research article a multistage control mechanism for group...

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2013 Article ID 548564 12 pageshttpdxdoiorg1011552013548564

Research ArticleA Multistage Control Mechanism for Group-BasedMachine-Type Communications in an LTE System

Wen-Chien Hung1 Sun-Jen Huang1 Feng-Ming Yang2 and Chun-Yen Hsu2

1 Department of Information Management National Taiwan University of Science and Technology Taipei Taiwan2 Smart Network System Institute Institute for Information Industry Taipei Taiwan

Correspondence should be addressed to Wen-Chien Hung d10116002mailntustedutwand Feng-Ming Yang fengmingyangiiiorgtw

Received 18 March 2013 Accepted 17 July 2013

Academic Editor Anyi Chen

Copyright copy 2013 Wen-Chien Hung et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

When machine-type communication (MTC) devices perform the long-term evolution (LTE) attach procedure without bit ratelimitations they may produce congestion in the core network To prevent this congestion the LTE standard suggests using group-based policing to regulate the maximum bit rate of all traffic generated by a group of MTC devices However previous studieson the access point name-aggregate maximum bit rate based on group-based policing are relatively limited This study proposes amultistage control (MSC)mechanism to process the operations of maximum bit rate allocation based on resource-use informationFor performance evaluation this study uses a Markov chain with119872119866119896119896 to analyze MTC application in a 3GPP network Trafficflow simulations in an LTE system indicate that theMSCmechanism is an effective bandwidth allocation method in an LTE systemwith MTC devices Experimental results show that the MSC mechanism achieves a throughput 225 higher than that of the LTEstandard model using the group-based policing and it achieves a lower delay time and greater long-term fairness as well

1 Introduction

Machine-type communication (MTC) applications are grad-ually becoming available for a wide range of potential appli-cations because of the tremendous interest inmobile networkoperators This emerging technology is used in machine-to-machine (M2M) communication to provide wireless broad-band communications for various types of applications [1 2]This dynamic network provides MTC devices with serv-ing network capabilities for various applications includingmetering road security and consumer electronic devices[3 4] The 3GPP TS 22368 specification initially defined theservice requirement for MTC services and MTC devices [56] The SA2 committee extended architecture requirementsto support the aggregate maximum bit rate (AMBR) inquality-of-service (QoS) parameters creating the TR 23888specification for group service application requirements [7]This extension created new challenges and opportunitiesin the resource allocation problem The efficiency of thedynamic bandwidth allocation mechanism plays a vital role

in system performance because MTC devices can causenetwork congestion when performing the attach procedurewithout bit rate limitations [8] Figure 1 shows a typicalMTC network architecture In a long-term evolution (LTE)system the mobility management entity (MME) regulates allcommunication between the enhanced node B (eNB) andMTC devices in the radio coverage cell of the eNBThe policyand charging rules function (PCRF) is a software node fordetermining policy rules in a 3GPP network To meet QoSrequirements the MME can send an attachment report tothe Home Subscriber Server (HSS) and the HSS attemptsto inform the MME by group-based policing to compute theQoS parameter value To allow all MTC devices to send theattach request separately the aggregate maximum bit rate(AMBR) must regulate the bit rate of all traffic generatedthrough a group of nonguaranteed bit rate bearers In this sit-uation users are unable to receive proper bandwidth whichcauses the attach reject for the user equipment-aggregatemaximum bit rate (UE-AMBR) and therefore degrades theQoS [9]

2 Journal of Applied Mathematics

eNB

MTC device

MTC device group

eNB

X2

MME

SGWPGW

S1-MME

S11

S1-U

S5HSS

S6a

PCRF

Gx

S1-U

MTC device domain

Network domain

LTE-Uu

LTE-

Uu

LTE-U

u LTE-Uu

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC deviceMTC device

MTC device

Figure 1 MTC architecture in an LTE system

A crucial bandwidth group-based policing issue in thedesign of 3GPP networks is the QoS support requiredfor the tremendous global growth in data and traffic ofmobile MTC subscribers [10] A service flow is based on thereport information with a particular set of QoS requirementparameters (eg packet delay tolerance acceptable packetloss rates required minimum bit rates and AMBR) TheLTE systemdefines several end-to-endQoS requirements andthe QoS information for each evolved packet system (EPS)bearer based on the concept of data flows including the QoSclass identifier (QCI) allocation and retention policy (ARP)guaranteed bit rate (GBR) andmaximumbit rate (MBR)TheQCI is a scalar that indicates a specific priority maximumdelay and packet error rate This index also refers to a setof packet-forwarding treatments (eg scheduling weightsadmission thresholds queue management thresholds andlink layer protocol configuration) The ARP is involved inprioritization and preemption decisions regarding bearersand its primary purpose is to decide whether to accept abearer establishment request when resources are limitedTheGBR denotes the minimum bit rate to be provided to aGBR bearer For a rate-shaping function the MBR limits theGBR value to discard excess traffic The MBR and AMBRregulate the bit rate of traffic generated through one GBR

bearer and a group of non-GBR bearers respectively TheLTE system also supports QoS for EPS bearer aggregatesat both the UE-AMBR and access point name-aggregatemaximum bit rate (APN-AMBR) The UE-AMBR combinesthemaximumbit rate across all non-GBR bearers of a UE andenforces bandwidth allocation by the eNB for both uplink anddownlinkThe APN-AMBR aggregates the maximum bit rateacross all non-GBRbearers and across all packet data network(PDN) connections of the sameAPNand enforces bandwidthallocation by the PDN gateway (PGW) for a downlink [11 12]

This study considers MTC devices with an Event-TriggerMTC feature for transmission data only at certain predefinedtimes which include a grant time interval and a forbiddentime interval The network permits an MTC device to trans-mit data during the grant time interval and prevents it fromtransmitting data outside the grant time interval for examplethe grant time interval does not overlap with the forbiddentime interval The network does not permit an MTC deviceto transmit data during the forbidden time interval forvarious reasons such as maintenance of the MTC serverMTC device is to communicate with the MTC server Thecommunication windows of the devices shall be distributedover the predefined time for a group of MTC devices toavoid network overload This study focuses on a centralized

Journal of Applied Mathematics 3

point-to-multipoint (PMP) architecture that the eNB usesto distribute bandwidth resources to multiple MTC devicesThis architecture mode provides superior QoS performanceto that of the distributed bearer mode After receiving anattach request from an MTC device the centralized MMEreports an attach report opportunity in time slots to the HSSfromall authorizedMTCdevices currently using the availablebandwidth resource

The remainder of the paper is organized as followsSection 2 presents a brief literature review of the attach pro-cedure and MTC application over the LTE system Section 3provides a description of the system model and the pro-posed MSC mechanism Section 4 introduces the simulationenvironment Section 5 presents the simulation results of theproposed scheme Finally Section 6 offers the conclusion

2 Attach Procedures in LTE

The attach procedure involves one or multiple dedicatedbearer establishment procedures to establish a dedicated EPSbearer for that UE Each bearer is associated with a set ofQoS parameters that describes the properties of the trans-port channel This leads to a flexible bandwidth allocationalgorithm that enables differential treatment for traffic withvarying QoS requirements Network operators allow MTCdevices to attach to the network during the predefined period

21 Attach Procedure In the attach procedure one UEtransmits an attach request message to the eNB The eNBdelivers the initial UE message to the MME to enable sessionmanagementTheMMEprovides the serving gateway (SGW)with the UE of the out-of-synchronization (OoS) parameterin the create session request message In the initial contextsetup request message the MME determines the bearer IDand OoS parameter based on the create session informationSession creation management is only defined for the uplinkdata path and not for the received downlink data path TheeNB generates the initial context setup response messagein response to the initial context setup request messagefrom MME to report the eNB address The 3GPP standardproposes that the modifying bearer management reports theeNB address to the SGW enabling the PGW to determinethe downlink data path The UE obtains the downlink dataaccording to the modifying bearer management [13]

The Policy Control Enforcement Function (PCEF) sendsan Internet Protocol Connectivity Access Network (IP-CAN)session modification message if the IP-CAN QoS exceedsthe authorized QoS provided by the PCRF The dedicatedbearer establishment contains the create bearer and bearersetup messages without data payload The PGW sends acreate bearer request message (while maintaining the OoSparameter) to the MME by triggering a dedicated bearerestablishment When the MME is ready to switch the bearerto dedicated bearer activation mode it sends a bearersetup request message to the eNB After the eNB receivesthe bearer setup request message it replies with a bearersetup response message To report the bearer setup responsemessage the eNB sends its address to the MME without any

QoS parametersThe reported effective bearer setup feedbackis consistent with the RRC connection reconfiguration ThePCEF can then be obtained by the optimalQoS report tomeetthe specified target error rate before the dedicated bearerestablishment

Figure 2 shows a sequence diagram of the attach pro-cedure For the enabled service a UE must register withthe network by network attachment The eNB derives theMME from the initial UEmessage carrying the attach requestand the PDN connectivity The MME sends a create sessionrequest (PGW address APN default EPS bearer QoS APN-AMBR etc) message to the selected SGW The SGW sendsa create session request message to the PGW using the PGWaddress received in the previousmessageThePGWconsidersthe received message and returns a create session response(PDN type PDN address EPS bearer ID EPS bearer QoSAPN-AMBR etc) message to the SGW The eNB sends theRRC connection reconfiguration message including the EPSbearer ID and attach accept message to the UE and theUE returns the RRC connection reconfiguration completemessage to the eNBTheMME sends a modify bearer request(EPS bearer ID eNB address etc) message to the SGW andthe SGW acknowledges by sending a modify bearer response(EPS bearer ID) message to the MME

22 Event-Trigger MTC Applications Although some exist-ing MTC applications use short-range radio technologiesMTC solutions based on mobile access technologies areeasier to install Mobile access-based MTC solutions arealso better suited to supporting MTC applications whichrequire reliable delivery of data to distant MTC devices [14]Figure 3 shows aMTC application that consists of a modifiedtime and reported device ID at the S6a interface The MTCdevice performs initial attach and authentication proceduresWhen the MME is unaware of the context information ofthe MTC device it sends a time period report requestwhich includes a device ID to the HSS After receivingthe time period report request from the MME the HSSdetermines the period of the MTC device The HSS returnsa time period report which includes the device ID and timeperiod information of the MTC device to the MME Toavoid network signaling overhead the MME calculates themodified grant time interval and determines whether theattach request is from the MTC device When the attachrequest is received outside the grant time interval the MMEsends an attach reject message to the MTC device [7] Afteran attach request message is accepted the MME sends atime period report request to the HSS The time periodreport request includes a device ID and QoS parameterscorresponding to the MTC device making the initial attachrequest When the received attach report corresponds to aninitial attach report the HSS determines an APN-AMBR bydividing the group-APN-AMBR assigned to the MTC groupby using the group-based policing method After applyingthis group-based policing method the HSS sends an APN-AMBR report which includes the determined APN-AMBRto the MME Finally the MTC device establishes a PDNconnection [9]


UE Serving GWMME PDN GWAttach request

eNodeB

Initial UE message

Initial context setup request

Initial context setup response

Create bearer response Create bearer

response

Create bearer request Create bearer

requestBearer setup request

Bearer setup response

Dedicated bearer establishment

First DL data

First UL data First UL data

First DL data

PCRF

IP-CAN session modification


Create session Create session

RRC connection reconfiguration

Modify bearer Modify bearer


Figure 2 Sequence diagram of LTE attach procedure

MTC device Serving GWMME PDN GWeNodeB

Time period report request

Attach reject

Perform initial attach procedure and authentication

Time period report

HSS

Perform procedure for establishing PDN connection

When the MTC device is operated by MTC application

Modify grant time interval if necessary

If the MME is unaware of the grant time interval


APN-AMBR report

Group-based policing

Figure 3 Sequence diagram of MTC application in an LTE system

3 Proposed Model and Mechanism

This section presents an analysis of the blocking probabilitiesof a MTC application that distinguishes multiple classes ofequal mean grant time interval Based on the group-basedpolicing the HSS uses extended APN-AMBR report fields

in 3GPP networks As the APN-AMBR parameter travelsthrough an MME UE-AMBR losses occurrence for variousAPN-AMBR types because of inaccessible bandwidth afterthe group-based policing Let 119879 be the grant time intervalLet 119866 be the group-APN-AMBR to group MTC deviceswhen they are served which is the parameter to fulfill


the grant time proportion already servedRi(j) the remaining grant time interval in Ti(j)

ti(j) initial point of Ti(j)Ti(j) grant time interval of MTC device i

Ui MTC device ij MME j

j

U1

MGkk k = 1

T1t1

U2

t2 R2(j)Time

Figure 4 Corresponding queuing model for MTC application

the satisfaction of the bandwidth requirement of applicationThe terms 119879 and 119866 are the two operational parameters of theproposed framework

31 Queuing Model for MTC Application The MTC Appli-cation being considered is Event-Trigger MTC Assume therequests arrive at the MME following a Poisson process Let119873 be the number of all MTC devices in the network If theMME can modify the service time the system behaves asan 119872119866119896119896 system and the blocking probability can beobtained using the Erlang B formula [15] However when thesystem includes more than one priority class the applicationof119872119866119896119896 becomesmore complex Assume that the systemcontains two MTC devices Figure 4 shows the case whenMTC Device 2 (119880

2) arrives at the MME before MTC Device

1 (1198801) However 119880

2is stopped because the priority ensures

the grant time interval of 1198801by modifying the grant time

interval of 1198802 The remaining portion of the overlapping

grant time interval at MME 119895 of MTC device 119894 is denotedby 119877119894(119895) and this represents the residual service time If the

basic MTC device and all QoS MTC devices are constantthe degree of isolation between two arbitrary classes dependsonly on their effective overlapping grant time intervalThis isbecause a basic MTC device can be interpreted as a constantshift in time of the reservation process and thus neitherarrival nor reservation events are reordered in the grant timeinterval This result has also been proven by simulation forvarious arrival and service time distributions Hence assumethat 119877

119894(119895) = 0 without loss of generality and consider the

overlapping grant time interval between MTC Device 1 andMTCDevice 2 as 119877

2(119895) = 119879

2minus (1199052minus 1199051) gt 0 In this case 119879

1(119895)

has preemptive priority over 1198772(119895) The blocking probability

of 1198801is simply obtained using the Erlang B formula This

study uses the Erlang B formula to evaluate the blockingprobability of the all the 119879

119894(119895) traffic of MTC devices

Consider a time period report request arriving at a certaintime instant in the HSS and requesting to reserve a granttime interval 119902 time slots after its arrival timeWithout loss of

generality consider the arrival time of the time period reportrequest to be slot 0 and the start of theMTCdevice requestedduration to be slot 119902 To calculate the blocking probability ofthis MTC device request consider the traffic load at slot 119902 asseen at the time of the request Any MTC device requestedduration generated in the future (from time slots after slot 0)for slot 119902 will not affect the probability of acceptingblockingthe MTC device request The number of grant time intervalswith a start time within slot 119902 as seen at the instant in whichthe time period report request arrives is Poisson-distributedwith mean

120582(119902)

=

120582 for 119902 le 0

1205821 minus

119902minus1

sum

119886=0

119891 (119886) for 119902 gt 0(1)

The number of MTC device requests for time slot 119902 fromall previous slots including slot 119902 is 120582 Given a time periodreport request arriving in time slot 0 the probability that thisMTC device requested duration requests that time slot 119902 is119891(119902) Therefore the number of MTC device requests fromslot 0 for slot n is 120582119891(119902) From a time period report requestviewpoint the number of grant time interval arrivals in slot nis the sum of MTC device requests from all time slots beforeslot 0 in addition to the MTC device requests from slot 0Thus the number of arrivals in slot 119902 as seen by the timeperiod report request is the sum of all possible MTC devicerequests (120582) minus any future MTC device requests to bemade in time slots 1 to 119902 for slot 119902

Based on this assumption define 120583119894

= 1119864[119879119894] where

119864[119879119894] is the expected value of theMTCdevice 119894(119880

119894) grant time

interval at the same MME To determine the effective servicetime of a grant time interval under theMTC application referto Figure 4 For a predefined time a bandwidth is reserved fora length of time that is equal to the sum of two time intervalsThe duration of the first interval is equal to that of the granttime interval and is distributed according to119879

119894(119895)with amean

1120583 The conventional Markov model was implemented toanalyze the MTC requests queue model The Markov model


0 1 2

120582f(0)

120582f(1)120582f(2)

120583

n minus 1n minus 2 n n + 1 n + 2 n + 3middot middot middot middot middot middot

120582f(2)

120582f(1) 120582f(1)

120583120583

120582f(2)

120582f(0)

Figure 5 Markov model for the MTC requests queue

was constructed for the MTC requests queue The state 119899

represents the number of MTC requests within the frameduration The process of the MTC requests queue assumesthat time slot 119902 is working The Markov process is illustratedin Figure 5 based on the assumptions in our study The staten represents the number of requests in the MTC system

The duration of the second interval is equal to that ofthe forbidden time interval and is distributed according to119877119894(119895) with a mean 119877 Based on these observations an output

port of anMME node using aMTC application behaves as an119872119866119896119896 loss system The traffic intensity 120588

(TC) of the queueis

120588(TC)

= 120582(119902)

(1

120583+ 119877) (2)

This study first presents modeling the MME using an119872119872119896119896 queue with preemptive priorities where thearrival rate of 119905

119894is 120582119894and the service rate is 120583

119894 Let 119896 be

the number of classes in the MTC application Denote 120588119894=

(120582119894120583119894) as the traffic load of 119905

119894 If 1199051has an absolute priority

(ie all other MTC devices have signaling overhead) theblocking probability of one class can be obtained using theErlang B formula in the 119872119872119896119896 queue expressed as

119875 (1205881 119896) =

(120588119896

1119896)

(sum119896

119898=0120588119898

1119898)

(3)

Similar to (3) the blocking probability of the superposi-tion of the two classes with total traffic load 120588

1+ 1205882can be

calculated as follows

119875 (12058812

119896) =

(120588119896

12119896)

(sum119896

119898=0120588119898

12119898)

(4)

where 12058812

= 1205881+ 1205882 In the multiclass case for the 119872119866

119896119896 queue the blocking probabilities for service classeswith different QoS values can be obtained by heuristicallygeneralizing (3) and (4) to an arbitrary number of 119896 classesA conservation law can be formulated for every set of classes119864119909= 0 119909 with 0 lt 119909 le 119896 minus 1

(

119909

sum

119910=0

120582119894)119875(120588

12119864119909

119896) =

119909

sum

119910=0

120582119910sdot 119875 (12058812119910

119896) (5)

where 119875(12058812119864

119909

119896) is the total blocking probability of allclasses in 119864

119909 It describes the probability that a low-priority

MTC device that started the grant time interval prior to

the grant time interval of otherMTC devices has not finishedits grant time interval In general the blocking probabilityof a MTC application can be calculated based on (3)ndash(5) asfollows

119875 (12058812119864

119909

119896)

= (1

120582119864119909

)(

119864119909

sum

119910=0

120582119910)

times [119875 (1 2 119864119909) minus 11990112119864

119909minus1

119875 (1 2 119864119909minus 1)]

(6)

where 11990112119864

119909minus1

= (sum119864119909minus1

119910=1120582119910)(sum119864119909

119910=1120582119910) and 119875(1 2

119864119909) = ((sum

119864119909

119910=1120588119910)119896

119896)(sum119896

119898=0(sum119864119909

119910=1120588119910)119898

119898)

32 Multistage Control Mechanism The attach report mes-sage is selected from each MTC device after reaching theHSS because theMTC application identifies acceptable attachMTC devices The goal of the MSC mechanism is to improvethroughput requirement with a QoS guarantee Figure 6shows a flowchart of the APN-AMBR allocation process TheMME receives an attach request and determines whethera MTC application operates the attached MTC device Ifa MTC application operates the MTC device the MMEalso determines whether to modify the grant time intervalThe MME sends an attach report to the HSS and the HSScollects all MTC devices requesting attachment The HSSdetermines whether a new attach report has been receivedfrom the MME When the HSS knows the already attachedMTC device it can process the MSC mechanism withoutwaiting for a duration The HSS sends the APN-AMBRreport information after the MSC mechanism The currentAMBR definitions enable system operators to differentiatethe service level provided for each of these services In theproposed architecture rate policing prevents the networkfrombecoming overloaded and ensures that the services senddata in accordance with the specified maximum bit ratesBecause MTC devices are encouraged to adapt their APN-AMBR to starvation resource starvation is confined to thosewho ignore starvation The uplink and downlink schedulingfunctions implemented by the LTE system are largely respon-sible for fulfilling the QoS characteristics associated with thedifferent bearers

These APN-AMBRs are APN-level quantities and aretherefore known at the HSS These APN-AMBRs propagatethrough UE attach procedures down to the MME to enforce


MTC device is operated by time- controlled MTC application

MME sends attach report to HSS

MME receive attach request form MTC device

MTC application

Yes

Start

New attach report is received

End

Yes

No

No

Multistage control mechanism

HSS sends APN-AMBR to MTC device via MME

Figure 6 Flowchart of the APN-AMBR allocation process

the data rate from the specific APN through rate policingEach MTC device may have various packets and the streamtypes of these packets may have various UE-AMBRs Thismechanism also uses the following parameters

(i) 119873 the number of MTC devices that must be bufferedwithin an MME in the LTE system

(ii) 119876 the number of MMEs in a MME pool area(iii) 119878 the number of stages in the MSC mechanism(iv) 119866

119894119895 the groupAPN-AMBR size of the 119894thMTCdevice

at the 119895th MME(v) 119877119894119895 the UE-AMBR size of the 119894th MTC device at the

119895th MME(vi) 119863

119894 the default APN-AMBR size of the 119894th MTC

device(vii) 119872

119894 the minimum APN-AMBR size of the 119894th MTC

device(viii) 119860

119894 the allocation APN-AMBR size of the 119894th MTC

device

Consider the MSCmechanism in which resource use canbe calculated Let 119862

119894119895be the resource use of the 119894th MTC

device at the 119895thMME where119862119894119895

= (119877119894119895119866119894119895)The challenge

of this utilitymaximization problem is to determine theAPN-AMBR of each subscribed MTC device to be served and theamount of resources to be allocated to each APN-AMBR ofall subscribed MTC devices When resources are limited theHSS must determine the number of APN-AMBRs for eachMTC device to receive resources in order to maximize thetotal utility of the system We could find an allocation Γ =

1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876

denotes the set of allocated resource to each APN-AMBR ofthe 119894thMTC device Formally the objective of this problem isto find a Γ to

Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)

By solving this equality the MTC application can easilybe obtained for the user Resource use can be maximizedwith the optimal values which can be obtained by 119877

119894119895and

119862119894119895

parameters However the solution of this optimizationequation is not explicit because the MME does not knowthe group APN-AMBR size and the number of MMEs inthe MME pool area in this stage How to evaluate the APN-AMBR for eachMTCdevice is important Oneway to addressthis is to refer to resource use by employing the utilizationrange to evaluate the APN-AMBR for each MTC device atthe HSS The utilization ranges for various stages exhibitup-bound and low-bound utilization Let 119867

1199041015840 and 119871

1199041015840 be

the up-bound and low-bound utilization of the 1199041015840th stage

respectively Define up-bound utilization as

1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)

The up-bound utilization and low-bound utilization canbe determined by the HSS Hence low-bound utilization canbe represented as

1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)

This method focuses on improving resource utilizationThe MSC mechanism helps the MME allocate the APN-AMBR for each MTC device to maximize the resource useand satisfy the target UE-AMBR The granted bit rate of theAPN-AMBR is a critical parameter in the MSC mechanismFirst the MME assigns the initial resource use levels 119867

1199041015840

and 1198711199041015840 based on the required resource use of up bound and

low bound respectively Therefore it is necessary to checkall utilization ranges (119867

1199041015840 1198711199041015840) to find the utilization ranges


Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894

for 119895 = 1 to 119876 dofor 119894 = 1 to 119873 do allocate resource

119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862

119894119895ge 1198711199041015840 ) use (8) and (9) with given 119904

1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break

case(1199041015840 isin Φ) MME sends attach reject message breakdefault 119860

119894= 119863119895119890(1199041015840minus1) break

end forend for

Algorithm 1 Multistage control mechanism

that maximize resource use as candidate solutions Amongthese candidates the candidate with the maximum resourceutilization is the solution for the MSC decision If multiplecombinations produce the same maximum resource useselect the one with the maximum number of MTC device-rejected attachments Algorithm 1 describes the assignmentof the APN-AMBR by using theMSCmechanism in anMMEpool area

To improve fairness theMTCdevices should be allocatedtheir APN-AMBR from the group APN-AMBR in order Ifthe UE-AMBR of the signaling overhead type is incompletesignaling nonoverhead UE-AMBR will occupy the resourceof the group APN-AMBR in theMTC applicationsTheMTCdevice allocation process ensures that FCFS scheduling isbased on fairness if the stream types have the same prioritiesThe frame allocation process guarantees higher throughputand achieves fairness between several MTC device streamtypes For this reason MTC devices with a better resourcecondition enjoy better perceived quality between severalstream types Jainrsquos fairness index is a conventional methodof assessing the quality of the traffic type [16] The term119891 represents the total number of QCIs for the duration ofthe MTC application The value of Jainrsquos fairness index isgenerally between 1119891 and 1 When the LTE system indicatesan increase in Jainrsquos fairness index value the systemhas higherfairness for all CQIs This model can be written as follows

FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)

where 119883119899is the APN-AMBR for the 119899 MTC devices In this

description the bit rate of all traffic generated by a group ofMTC devices can be controlled by determining the APN-AMBR of each MTC device according to current resourceuse of the MTC group Group-based policing regulates themaximum bit rate of all traffic generated and the total bit rateof traffic generated through all non-GBR bearers connects tothe same APNTheMME sends the APN-AMBR to theMTC

Figure 7 Network topology of the simulation

device requesting attachment by using the PDN connectionestablishment procedure The MME may store 119866

119894119895 119863119894 119872119894

1198671199041015840 and 119871

1199041015840 in individual groups of MTC devices by using a

multistage controlled bit rate feature

4 Simulation Environment

The experiments in this study were performed using OPNETModeler 171 with LTEmodule capability to simulate anMTCenvironment [20] The simulation was conducted for 3600seconds to investigate the stable state result for all MTCdevice nodes

This simulation tests the performance of the proposedmechanism in a typical network consisting of one EPC and160 randomly distributed MTC device nodes As Figure 7shows this experimental environment is based on a sim-ulated OPNET MTC network topology containing twocells Each cell has an eNB and each eNB has 80 MTC


Table 1 LTE simulation system parameters [17 18]

Parameters ValuePHY profile FDDBandwidth 20MHzPacket size 1024 byteCycle prefix NormalUL SC-FDMA channel (base frequency) 1920MHzDL OFDMA channel (base frequency) 2110MHzMax retransmission (HARQ) 3Handover type IntrafrequencyPath-loss parameter Free space

devices The transmission powers of the MTC deviceand eNB Node were set to 0006 watts and 0012 wattsrespectively The OPNET node models of the eNB andMTC devices are lte enodeb atm4 ethernet4 slip4 router andlte wkstn adv respectively These simulations assume thatthe moving mode of the MTC devices follows the randomwaypoint model The movement speed of each MTC devicewas uniformly distributed between 1 and 5ms The fixedeNB node model featured router functionality The UE nodemodel featured workstation functionality [21] The globalconfiguration object was used to configure the parameterssuch as EPS bearer definitions and PHY profiles in the LTEattributes node [17 18]

The UEs have a CQI index to provide QoS awarenessThe services are grouped into different QoS classes Themain contribution of the proposed mechanism is the MAClayer whereas the actual physical transmission is adoptedfrom the OPNET LTE model Table 1 presents a summaryof the simulation parameters This system considers both thedownlink and uplink The MAC layer scheduler implies thatthe GBR bearers are always allocated radio resources beforethe non-GBR bearers The eNB module implements priorityscheduling for GBR and non-GBR bearers Table 2 presentsthe experimental data for QoS class servicesTheMTC trafficon the EPS bearer is generated between the eNB and MTCdevices [19] The EPS bearer configuration attribute definesfour bearers platinum gold silver and bronze

5 Results and Discussion

Figure 8 shows a comparison of the blocking probability andtraffic load of the MTC application validating the analyticalresults by simulationThegeneral distribution is set accordingto the assumption that 20 of grant time intervals are long(with a service rate of 12) 30 of grant time intervals areshort (with a service rate of 09) and the remaining 40grant time intervals have a service rate of 1 Simulation resultsindicate that saturation occurs when the number of MTCdevices reaches 80 and 120588 gt 0002 (using theMTC applicationin the LTE system) Saturation means that all grant timeintervals of MTC devices have been blocked However thelower-priority grant time intervals cannot be scheduled whenthe number of MTC devices increases and the blockingprobability is more than 1 To prevent the transmission of

0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity

1 2 3 4 5 6 7 8 9 10times10minus3Traffic load per MTC device

n = 10 MTC devices (analytical)n = 20 MTC devices (analytical)n = 80 MTC devices (analytical)n = 10 MTC devices (simulation)n = 20 MTC devices (simulation)n = 80 MTC devices (simulation)

k = 2 MMEs

Figure 8 Comparisons of blocking probability and traffic load

2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard

Average (in LTE throughput (bitss))

Event-trigger MTC application

Figure 9 System throughput in the simulation (in bitssecond)

blocked MTC devices from wasting AMBR it is necessaryto periodically verify the inaccessible bandwidth from theMME

Figure 9 shows the system throughput for the LTE stan-dard Event-Trigger MTC application and our proposedMSC mechanism The simulation results in Figure 9 indicatethat saturation occurs when the simulation time reaches1800 seconds Saturation indicates that all the MTC devicesof one eNB have been scheduled The Event-Trigger MTCapplication reserves the extra bandwidth and reallocatesthe remaining bandwidth Using the Event-Trigger schemethe maximal average throughput reaches 2Mbps before thesystem becomes saturatedTheMSCmechanismwith aMTC


Table 2 Standardized QCI characteristics [19]

Service class Priority Type Packet delay budget Packet error loss rate Guaranteed bit rate

Platinum 1 Non-GBR 100ms 10minus6 mdash2 GBR 100ms 10minus2 128 kbps

Gold 3 GBR 50ms 10minus3 858 kbps4 GBR 150ms 10minus3 384 kbps

Silver 5 GBR 300ms 10minus6 384 kbps6 Non-GBR 300ms 10minus6 mdash

Bronze 7 Non-GBR 100ms 10minus3 mdash8 Non-GBR 300ms 10minus6 mdash

application and a multistage controlled process achieveshigher performance because it has a higher average through-put This is the main reason for obtaining the time periodreport information and an appropriate bandwidth-controlledfeature After the bandwidth allocation reaches an improvedstate because of the resource use the MTC device can trans-mit at a higher data rate using previously inaccessible band-width Because the MSC mechanism considers the methodof allocation of the APN-AMBR the MTC device can selectthe appropriate APN-AMBR with a superior MTC appli-cation to the data transmission thereby achieving a max-imal average throughput of 243Mbps This phenomenondemonstrates that the proposed MSC mechanism markedlyimproves throughput compared to the LTE standard becauseof the extra bandwidth consumed and the inferior group-based control method of the LTE standard The final val-ues of throughput after 3600 seconds in the simulationare 1611256 bps for LTE standard system 1987032 bps forEvent-Trigger MTC application and 2434100 bps for MSCmechanism Compared to the LTE systemwith Event-TriggerMTC application the MSC mechanism achieves a 225higher throughput in this simulation

Figure 10 shows the relationships among the packet delaytimes of the MTC application For the Event-Trigger MTCapplication the MME requests an additional period withoutmodifying resource use at the HSS Additional periods causethe time period report time to increase as the delay timeincreases The final values of packet delay time after 3600seconds in the simulation are 0123 seconds for LTE standardsystem 0132 seconds for Event-Trigger MTC applicationand 0100 seconds for MSC mechanism Compared tothe LTE standard and Event-Trigger MTC applicationthe packet delay time of the MSC mechanism achieveshigher performance in the LTE system because each MMEcontinuously monitors its APN-AMBR The HSS gathers theAPN-AMBR information received through the create sessionrequest messages sent by the MMEs When the group-based policing is optimal or the resource use is low the MTCapplication should also be served using theMSCmechanism

Figure 11 shows the simulation results of Jainrsquos fairnessindex value at various MTC traffic applications for 80 nodesindicating that all of the MTC traffic applications in thispaper have relatively high Jainrsquos fairness index values (062lt FI) This chart shows that the MSC mechanism has ahigher fairness than the LTE standard and Event-Trigger

0132

0123

0100

Average (in LTE delay (s))

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m

MSC mechanismLTE standard

007000750080008500900095010001050110011501200125013001350140


Figure 10 Packet delay time of the MTC application in the simula-tion (in seconds)

MTC application For the MSC mechanism the fairness ofMTC traffic applications depends on the amount of traffictransmitted by the selected APN-AMBR This is the mainreason the MSC mechanism has more resource utilizationFor the transmission model of an Event-Trigger MTC appli-cation a number of MTC traffic applications are reallocateda portion of bandwidth by the attach reject message In theMTC traffic type the fairness index of Event-Trigger MTCapplication is higher than that of the LTE standard becausethe Event-Trigger MTC application considers the methodof allocating AMBR based on the modified period and theamount of controlled time

Markov chain with 119872119866119896119896 and Jainrsquos fairness indexare used to analyze machine-type communication in a 3GPPnetwork Table 3 compares the results between analysis andsimulation of Jainrsquos fairness index (FI) values which showsthat analysis can be validated by simulation

6 Conclusion

This study proposes an MSC mechanism in an LTE systemto process the operations of bandwidth allocation based


Table 3 Comparison of results between analysis and simulation of Jainrsquos fairness index (FI) value

Service class Gold Silver Bronze PlatinumSimulation or analysis Sim Ana Sim Ana Sim Ana Sim AnaMSC mechanism 089 089 080 079 072 070 071 070Event-Trigger MTC application 089 089 079 079 070 070 070 070LTE standard 089 089 076 075 067 066 063 063

Number of nodes = 80

MSC mechanismEvent-Trigger MTC applicationLTE standard

0

01

02

03

04

05

06

07

08

09

FI

Gold Sliver Bronze PlatinumService class

Figure 11 The comparison of Jainrsquos fairness index (FI) values

on MTC application QoS parameters and the bandwidthrequirements of MTC devices and the eNB This studypresents a comparison of the performance of the proposedMSC mechanism and the LTE standard mechanism of MTCapplication The service flow simulations of the OPNETmodeler indicate the MSC mechanism achieves a highersystem throughput a lower delay time and greater long-term fairness for multipleMTC devices Experimental resultsindicate that the throughput of the MSC mechanism is225 higher than that of the LTE standard model using thegroup-based policing which implies that the proposed MSCmechanism is an effective bandwidth allocationmethod in anLTE system with MTC devices

Conflict of Interests

No conflict of interests exists between the authors and allof the mentioned organizations or corporations including3GPP and OPNETModeler The 3rd Generation PartnershipProject (3GPP) is a nonprofit international telecommuni-cation standard development organization which definesnew-generation telecommunication standards including LTE(long-term evolution) In this study we perform the sim-ulation by OPNET Modeler ver 171 which is a popularsimulation tool for analyzing and designing communication

networks devices protocols and applications They havepaid the licensing fee for legal use of OPNET Modeler ver171 in our research

Acknowledgment

A special thanks goes to Institute for Information Industryin Taiwan for its great help in supporting the simulationenvironment and key LTE simulation modules to this study

References

[1] P Jain P Hedman and H Zisimopoulos ldquoMachine typecommunications in 3GPP systemsrdquo IEEE CommunicationsMagazine vol 50 no 11 pp 28ndash35 2012

[2] T Taleb and A Kunz ldquoMachine type communications in 3GPPnetworks potential challenges and solutionsrdquo IEEE Communi-cations Magazine vol 50 no 3 pp 178ndash184 2012

[3] O Del Rio Herrero and R De Gaudenzi ldquoHigh efficiencysatellite multiple access scheme for machine-to-machine com-municationsrdquo IEEE Transactions on Aerospace and ElectronicSystems vol 48 no 4 pp 2961ndash2989 2012

[4] K Chang A Soong M Tseng and Z Xiang ldquoGlobal wirelessmachine-to-machine standardizationrdquo IEEE Internet Comput-ing vol 15 no 2 pp 64ndash69 2011

[5] 3GPP ldquoService Requirements for Machine-Type Communica-tions TS 22368 V1200rdquo 2012

[6] A Ksentini Y Hadjadj-Aoul and T Taleb ldquoCellular-basedmachine-to-machine overload controlrdquo IEEE Network vol 26no 6 pp 54ndash60 2012

[7] 3GPP ldquoSystem Improvements for Machine-Type Communica-tions TR 23888 V1100rdquo 2012

[8] K Zheng F Hu W Wang W Xiang and M Dohler ldquoRadioresource allocation in LTE-advanced cellular networks withM2M communicationsrdquo IEEE Communications Magazine vol50 no 7 pp 184ndash192 2012

[9] C Songyean R Heetae L Jangwon B Beomsik L Chaegwonand J Sangsoo ldquoGroup-based controlmethod and apparatus forMTC devices in mobile communication systemrdquo United Statespatent US 20120209978 2012

[10] S Lien and K Chen ldquoMassive access management for QoSguarantees in 3GPP machine-to-machine communicationsrdquoIEEE Communications Letters vol 15 no 3 pp 311ndash313 2011

[11] Y Chen and W Wang ldquoMachine-to-machine communicationin LTE-Ardquo in Proceedings of IEEE 72nd Vehicular Technol-ogy Conference Fall (VTC rsquo10-Fall) pp 1ndash4 Ottawa CanadaSeptember 2010

[12] S Y Lien K C Chen and Y Lin ldquoToward ubiquitous massiveaccesses in 3GPPmachine-to-machine communicationsrdquo IEEECommunications Magazine vol 49 no 4 pp 66ndash74 2011


[13] 3GPP ldquoGPRS enhancements for E-UTRAN access TS 23401V1140rdquo 2012

[14] G Wu S Talwar K Johnsson N Himayat and K D JohnsonldquoM2M from mobile to embedded internetrdquo IEEE Communica-tions Magazine vol 49 no 4 pp 36ndash43 2011

[15] D Gross and C M Harris Fundamentals of Queuing TheoryWiley New York NY USA 3rd edition 1998

[16] R Jain D M Chiu and W Hawe ldquoA quantitative measure offairness and discrimination for resource allocation in sharedsystemrdquo DEC Research Report TR-301 1984

[17] M Torad A El Qassas and H Al Henawi ldquoComparisonbetween LTE and WiMAX based on system level simulationusing OPNET modeler (release 16)rdquo in Proceedings of 28thNational Radio Science Conference (NRSC rsquo11) pp 1ndash9 CairoEgypt April 2011

[18] K Andersson S A M Mostafa and R Ui-Islam ldquoMobile VoIPuser experience in LTErdquo in Proceedings of IEEE 36th Conferenceon Local Computer Networks (LCN rsquo11) pp 785ndash788 BonnGermany October 2011

[19] 3GPP ldquoPolicy and charging control architecture TS 23203V1180rdquo 2012

[20] ldquoOPNETLTESpecializedModelrdquo httpwwwopnetcomLTE[21] B H Lee and S L Kim ldquoMobility control for machine-to-

machine LTE systemsrdquo in Proceedings of Wireless Conference2011-Sustainable Wireless Technologies (European Wireless) pp1ndash5 Vienna Austria April 2011

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


eNB

MTC device

MTC device group

eNB

X2

MME

SGWPGW

S1-MME

S11

S1-U

S5HSS

S6a

PCRF

Gx

S1-U

MTC device domain

Network domain

LTE-Uu

LTE-

Uu

LTE-U

u LTE-Uu

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC device

MTC deviceMTC device

MTC device

Figure 1 MTC architecture in an LTE system

A crucial bandwidth group-based policing issue in thedesign of 3GPP networks is the QoS support requiredfor the tremendous global growth in data and traffic ofmobile MTC subscribers [10] A service flow is based on thereport information with a particular set of QoS requirementparameters (eg packet delay tolerance acceptable packetloss rates required minimum bit rates and AMBR) TheLTE systemdefines several end-to-endQoS requirements andthe QoS information for each evolved packet system (EPS)bearer based on the concept of data flows including the QoSclass identifier (QCI) allocation and retention policy (ARP)guaranteed bit rate (GBR) andmaximumbit rate (MBR)TheQCI is a scalar that indicates a specific priority maximumdelay and packet error rate This index also refers to a setof packet-forwarding treatments (eg scheduling weightsadmission thresholds queue management thresholds andlink layer protocol configuration) The ARP is involved inprioritization and preemption decisions regarding bearersand its primary purpose is to decide whether to accept abearer establishment request when resources are limitedTheGBR denotes the minimum bit rate to be provided to aGBR bearer For a rate-shaping function the MBR limits theGBR value to discard excess traffic The MBR and AMBRregulate the bit rate of traffic generated through one GBR

bearer and a group of non-GBR bearers respectively TheLTE system also supports QoS for EPS bearer aggregatesat both the UE-AMBR and access point name-aggregatemaximum bit rate (APN-AMBR) The UE-AMBR combinesthemaximumbit rate across all non-GBR bearers of a UE andenforces bandwidth allocation by the eNB for both uplink anddownlinkThe APN-AMBR aggregates the maximum bit rateacross all non-GBRbearers and across all packet data network(PDN) connections of the sameAPNand enforces bandwidthallocation by the PDN gateway (PGW) for a downlink [11 12]

This study considers MTC devices with an Event-TriggerMTC feature for transmission data only at certain predefinedtimes which include a grant time interval and a forbiddentime interval The network permits an MTC device to trans-mit data during the grant time interval and prevents it fromtransmitting data outside the grant time interval for examplethe grant time interval does not overlap with the forbiddentime interval The network does not permit an MTC deviceto transmit data during the forbidden time interval forvarious reasons such as maintenance of the MTC serverMTC device is to communicate with the MTC server Thecommunication windows of the devices shall be distributedover the predefined time for a group of MTC devices toavoid network overload This study focuses on a centralized













eNodeB

Initial UE message




response





First DL data


First DL data

PCRF










Attach reject


Time period report

HSS






APN-AMBR report










j

U1

MGkk k = 1

T1t1

U2

t2 R2(j)Time





1 (1198801) However 119880








2(119895) = 119879


1(119895)







120582(119902)

=

120582 for 119902 le 0

1205821 minus

119902minus1

sum

119886=0

119891 (119886) for 119902 gt 0(1)



= 1119864[119879119894] where


119894) grant time


119894(119895)with amean



0 1 2

120582f(0)

120582f(1)120582f(2)

120583


120582f(2)

120582f(1) 120582f(1)

120583120583

120582f(2)

120582f(0)






(TC) of the queueis

120588(TC)

= 120582(119902)

(1

120583+ 119877) (2)



119894 Let 119896 be





119875 (1205881 119896) =

(120588119896

1119896)

(sum119896

119898=0120588119898

1119898)

(3)


1+ 1205882can be


119875 (12058812

119896) =

(120588119896

12119896)

(sum119896

119898=0120588119898

12119898)

(4)

where 12058812



(

119909

sum

119910=0

120582119894)119875(120588

12119864119909

119896) =

119909

sum

119910=0

120582119910sdot 119875 (12058812119910

119896) (5)

where 119875(12058812119864

119909





119875 (12058812119864

119909

119896)

= (1

120582119864119909

)(

119864119909

sum

119910=0

120582119910)

times [119875 (1 2 119864119909) minus 11990112119864

119909minus1

119875 (1 2 119864119909minus 1)]

(6)

where 11990112119864

119909minus1

= (sum119864119909minus1

119910=1120582119910)(sum119864119909

119910=1120582119910) and 119875(1 2

119864119909) = ((sum

119864119909

119910=1120588119910)119896

119896)(sum119896

119898=0(sum119864119909

119910=1120588119910)119898

119898)







MTC application

Yes

Start


End

Yes

No

No









119895th MME(vi) 119863


device(vii) 119872


device(viii) 119860


device




= (119877119894119895119866119894119895)The challenge


1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876


Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)


119894119895and

119862119894119895


1199041015840 and 119871

1199041015840 be



1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)


1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)


1199041015840





Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra





















eNodeB

Initial UE message




response





First DL data


First DL data

PCRF










Attach reject


Time period report

HSS






APN-AMBR report










j

U1

MGkk k = 1

T1t1

U2

t2 R2(j)Time





1 (1198801) However 119880








2(119895) = 119879


1(119895)







120582(119902)

=

120582 for 119902 le 0

1205821 minus

119902minus1

sum

119886=0

119891 (119886) for 119902 gt 0(1)



= 1119864[119879119894] where


119894) grant time


119894(119895)with amean



0 1 2

120582f(0)

120582f(1)120582f(2)

120583


120582f(2)

120582f(1) 120582f(1)

120583120583

120582f(2)

120582f(0)






(TC) of the queueis

120588(TC)

= 120582(119902)

(1

120583+ 119877) (2)



119894 Let 119896 be





119875 (1205881 119896) =

(120588119896

1119896)

(sum119896

119898=0120588119898

1119898)

(3)


1+ 1205882can be


119875 (12058812

119896) =

(120588119896

12119896)

(sum119896

119898=0120588119898

12119898)

(4)

where 12058812



(

119909

sum

119910=0

120582119894)119875(120588

12119864119909

119896) =

119909

sum

119910=0

120582119910sdot 119875 (12058812119910

119896) (5)

where 119875(12058812119864

119909





119875 (12058812119864

119909

119896)

= (1

120582119864119909

)(

119864119909

sum

119910=0

120582119910)

times [119875 (1 2 119864119909) minus 11990112119864

119909minus1

119875 (1 2 119864119909minus 1)]

(6)

where 11990112119864

119909minus1

= (sum119864119909minus1

119910=1120582119910)(sum119864119909

119910=1120582119910) and 119875(1 2

119864119909) = ((sum

119864119909

119910=1120588119910)119896

119896)(sum119896

119898=0(sum119864119909

119910=1120588119910)119898

119898)







MTC application

Yes

Start


End

Yes

No

No









119895th MME(vi) 119863


device(vii) 119872


device(viii) 119860


device




= (119877119894119895119866119894119895)The challenge


1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876


Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)


119894119895and

119862119894119895


1199041015840 and 119871

1199041015840 be



1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)


1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)


1199041015840





Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













j

U1

MGkk k = 1

T1t1

U2

t2 R2(j)Time





1 (1198801) However 119880








2(119895) = 119879


1(119895)







120582(119902)

=

120582 for 119902 le 0

1205821 minus

119902minus1

sum

119886=0

119891 (119886) for 119902 gt 0(1)



= 1119864[119879119894] where


119894) grant time


119894(119895)with amean



0 1 2

120582f(0)

120582f(1)120582f(2)

120583


120582f(2)

120582f(1) 120582f(1)

120583120583

120582f(2)

120582f(0)






(TC) of the queueis

120588(TC)

= 120582(119902)

(1

120583+ 119877) (2)



119894 Let 119896 be





119875 (1205881 119896) =

(120588119896

1119896)

(sum119896

119898=0120588119898

1119898)

(3)


1+ 1205882can be


119875 (12058812

119896) =

(120588119896

12119896)

(sum119896

119898=0120588119898

12119898)

(4)

where 12058812



(

119909

sum

119910=0

120582119894)119875(120588

12119864119909

119896) =

119909

sum

119910=0

120582119910sdot 119875 (12058812119910

119896) (5)

where 119875(12058812119864

119909





119875 (12058812119864

119909

119896)

= (1

120582119864119909

)(

119864119909

sum

119910=0

120582119910)

times [119875 (1 2 119864119909) minus 11990112119864

119909minus1

119875 (1 2 119864119909minus 1)]

(6)

where 11990112119864

119909minus1

= (sum119864119909minus1

119910=1120582119910)(sum119864119909

119910=1120582119910) and 119875(1 2

119864119909) = ((sum

119864119909

119910=1120588119910)119896

119896)(sum119896

119898=0(sum119864119909

119910=1120588119910)119898

119898)







MTC application

Yes

Start


End

Yes

No

No









119895th MME(vi) 119863


device(vii) 119872


device(viii) 119860


device




= (119877119894119895119866119894119895)The challenge


1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876


Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)


119894119895and

119862119894119895


1199041015840 and 119871

1199041015840 be



1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)


1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)


1199041015840





Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










0 1 2

120582f(0)

120582f(1)120582f(2)

120583


120582f(2)

120582f(1) 120582f(1)

120583120583

120582f(2)

120582f(0)






(TC) of the queueis

120588(TC)

= 120582(119902)

(1

120583+ 119877) (2)



119894 Let 119896 be





119875 (1205881 119896) =

(120588119896

1119896)

(sum119896

119898=0120588119898

1119898)

(3)


1+ 1205882can be


119875 (12058812

119896) =

(120588119896

12119896)

(sum119896

119898=0120588119898

12119898)

(4)

where 12058812



(

119909

sum

119910=0

120582119894)119875(120588

12119864119909

119896) =

119909

sum

119910=0

120582119910sdot 119875 (12058812119910

119896) (5)

where 119875(12058812119864

119909





119875 (12058812119864

119909

119896)

= (1

120582119864119909

)(

119864119909

sum

119910=0

120582119910)

times [119875 (1 2 119864119909) minus 11990112119864

119909minus1

119875 (1 2 119864119909minus 1)]

(6)

where 11990112119864

119909minus1

= (sum119864119909minus1

119910=1120582119910)(sum119864119909

119910=1120582119910) and 119875(1 2

119864119909) = ((sum

119864119909

119910=1120588119910)119896

119896)(sum119896

119898=0(sum119864119909

119910=1120588119910)119898

119898)







MTC application

Yes

Start


End

Yes

No

No









119895th MME(vi) 119863


device(vii) 119872


device(viii) 119860


device




= (119877119894119895119866119894119895)The challenge


1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876


Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)


119894119895and

119862119894119895


1199041015840 and 119871

1199041015840 be



1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)


1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)


1199041015840





Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra













MTC application

Yes

Start


End

Yes

No

No









119895th MME(vi) 119863


device(vii) 119872


device(viii) 119860


device




= (119877119894119895119866119894119895)The challenge


1198601 1198602 119860

119873 where 119860

119894= 119886119894119895

119886119894119895

ge 0 119895 = 1 2 119876


Maximize

119876

sum

119895=1

119873

sum

119894=1

119877119894119895119862119894119895

Subject to

119876

sum

119895=1

119873

sum

119894=1

119886119894119895

le 119860

0 le 119862119894119895

le 1

119877119894119895

ge 0 forall119894 119895

(7)


119894119895and

119862119894119895


1199041015840 and 119871

1199041015840 be



1198671199041015840 =

1199041015840

sum

119894=1

(1

119890)

119894

if 1199041015840lt 119878

1 if 1199041015840= 119878

(8)


1198711199041015840 =

0 if 1199041015840= 1

1199041015840

sum

119894=2

(1

119890)

119894minus1

if 1 lt 1199041015840= 119878

(9)


1199041015840





Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Input 119873 119878 119866119894119895 119877119894119895 119863119894119872119894

Output 119860119894


119862119894119895

= (119877119894119895119866119894119895)

Find (119862119894119895

lt 1198671199041015840 and 119862


1015840

Switch (1199041015840)

case (1199041015840 == 119878) 119860119894= 119872119894 break


119894= 119863119895119890(1199041015840minus1) break

end forend for




FI =1

119891times

(sum119891

119899=1119883119899)2

sum119891

119899=11198832119899

(10)





119894119895 119863119894 119872119894

1198671199041015840 and 119871













0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















0

01

02

03

04

05

06

07

08

Bloc

king

pro

babi

lity



k = 2 MMEs


2434100

1987032

1611256

02468

10121416182022242628times105

0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

mMSC mechanism

LTE standard
















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra



















0132

0123

0100


0 h 0

m

0 h 5

m

0 h 1

0 m

0 h 1

5 m

0 h 2

0 m

0 h 2

5 m

0 h 3

0 m

0 h 3

5 m

0 h 4

0 m

0 h 4

5 m

0 h 5

0 m

0 h 5

5 m

1 h 0

m


007000750080008500900095010001050110011501200125013001350140





6 Conclusion







0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra














0

01

02

03

04

05

06

07

08

09

FI







Acknowledgment


References






























Volume 2014




Journal of











Journal of


Function Spaces






Algebra


























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article a multistage control mechanism for group...

Documents