stateand the throughout will approach a constant As is similar tothe influence of node number the throughput has the samechange trend with the increased packet rate


0

5

10 050

100150

0

05

1

Node numberPacket rate (packetss)

Nor

mal

ized

thro

ughp

ut

04

05

06

07

08

(a) Throughput of CQM system (3D)

0 2 4 6 8 100

20

40

60

80

100

120

Packet rate (packetss)

Nod

e num

ber

04

05

06

07

08

(b) Throughput of CQM system (top view)

Figure 3 Throughput versus node number and packet rate with 119879 = 100ms

001

02 40 60 80 100 120 140

04

06

08

1

Node number

Channel slot length (s)

Nor

mal

ized

thro

ughp

ut

04505055060650707508

Figure 4 Throughput versus node number and channel slot length with 120582 = 2

Table 2 CQM system parameters in numerical analysis

Packet length 8192 bitsMAC header 272 bitsPhysical header (PHY) 128 bitsACK 112 bits + PHY headerRTS 160 bits + PHY headerCTS 112 bits + PHY headerSIFS 28 usDIFS 128 us119898 61198981015840 5Slot duration 50 usPropagation delay 1 usChannel bit rate 1MbpsChannel number 3

As is shown in Figure 3(b) with the increase of nodenumber and packet rate the throughput increases graduallyWhen node number and packet rate reach a bound thenetwork will turn into saturation state and throughputreaches its maximum value In this paper we call it saturationbound

Figure 4 shows the relationship between throughputnode number and channel slot length This system consistsof 3 channels and the packet rate is set to 2 packetss

As is shown in Figure 4 on the one hand the throughputincreases with the increase of node number in a certainchannel slot length and it approaches a constant value whenthe network is at saturation state On the other hand thethroughput changes slowly with the increase of channel slotlength in a certain node number

The relation between parameters (119899 120582 119879) and 119878 canbe revealed by numerical analysis The most maximumthroughput can be obtained when parameters (119899 120582 119879) breakthrough the saturation bound And then the change trend ofaverage packet delay with the change of parameters (119899 120582 119879)can be shown in Figures 5(a) and 5(b)

As is shown in Figure 5(a) with a given 119879 = 100msthe average packet delay increases sharply with the increaseof node number in oversaturation case The increased packetrate has little influence on the average packet delay Howeverthe packet dropping rate will increase sharply with theincrease of packet rate in oversaturation case Figure 5(b)shows that with the given 120582 = 8 and 119899 = 36 the maximumthroughput andminimum average packet transmission delaycan be obtained when channel slot length is set to 01s Thatis to say for a given 120582 and 119899 the network can reach thesaturation situation onlywhen the channel slot length reachesone certain value

Based on the analysis in this section for a network witha certain channel slot length the maximum throughputminimum average packet delay and minimum drop rate canbe obtained only in the saturation bound case And we will


010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07

(a) Average packet transmission delay of CQM system with 119879 = 100ms(3D)

Average packet transmission delayNormalized throughput

002 004 006 008 018012 014 016 020 01Channel slot length (s)

02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut

(b) Average packet transmission delay of CQM system with 119899 = 36 120582 = 8

Figure 5 Average packet transmission delay in oversaturation case

find the saturation bound of CQM system based on birdswarm algorithm in Section 5

4 Bird Swarm Algorithm BasedSaturation Bound

In this section we will find the saturation bound of CQMsystem According to analysis in Section 3 the best perfor-mance of CQM system can be obtained when the networkis in saturation bound case In this way the problem can beconsidered to be an optimization problemThe goal is to findpairs of value of 119899 and 120582 in saturation bound case with acertain 119879

For this optimization problem to get the less averagepacket transmission delay and less drop rate under thesituation with the most maximum throughput we set theobjective function as follows

119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)

And the constraint conditions are as follows

119899 isin 119885120582 gt 00 lt 119875119905 success le 10 lt 119902 le 1(39)

According to (38) and (39) this optimization problemis nonlinear and nonconvex To attack this optimizationproblem bird swarm algorithm (BSA) is adopted

BSA has elegant properties of effectiveness superiorityand stability to solve nonlinear and nonconvex problemproposed by Meng et al in 2015 [26] It is based on thethree kinds of behaviors of bird foraging behavior vigilance

behavior and flight behavior The BSA concludes four searchstrategies associated with five simplified rules

(a) Foraging Behavior Each bird searches for food accordingto its experience and the swarmsrsquo experience This behaviorcan be expressed as follows

119909119905+1119894119895 = 119909119905119894119895 + (119901119894119895 minus 119909119905119894119895) times Cog times rand (0 1)+ (119892119895 minus 119909119905119894119895) times Soc times rand (0 1) (40)

where 119909119905119894119895 denotes the position of the 119894th bird at time step 119905rand(0 1) denotes independent uniformly distributed num-bers in (01) Cog and Soc are two positive numbers whichcan be respectively called cognitive and social acceleratedcoefficients 119901119894119895 denotes the best previous position of the 119894thbird and 119892119894 denotes the best previous position shared by theswarm

(b) Vigilance Behavior Birds would try to move to the centreof swarm and theywould inevitably competewith each otherThus each bird would not directly move towards the centreof the swarm These motions can be formulated as follows

119909119905+1119894119895 = 119909119905119894119895 + 1198601 (mean119895 minus 119909119905119894119895) times rand (0 1)+ 1198602 (119901119896119895 minus 119909119905119894119895) times rand (minus1 1)

1198601 = 1198861 times exp (minus 119901Fit119894sumFit + 120576 times 119873) 1198602 = 1198862

times exp(( 119901Fit119894 minus 119901Fit1198961003816100381610038161003816119901Fit119896 minus 119901Fit1198941003816100381610038161003816 + 120576) 119901Fit119894 times 119873sumFit + 120576)

(41)

where 119896 is a positive integer which is randomly chosenbetween 1 and 119873 1198861 and 1198862 are two positive constants in[0 2]119901Fit119894 denotes the 119894th birdrsquos best fitness value and sumFitrepresents the sum of the swarmsrsquo best fitness value mean119895


05

10 15 005

1


0

100

200

300

400

Nod

e num

ber


(a) The discrete results of BSA algorithm (3D)

0204060810 2 4 6 8 10 12

Channel slot length (s)Packet rate (packetss)

050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350

(b) The smooth results of BSA algorithm (3D)

Figure 6 The saturation bound results obtained by BSA algorithm

denotes the 119895th element of the average position of the wholeswarm And 120576 is the smallest constant in the computer

(c) Flight Behavior Birds may fly to another site in responseto predation threat foraging or any other reasons Thebehaviors of the producers and scroungers can be describedmathematically as follows respectively

119909119905+1119894119895 = 119909119905119894119895 + rand 119899 (0 1) times 119909119905119894119895119909119905+1119894119895 = 119909119905119894119895 + (119909119905119896119895 minus 119909119905119894119895) times FL times rand (0 1) (42)

where rand 119899(0 1) denotes Gaussian distributed randomnumber withmean 0 and standard deviation 1 FLmeans thatthe scrounger would follow the producer to search for food

Based on BSA algorithm for a certain channel slot length119879 we can get the tuple (119899 120582) at the saturation bound Theparameter values of BSA algorithm in this section are givenin Table 3

In this section the channel slot length 119879 is selected inrange of [001 1] And Figure 6(a) shows the results of BSAalgorithmwith 3 channels Figure 6(b) is the smooth result ofFigure 6(a)

The surface in Figure 6(b) can denote the saturationbound of CQM system obviously The point on the surfacedenotes one possible tuple (119899 120582 119879) in the saturation boundcase As is shown in Figure 6(b) the packet rate changesagainst the changes of node number with a certain channelslot

When 119879 is set to 100ms the relationship between nodenumber and packet rate for different channel number in thesaturation bound case can be illustrated in Figure 7 And thenormalized throughput for different node number with 120582 = 8can be shown in Figure 8

As is shown in Figure 7 in saturation bound case thenode number decreases with the increase of packet rate with119879 = 100ms for different channel number And the nodenumber needed increase with the increase of channel numberin a certain packet rate That is to say only when the systemload is larger than capacity of channel the network can reachthe saturation bound state

0

50

100

150

200

250

300

350

400

450

Nod

e num

ber

2 4 6 8 10 120Packet rate

ℎ = 7ℎ = 5

ℎ = 3

Figure 7 The saturation bound of CQM system with differentchannel number

5 Traffic Prediction Based DCQM Protocol

According to the analysis in Section 4 the accurate per-formance of CQM MAC protocol is obtained The metrics(throughput and average packet transmission delay) arecalculated in performance analysis with respect to nodenumber packet rate channel slot length and channel num-ber

In CQM protocol owing to its equal opportunity fornodes to transmit and to receive the optimal performance ofCQMprotocol can be obtained in saturation bound situation

However in unsaturation situation in a random time slotsome nodes have packets to be transmitted while others haveno packet to be transmitted In this situation the channel slotscan not be utilized effectively due to the fixed slot allocationscheme of CQM protocol

To get the optimal performance in both unsaturation andsaturation situations a dynamic time slot allocation schemeof CQM protocol is proposed based on traffic prediction


Table 3 The parameter values of the BSA algorithm

Parameters 119862 119878 1198861 1198862 FL FQ 119879 119873Values 15 15 1 1 FL isin [05 09] 3 50 100

e

x1

x2

xk

wij

wjk

xk+1

f1 (sumwi1xi minus b1a1)


fm (sumwimxi minus bmam

)

Figure 8 The prediction model of WNN

In traffic prediction slot each node predicts the real timearrival traffic 119882tra by wavelet neural network And then inallocation slot the next channel slot is allocated according tothe predicted traffic of network

51 The Prediction Model of Wavelet Neural Network Bycontrast with the traditional neural network WNN shows ahigher accuracy faster convergence and better fault toleranceto complex nonlinear uncertain and unknown systemWavelet neural network takes the topological structure ofBP neural network as the foundation and selects the Morletwavelet basis function as the transfer function of the hid-den layer [27 28] As a feed-forward network BP neuralnetwork includes the forward propagation of signal and thebackpropagation of errorWhile the network is in the trainingand learning process the weight is continuously adjustedto obtain the minimum total error which is relevant to theappropriate output of the network The 119896 minus 119898 minus 1 predictionmodel of WNN is shown in Figure 8

As is shown in Figure 8 where 119909119894 119894 = 1 2 119896 is theinput parameter 119909119896+1 is the predicted output value in 119896 + 1moment 119908119894119895 is the layer weight from input layer to hiddenlayer and 119908119895119896 is the layer weight from hidden layer to outputlayer where 119898 denotes the node number in hidden layer 119886is the expansion parameter of the wavelet function 119887 is thetranslation parameter of the wavelet function The Morletwavelet basis function can extract the amplitude and phaseinformation of the analyzed signal Here the Morlet waveletbasis function as the activation function is shown as follows

119891 (119909) = cos (175119909) exp(minus11990922 ) (43)

The wavelet neural network adopts the gradient descentalgorithm [29] to correct the connection weight The error

function 119864 = (119909119896+1 minus 119909119896+1) is used to correct the connectionweight so as to minimize the network error

52 The Dynamic Time Slot Allocation Scheme To get theoptimal performance in both unsaturation and saturationsituation the DCQM protocol is proposed Based on CQMprotocol and WNN the traffic prediction slot and allocationslot are added in CQM protocol Figure 10 is an example ofDCQM operation under 1198856 with two channels (numberedfrom 0 to 1) Nodes 0 1 and 119873 with IDs 0 1 and 119873respectively are within each otherrsquos transmission range Theprotocol processing of DCQM protocol is shown in Figure 9

As is shown in Figure 9 the traffic prediction slot andallocation slot are added in front of each channel slot Inthe end of a channel slot number of packets transmitted inchannel slot and that in the former channel slots are sentto WNN prediction processing In traffic prediction slot thepredicted traffic to be transmitted in next channel slot of eachnode can be obtained And during the allocation slot if thepredicted traffic is 0 the next channel slot is turned to defaultslot Otherwise nodes will broadcast their predicted traffic intheir current channel in a random slot Each node can get thepredicted traffic of nodes in same channel which can denotethe traffic of network And then the next channel slot of eachnode can be allocated according to one judgment criteria

According to analysis of Figure 9 the judgment criteriaare the key to allocate the channel slot To utilize the channelefficiently the switching channel slot should be preferentiallyallocated to the nodes that having packets to be transmittedHowever when more and more nodes have packets to betransmitted if all of them are allocated to switching channelslot the problem of missing destination node exists To avoidthis problem the probability 119875allo switch that the switchingchannel slot is allocated to a node is introduced And let


Default slotSwitching slot

0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0

Trac prediction slot

Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac

Number of packetstransmitted

Y

N

Broadcast inrandom slot

Meet condition

Turn toswitching slot

Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B

= 1 2 4middot middot middot



Figure 9 The protocol processing of DCQM protocol with two channels

01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7

Figure 10 The relationship between 119875allo switch and 119903traffic

119903traffic denote the ratio of busy node number to network nodenumber And119875allo switch shouldmeet the conditions as follows

119875allo switch

prop 1119903traffic

0 lt 119903traffic lt 1= 1 119903traffic is small enough= 0 119903traffic is big enough

(44)

As is shown in (44) 119875allo switch is inversely proportional to119903traffic And 119903traffic is obtained through broadcast in allocationslot After traffic prediction slot each node obtained theirpredicted packet number by WNN algorithm During allo-cation slot the nodes that having packets to be transmittedbroadcast their predicted packet number in random slot Inthis way each node can obtain the approximate 119903traffic of


network And then each node will turn to switching channelslot according to corresponding 119875allo switch

To obtain the optimal 119875allo switch that meets the conditionin (44) lots of Monte Carlo simulations are adopted withℎ = 3 5 7 and 60 nodes considered For one unsaturationsituation (119903traffic isin [01 1]) lots of value of 119875allo switch isin[001 1] are considered The optimal 119875allo switch is obtainedwhen the throughput of network reaches its maximumThe relationship between 119875allo switch and 119903traffic is revealed inFigure 10

As is shown in Figure 10 119875allo switch is inversely propor-tional to 119903traffic whichmeets the condition in (44) And for thesame 119903traffic 119875allo switch increases with the increase of channelnumber With more channel numbers the probability thatnodes meet their destination nodes becomes bigger And theutilization rate of frequency increases with the increase ofchannel number

6 Performance Evaluation

To verify our analytical results we compared analytic resultswith simulation results obtained from Qualnet simulator Inaddition the performance of CQM and DCQM protocols isalso compared throughQualnet simulator Qualnet simulatoris the only parallel and message level network simulationtool developed by Scalable Networks Technologies It has thefaster running speed higher accuracy and better extensibilityand is suitable for development and simulation of ad hocnetwork and wireless sensor networks

In our simulations nodes are uniformly placed in anarea of 170m times 170m The transmission range of a node is250m In this way all nodes can stay in the transmissionrange of others A node keeps a separate FIFO queue for eachof its neighbors Each node may act as a sender where thedestination is chosen from its one-hop neighborsThe packetrate is selected in [2 6] And the channel slot is set to 100msTo get the performance of different channel number everynode is equipped with several interfaces The interface canbe assumed to be different channels and the CQM channel-hopping strategy is used in our simulations The number ofinterface is set to 3 5 and 7 The system parameters are thesame as the numerical analysis in Section 3

Firstly we will verify the saturation bound of analysisresults Figure 11 shows results comparison between numeri-cal analysis and simulation when 120582 is set to 2 3 4 5 6 7 and8

As is shown in Figure 11 the numerical analysis results canbe verified by simulating In addition the more nodes can beaccommodated with the increase of channel number It canbe verified that the multichannel system can perform betterthan the single system in high diversity node situation

And then we present the aggregate throughput betweenthe CQM and proposed DCQM protocol as shown inFigure 12 The simulation parameters of DCQM protocolare the same as that of the CQM protocol In addition forDCQM 119879prediction and 119879allocation denote the time in the trafficprediction stage and allocation stage respectively In thissimulation 119879prediction is set to 1ms and the 119879allocation is set to5ms Each traffic flow in the network uses the constant bit

2 3 4 5 6 7 8Packet rate (packetss)

20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber

Simulation ℎ = 7 T = 100ＧＭ


Simulation ℎ = 3 T = 100ＧＭAnalysis ℎ = 7 T = 100ＧＭ

Analysis ℎ = 5 T = 100ＧＭ


Figure 11 The comparison between analysis results and simulationresults with different channel number

0 2 4 6 8 10 12 14Packet rate (packetss)

055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7

CQM ℎ = 7DCQM ℎ = 5

CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3

Figure 12Theperformance comparison betweenCQMandDCQMprotocol

rate (CBR) trafficmodel the packet size is 1024 bytes and thepacket rate is set to 8

As is shown in Figure 12 for CQM andDCQMprotocolswith different channel number the normalized throughputincreases with the increase of packet rate And then itreaches its maximum value when node number reaches onecertain value Finally it decreases with the increase of nodenumber gradually In addition in unsaturation situation thenormalized throughput of DCQM is bigger than that ofCQM protocol This is because the utilization of frequencyincreases due to dynamic channel slot allocation And insaturation situation the performance of CQM protocol isslightly better than DCQM protocol For DCQM protocol insaturation situation 119875allo switch is almost 0 and the channelslot allocation is the same as CQM protocol However theadditional overhead is needed in DCQM protocol because of


the additional traffic prediction slot 119879prediction and allocationslot 119879allocation7 Conclusions

IEEE 80211 DCF suffers from many collisions in high diver-sity node situation Multichannel MAC protocol can helpto share the traffic loads among different channels And theCQM protocol performed better among MMAC protocolswith only one transceiverHowever the performance of CQMprotocol is not analyzed theoretically And the performanceis not optimal for the fixed channel slot allocation scheme inunsaturation situation

In this paper a Markov chain model is proposed toanalyze the performance of CQM protocol theoreticallyThe throughput and average packet transmission delay ofCQM system are revealed too And the saturation boundof CQM protocol is obtained based on BSA algorithmIn addition to obtain the optimal performance of CQMprotocol in unsaturation situation a traffic prediction baseddynamic channel slot allocation scheme of CQM protocol isproposed based on WNN prediction model In the end theperformance theoretical analysis of CQM protocol is verifiedby simulating on Qualnet platform And the performancecomparison of CQM and DCQM protocol is simulated tooThe results show that the simulation results and analyticalresults match very well and the DCQM protocol performsbetter than CQM protocol in unsaturation situation

Conflicts of Interest

The authors declare that they have no conflicts of interest

Acknowledgments

Xing HU wishes to thank Lin-hua MA for their helpful dis-cussions on information theoretic aspects of the subject Thiswork has been supported by the Nature Science Foundationof China (61072102) and the State Key Laboratory of XidianUniversity (ISN15-13)

References

[1] G Bianchi ldquoPerformance analysis of the IEEE 80211 distributedcoordination functionrdquo IEEE Journal on Selected Areas inCommunications vol 18 no 3 pp 535ndash547 2000

[2] C-M Chao and H-C Tsai ldquoA channel-hopping multichannelMAC protocol for mobile ad hoc networksrdquo IEEE Transactionson Vehicular Technology vol 63 no 9 pp 4464ndash4475 2014

[3] K H Almotairi and X Shen ldquoMultichannel medium accesscontrol for ad hoc wireless networksrdquoWireless Communicationsand Mobile Computing vol 13 no 11 pp 1047ndash1059 2013

[4] D N M Dang and C S Hong ldquoH-MMAC A hybridmulti-channel MAC protocol for wireless ad hoc networksrdquoin Proceedings of the 2012 IEEE International Conference onCommunications ICC 2012 pp 6489ndash6493 can June 2012

[5] J Shi T Salonidis and E W Knightly ldquoStarvation mitigationthroughmulti-channel coordination in CSMAMulti-hop wire-less networksrdquo in Proceedings of the 7th ACM International

Symposium on Mobile Ad Hoc Networking and Computing(MOBIHOC rsquo6) pp 214ndash225 ACM India May 2006

[6] M Maiya and B Hamdaoui ldquoAn improved IEEE 80211 MACprotocol for wireless ad-hoc networks with multi-channelaccess capabilitiesrdquo in Proceedings of the 2011 InternationalConference on High Performance Computing and SimulationHPCS 2011 pp 162ndash168 tur July 2011

[7] H Lei Z Ren C Gao and Y Guo ldquoA new multi-channelMAC protocol for 80211-based wireless mesh networksrdquo inProceedings of the 2012 International Conference on ComputerScience and Electronics Engineering ICCSEE 2012 pp 27ndash31chn March 2012

[8] O D Incel L Van Hoesel P Jansen and P Havinga ldquoMC-LMAC A multi-channel MAC protocol for wireless sensornetworksrdquo Ad Hoc Networks vol 9 no 1 pp 73ndash94 2011

[9] T Luo M Motani and V Srinivasan ldquoCooperative asyn-chronous multichannel MAC Design analysis and implemen-tationrdquo IEEE Transactions on Mobile Computing vol 8 no 3pp 338ndash352 2009

[10] J So and N Vaidya ldquoMulti-channel MAC for Ad Hoc net-works Handling multi-channel hidden terminals using a singletransceiverdquo in Proceedings of the 5th ACM international sympo-sium on Mobile as hoc networking and computing pp 222-223ACM India 2004

[11] J Wang Y Fang and D O Wu ldquoA power-saving multi-radiomulti-channel MAC protocol for wireless local area networksrdquoin Proceedings of the 25th IEEE International Conference onComputer Communications (INFOCOM rsquo06) pp 1ndash12 IEEEBarcelona Spain April 2006

[12] P-J Wu and C-N Lee ldquoOn-demand connection-orientedmulti-channel MAC protocol for ad-hoc networkrdquo in Proceed-ings of the 2006 3rd Annual IEEE Communications Society onSensor and Ad hoc Communications and Networks Secon 2006pp 621ndash625 usa September 2006

[13] S-LWu Y-C Tseng C-Y Lin and J-P Sheu ldquoAmulti-channelMAC protocol with power control for multi-hop mobile ad hocnetworksrdquo Computer Journal vol 45 no 1 pp 101ndash110 2002

[14] S-L Wu C-Y Lin Y-C Tseng and J-P Sheu ldquoA new multi-channel MAC protocol with on-demand channel assignmentfor multi-hop mobile ad hoc networkrdquo Parallel ArchitecturesAlgorithms and Networks pp 232ndash237 2000

[15] Z Xiangquan G Lijia and G Wei ldquoA load-balanced MACprotocol for multi-channel ad-hoc networksrdquo in Proceedingsof the ITST 2006 - 2006 6th International Conference on ITSTelecommunications Proceedings pp 642ndash645 chn June 2006

[16] J-H Kim and S-J Yoo ldquoTMCMP TDMAbasedmulti-channelMAC protocol for improving channel efficiency in wireless Adhoc networksrdquo in Proceedings of the 2009 IEEE 9th MalaysiaInternational Conference on Communications with a SpecialWorkshop on Digital TV Contents MICC 2009 pp 429ndash434mys December 2009

[17] P Kyasanur andNH Vaidya ldquoRouting and link-layer protocolsfor multi-channel multi-interface ad hoc wireless networksrdquoACM SIGMOBILE Mobile Computing and CommunicationsReview vol 10 no 1 pp 31ndash43 2006

[18] J S Pathmasuntharam A Das and A K Gupta ldquoPrimarychannel assignment based MAC (PCAM)-A multi-channelMACprotocol forMulti-Hopwireless networksrdquo in Proceedingsof the IEEE Wireless Communications and Networking Confer-ence (WCNC rsquo04) vol 2 pp 1110ndash1115 March 2004

[19] H-S W So G Nguyen and J Walrand ldquoPractical synchro-nization techniques for multichannel MACrdquo in Proceedings of


the 12Th Annual International Conference on Mobile ComputingAnd Networking pp 134ndash145 ACM India 2006

[20] L Tang Y Sun O Gurewitz and D B Johnson ldquoEM-MACa dynamic multichannel energy-efficient MAC protocol forwireless sensor networksrdquo in Proceedings of the 12th ACMInternational Symposium on Mobile Ad Hoc Networking andComputing (MobiHoc rsquo11) ACM LasVegasNevUSAMay 2011

[21] P Bahl R Chandra and J Dunagan ldquoSSCH Slotted seededchannel hopping for capacity improvement in IEEE 80211 Ad-Hoc wireless networksrdquo in Proceedings of the MobiCom 2004- Proceedings of the Tenth Annual International Conference onMobile Computing and Networking pp 216ndash230 India October2004

[22] C-M Chao J-P Sheu and I-C Chou ldquoAn adaptive quorum-based energy conserving protocol for IEEE 80211 ad hocnetworksrdquo IEEE Transactions on Mobile Computing vol 5 no5 pp 560ndash570 2006

[23] J-R Jiang Y-C Tseng C-S Hsu and T-H Lai ldquoQuorum-based asynchronous power-saving protocols for IEEE 80211 adhoc networksrdquoMobile Networks and Applications vol 10 no 1-2 pp 169ndash181 2005

[24] P Chatzimisios A C Boucouvalas andV Vitsas ldquoPerformanceanalysis of the IEEE 80211 MAC protocol for wireless LANsrdquoInternational Journal of Communication Systems vol 18 no 6pp 545ndash569 2005

[25] IEEE Computer Society LAN MAN Standards CommitteeWireless LAN Medium Access Control (MAC) and PhysicalLayer (PHY) Specifications[J] 1997

[26] X B Meng X Z Gao L H Lu et al ldquoA new bio-inspiredoptimisation algorithm Bird Swarm Algorithmrdquo Journal ofExperimental Theoretical Artificial Intelligence pp 1ndash15 2015

[27] H Yang W Zhao W Chen and X Chen ldquoThe study ofprediction model based on morlet wavelet neural networkrdquoApplied Mechanics and Materials vol 121-126 pp 4847ndash48512012

[28] Y-S Lu B-X Wu and S-F Lien ldquoAn improved sliding-moderepetitive learning control scheme using wavelet transformrdquoAsian Journal of Control vol 14 no 4 pp 991ndash1001 2012

[29] Y Y Yan and B L Guo ldquoApplication of wavelet neural network(WNN) and gradient descent method (GDM) in natural imagedenoisingrdquo Journal of Computational Information Systems vol2 no 2 pp 625ndash631 2006

Submit your manuscripts athttpswwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


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Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

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Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


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Algebra

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


80211 power-saving mode (PSM) for nodes to negotiate thedata channels Using either a dedicated control channel or acommon control period these protocols are referred to as thesingle-transceiver channel negotiating solutions Howeverthe bottleneck still exists and no concurrent handshaking isallowed

Different from the channel negotiating pattern someother solutions utilize the channel-hopping concept to switchamong data channels to achieve concurrent handshakingSimilarly some of channel-hopping pattern protocols areequippedwith at least two transceivers such as protocols [16ndash18] However owing to the high hardware cost and difficultyto be realized in current equipment we only discuss thesingle-transceiver protocols in the rest of paperThe protocols[19ndash21] are equipped with only one transceiver In theseprotocols different nodes have different channel-hoppingsequences and each pair of nodes is able to communicatewith each other when they switch to the same channel atthe same time slot In [19] a multichannel protocol calledmultichannel MAC protocol (McMAC) uses a commonlinear congruential generator to build each nodersquos channel-hopping sequence An asynchronous efficient multichannelMAC protocol (EM-MAC) also adopts the pseudorandomchannel-hopping mechanism in [20] In the slotted seededchannel-hopping protocol (SSCH) [21] a channel-hoppingmechanism is proposed such that any two nodes are guaran-teed to have a rendezvous once in one cycle A flaw of thesechannel-hopping protocols is that they may suffer from themissing receiver problem This problem frequently occursparticularly in a heavy-loaded environment [5] In [2]Chao and Tsai propose a cyclic quorum-based multichannel(CQM) MAC protocol According to channel-hopping strat-egy of CQM protocol based on cyclic quorum system everychannel has the same chance to be accessed Hence it canovercome the bottleneck of channel negotiating pattern andthe missing receiver problem of channel-hopping pattern

However as is known to us the most optimal per-formance of CQM protocol is not analyzed theoretically

yet And in unsaturation situation the performance of thefixed channel slot allocation scheme cannot be optimalHence to obtain the optimal performance we analyze theperformance of CQMprotocol theoretically based onMarkovchain model And a traffic prediction based dynamic channelslot allocation scheme of CQM protocol is proposed

The rest of this paper is organized as follows Thecyclic quorum system and CQM protocol are introduced inSection 2TheMarkov chainmodel and performance analysisof CQMprotocol are given in Section 3The saturation boundis obtained by bird swarm optimal algorithm in Section 4The traffic prediction based dynamic channel slot allocationscheme of CQM protocol is introduced in Section 5 Inaddition the theoretical performance analysis CQMprotocolis verified and the performance comparison between CQMand DCQM protocols is also given in Section 6 The paper isconcluded in Section 7

2 Introduction of CQM Protocol

21 Cyclic Quorum System Quorum systems have beenwidely used forMACprotocol designing inwireless networks[22 23] And a quorum system can be defined as follows

Given a universal set119880 = 0 119899 minus 1 a quorum system119876 under 119880 is a collection of nonempty subsets of 119880 eachcalled a quorum which satisfies the intersection property

119866 cap 119867 = 120601 forall119866119867 isin 119876 (1)

There are many quorum systems such as the cyclicquorum system the grid quorum system and the torusquorum system The cyclic quorum system has the elegantfeature of rotation closure property and it can provide equalopportunity for a node to transmit and to receive Therotation closure property is as follows

119866 cap rotate (119867 119894) = forall119866119867 isin 119876 119894 isin 0 119899 minus 1 where rotate (119867 119894) = (119895 + 119894) mod 119899 | 119895 isin 119867 (2)

A cyclic quorum system can be constructed from adifference set The definitions of a difference set and a cyclicquorum system are as follows

Given a set 119863 = 1198891 119889119896 119889119896 isin 119885119899 the set 119863 can be adifference set if forall (119890 = 0) mod 119899

exist (119889119894 minus 119889119895) = 119890 mod 119899 where 119889119894 119889119895 isin 119863 (3)

Given a difference set 119863 = 1198891 119889119896 119889119896 isin 119885119899 a cyclicquorum 119876 can be defined as follows119876 = 1198760 119876119899minus1

where 119876119894 = 1198891 + 119894 119889119896 + 119894 mod 119899 119894 = 1 119899 (4)

22 CQM Protocol Based on cyclic quorum system Chaoand Tsai propose a cyclic quorum-based multichannel(CQM)MAC protocol [2] The CQM protocol does not needchannel negotiating so the bottleneck of channel negotiatingmechanism can be avoided In CQM protocol nodes cancommunicate with others when they meet at the samechannel and same channel slot And it can provide equalopportunity for nodes to transmit and to receive through thecyclic quorum system

In CQM protocol time is divided into a series of cyclesEach cycle consists of default channel slots and switchingchannel slots numbered from 0 to 119911 minus 1 The value of 119911is determined by the integer set from which the adopteddifference set is derived According to [2] CQM system


0 1 1

1 2 3 4 5 1 2 3 4 5

1 1 1 10 0 00 0

10

0 0

0 0 0 0 01 111 1

Cycle t Cycle t

Default slot

Switching slot

Idle

Look up tableY

1

N

1

q

10 0 0 0 0 01 111 1

hellip

sucient

Transmission

Y

1

N

1

Channelslot T

Node 0

Node 1

Node N

＄A = 0＄SA = 0 1 3

＄B = 1

＄N = 1

＄SB = 1 2 4

＄３N = 1 2 4

７ＣＮ1

７ＣＮ2ij

７ＣＮ3i0

1 minus q

７i = 0



７i




+ 1

P_trac













Meetingstate

Waitingstate

Meetingslots
















0 0

m 0

0 1

m 11

Idle

1

Queuing stage

Checkingstage

Back-ostage

11

1

1

1 1

11

C0

C1

C2

q

1 minus q

1 minus PＮrac

Ｎrac

1 minus Pmeeting

1 minus Pt_sucient

Pt_sucient

Pt_sucient

1 minus Pt_sucient

Pmeeting

P

７ＣＮ1

1W0

Pt_sucient

Pt_sucientP


Pt_sucient


t_sucient

Pt_sucient

1 minusPt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus P t_sucient

m 1m 0

Cm

７ＣＮ3m0

７ＣＮ2m1

C0










７ＣＮ2mWminus1

７ＣＮ300

Pt_Ｍucient

７ＣＮ201

Cm

0W0 minus 1

Pt_succss

７ＣＮ20W0minus1

７ＣＮ3m 0



1

mWm minus 1

mWm minus 1





1198751198940 =

119908119894minus1sum119906=0


1199080minus1sum119906=0

1198751198622 lowast 11199080 = 1198751198622 119894 = 0


119875119894119896 =

119908119894minus119896minus1sum119906=0


1199080minus119896minus1sum119906=0







120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0




1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0


(12)


11987500 (13)





119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)











(17)


119902 = 119890minus120582lowast119864[119878119887] (18)









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 1 1

1 2 3 4 5 1 2 3 4 5

1 1 1 10 0 00 0

10

0 0

0 0 0 0 01 111 1

Cycle t Cycle t

Default slot

Switching slot

Idle

Look up tableY

1

N

1

q

10 0 0 0 0 01 111 1

hellip

sucient

Transmission

Y

1

N

1

Channelslot T

Node 0

Node 1

Node N

＄A = 0＄SA = 0 1 3

＄B = 1

＄N = 1

＄SB = 1 2 4

＄３N = 1 2 4

７ＣＮ1

７ＣＮ2ij

７ＣＮ3i0

1 minus q

７i = 0



７i




+ 1

P_trac













Meetingstate

Waitingstate

Meetingslots
















0 0

m 0

0 1

m 11

Idle

1

Queuing stage

Checkingstage

Back-ostage

11

1

1

1 1

11

C0

C1

C2

q

1 minus q

1 minus PＮrac

Ｎrac

1 minus Pmeeting

1 minus Pt_sucient

Pt_sucient

Pt_sucient

1 minus Pt_sucient

Pmeeting

P

７ＣＮ1

1W0

Pt_sucient

Pt_sucientP


Pt_sucient


t_sucient

Pt_sucient

1 minusPt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus P t_sucient

m 1m 0

Cm

７ＣＮ3m0

７ＣＮ2m1

C0










７ＣＮ2mWminus1

７ＣＮ300

Pt_Ｍucient

７ＣＮ201

Cm

0W0 minus 1

Pt_succss

７ＣＮ20W0minus1

７ＣＮ3m 0



1

mWm minus 1

mWm minus 1





1198751198940 =

119908119894minus1sum119906=0


1199080minus1sum119906=0

1198751198622 lowast 11199080 = 1198751198622 119894 = 0


119875119894119896 =

119908119894minus119896minus1sum119906=0


1199080minus119896minus1sum119906=0







120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0




1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0


(12)


11987500 (13)





119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)











(17)


119902 = 119890minus120582lowast119864[119878119887] (18)









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of








Meetingstate

Waitingstate

Meetingslots
















0 0

m 0

0 1

m 11

Idle

1

Queuing stage

Checkingstage

Back-ostage

11

1

1

1 1

11

C0

C1

C2

q

1 minus q

1 minus PＮrac

Ｎrac

1 minus Pmeeting

1 minus Pt_sucient

Pt_sucient

Pt_sucient

1 minus Pt_sucient

Pmeeting

P

７ＣＮ1

1W0

Pt_sucient

Pt_sucientP


Pt_sucient


t_sucient

Pt_sucient

1 minusPt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus P t_sucient

m 1m 0

Cm

７ＣＮ3m0

７ＣＮ2m1

C0










７ＣＮ2mWminus1

７ＣＮ300

Pt_Ｍucient

７ＣＮ201

Cm

0W0 minus 1

Pt_succss

７ＣＮ20W0minus1

７ＣＮ3m 0



1

mWm minus 1

mWm minus 1





1198751198940 =

119908119894minus1sum119906=0


1199080minus1sum119906=0

1198751198622 lowast 11199080 = 1198751198622 119894 = 0


119875119894119896 =

119908119894minus119896minus1sum119906=0


1199080minus119896minus1sum119906=0







120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0




1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0


(12)


11987500 (13)





119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)











(17)


119902 = 119890minus120582lowast119864[119878119887] (18)









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0 0

m 0

0 1

m 11

Idle

1

Queuing stage

Checkingstage

Back-ostage

11

1

1

1 1

11

C0

C1

C2

q

1 minus q

1 minus PＮrac

Ｎrac

1 minus Pmeeting

1 minus Pt_sucient

Pt_sucient

Pt_sucient

1 minus Pt_sucient

Pmeeting

P

７ＣＮ1

1W0

Pt_sucient

Pt_sucientP


Pt_sucient


t_sucient

Pt_sucient

1 minusPt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus Pt_sucient

1 minus P t_sucient

m 1m 0

Cm

７ＣＮ3m0

７ＣＮ2m1

C0










７ＣＮ2mWminus1

７ＣＮ300

Pt_Ｍucient

７ＣＮ201

Cm

0W0 minus 1

Pt_succss

７ＣＮ20W0minus1

７ＣＮ3m 0



1

mWm minus 1

mWm minus 1





1198751198940 =

119908119894minus1sum119906=0


1199080minus1sum119906=0

1198751198622 lowast 11199080 = 1198751198622 119894 = 0


119875119894119896 =

119908119894minus119896minus1sum119906=0


1199080minus119896minus1sum119906=0







120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0




1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0


(12)


11987500 (13)





119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)











(17)


119902 = 119890minus120582lowast119864[119878119887] (18)









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





119875119894119896 =

119908119894minus119896minus1sum119906=0


1199080minus119896minus1sum119906=0







120591 = 119898sum119894=0

1198751198621015840119894= 119898sum119894=0




1198751198620 = 119898minus1sum119894=0

1198751198621015840119894lowast 119875119905 success + 1198751198621015840119898

= 119898minus1sum119894=0


(12)


11987500 (13)





119875meeting = 119864 (119872 slots)6 = 3ℎ + 112ℎ (16)











(17)


119902 = 119890minus120582lowast119864[119878119887] (18)









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of









119894=0


(119879119878+ 119879Wait3


sdot 119875119905 success + 119898sum119894=1



(22)



(23)

Assume







= (119879 minus 120590) 120590119879 + (15ℎ + 1) 1205906ℎ (26)

And then we can get












119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of








119898sum119894=0

119908119894minus1sum119896=0

119875119894119896 + 119875Wait1 + 119875Idle + 119898sum119894=0

119908119894minus1sum119896=1

119875Wait2119894119896+ 119898sum119894=0

119875Wait31198940

= 1



(31)




119894119896 and119875Wait3



119878 = ℎsum119894=1

119878 = ℎ lowast 119864 [119897]119864 [slot] (33)







(36)



119894=0

119882119894 minus 12 ) (37)





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





0

5

10 050

100150

0

05

1


Nor

mal

ized

thro

ughp

ut

04

05

06

07

08


0 2 4 6 8 100

20

40

60

80

100

120


Nod

e num

ber

04

05

06

07

08



001

02 40 60 80 100 120 140

04

06

08

1

Node number


Nor

mal

ized

thro

ughp

ut

04505055060650707508











010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





010 20 50 100 150

04

05

06

07

08


Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

04

045

05

055

06

065

07




02803

032034036038

04

Aver

age p

acke

t tra

nsm

issio

n de

lay (s

)

08081082083084085086

Nor

mal

ized

thro

ughp

ut







119865 = 119878 lowast 1000 + 119864 [119863tr] + 120582 (38)













(41)



05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of





05

10 15 005

1


0

100

200

300

400

Nod

e num

ber



0204060810 2 4 6 8 10 12


050

100150200250300350400

Nod

e num

ber

50

100

150

200

250

300

350












0

50

100

150

200

250

300

350

400

450

Nod

e num

ber


ℎ = 7ℎ = 5

ℎ = 3










e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of







e

x1

x2

xk

wij

wjk

xk+1




)





119891 (119909) = cos (175119909) exp(minus11990922 ) (43)








0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of






0 0 1 0 1 1cycle t

Channel slot T

0

21 3 4 5 6Node 0

110

0

10 0 0


Allocation slot

Node 1

nn0 n0 0 0Node n

Formertrac


Y

N


Meet condition


Y

N

Turn to defaultslot

Tracprediction slot

Allocation slot

WNN

WＮＬ_ＪＬ gt 0

＄A = 0＄A = 0 1 3

＄B = 1

＄B = n

= 1 2 4

＄３B

＄３B





01 02 03 04 05 06 07 08 09 10

010203040506070809

1

rＮＬc

PＦＦＩ_

switc

h

ℎ = 3

ℎ = 5

ℎ = 7



119875allo switch

prop 1119903traffic


(44)













20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of















20

40

60

80

100

120

140

160

180

200

220

Nod

e num

ber








055

06

065

07

075

08

085

09

Nor

mal

ized

thro

ughp

ut

DCQM ℎ = 7


CQM ℎ = 5

DCQM ℎ = 3

CQM ℎ = 3










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of










Acknowledgments


References








































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





Journal of




dynamic channel slot allocation scheme and performance...

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