2-layered architecture of vague logic based multilevel queue

Research Article2-Layered Architecture of Vague Logic BasedMultilevel Queue Scheduler

Supriya Raheja1 Reena Dadhich2 and Smita Rajpal3

1 Department of Computer Science amp Engineering ITM University Gurgaon India2Department of Computer Science University of Kota Near Kabir Circle MBS MargSwami Vivekanand Nagar Kota Rajasthan 324 005 India

3 Alpha Global IT 1262 Don Mills Road Toronto ON Canada M3B 2W7

Correspondence should be addressed to Supriya Raheja supriyarahejagmailcom

Received 28 July 2014 Revised 10 September 2014 Accepted 22 September 2014 Published 9 October 2014

Academic Editor Baoding Liu

Copyright copy 2014 Supriya Raheja et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In operating system the decisions which CPU scheduler makes regarding the sequence and length of time the task may run are noteasy ones as the scheduler has only a limited amount of information about the tasks A good scheduler should be fair maximizesthroughput and minimizes response time of system A scheduler with multilevel queue scheduling partitions the ready queue intomultiple queues While assigning priorities higher level queues always get more priorities over lower level queues Unfortunatelysometimes lower priority tasks get starved as the scheduler assures that the lower priority tasks may be scheduled only afterthe higher priority tasks While making decisions scheduler is concerned only with one factor that is priority but ignores otherfactors which may affect the performance of the systemWith this concern we propose a 2-layered architecture of multilevel queuescheduler based on vague set theory (VMLQ) The VMLQ scheduler handles the impreciseness of data as well as improving thestarvation problem of lower priority tasks This work also optimizes the performance metrics and improves the response timeof system The performance is evaluated through simulation using MatLab Simulation results prove that the VMLQ schedulerperforms better than the classical multilevel queue scheduler and fuzzy based multilevel queue scheduler

1 Introduction

In multitasking operating systems multiple tasks need tobe executed concurrently Therefore CPU scheduler playsa pivot role in operating system as it shares the CPU timeamong different tasks For making the decision of schedulingnext task for CPU scheduler runs scheduling algorithmHence the performance of system varies very much withscheduling algorithmusedMultilevel queue (MLQ) schedul-ing algorithm is among one of the preferable algorithms byOS designers [1 2]

The kernel of operating system divides the CPU timeamong different queues depending on its requirement ofIO and CPU But this share is fixed it cannot be changeddynamically with variations in usage since kernel is notaware of the exact parameters of task like priority of taskHowever in case ofMLQ priority plays a key role in decisionsof scheduler Recent evolutions in MLQ schedulers have

contributed towards improvement of MLQ approach but nosignificant enhancements to the approach which considersuncertainty factors [3] There is one approach in literaturethat adapts the variations using fuzzy logic [4]

This paper concentrates on the dealing of uncertainty andimpreciseness of taskrsquos parameters using another approachthat is vague logic Vague logic is an extended formationof fuzzy logic which becomes a dedicated tool to handlethe imprecise information With this aim a vague inferencesystem is designed inside the scheduler that deals withthe uncertainty and impreciseness of tasks This work alsofocuses on improving the performance of MLQ schedulerWe are introducing a new vague logic based MLQ schedulerwhich performs two main functions First it distributes theCPU time among different queues dynamically and adaptschanges with the variations in usage Second it resolvesthe starvation problem of lower priority tasks by makingdecisions using vague based multilevel queue scheduling

Hindawi Publishing CorporationApplied Computational Intelligence and So ComputingVolume 2014 Article ID 341957 12 pageshttpdxdoiorg1011552014341957

2 Applied Computational Intelligence and Soft Computing

algorithm With these two functions the VMLFQ schedulerimproves the response time of system as well which makesthe system more responsive

The paper is organized as follows Section 2 discusses theintroduction to MLQ scheduling algorithm and the relatedworkwithMLQ Section 3 gives the brief idea about the vagueset theory and how it is different from fuzzy set theory InSection 4 we introduce the 2-layered architecture of VMLQscheduler Section 5 describes the simulation and results indetail Finally Section 6 concludes the proposed work anddiscusses the future scope

2 Related Work

MLQ scheduling algorithm has been created where differ-ent tasks can be classified into different groups Schedulerorganized the ready queue of system into multiple separatequeues mainly for interactive and background tasks [5] Itis an extended form of priority scheduling where schedulerassigns each task permanently to one queue based on itspriority type of task andmemory size Each task has differentresponse time requirements and may have different schedul-ing needs Most operating systems including WindowsLinux and OS X support a form of multilevel queues [6]Let us consider two queues of two different types of tasksinteractive and batch tasks in which interactive tasks arehaving higher priorities over batch tasks In this type ofsystem scheduler schedules the tasks from those two queuesas shown in Figure 1

However each queue has its own scheduling algorithmusually interactive tasks run round robin scheduling tech-nique and batch tasks run first come first serve [7] Thesescheduling algorithms must be run between the queuesScheduler dispatches the tasks from the highest priorityqueue and executes that task either preemptively or nonpre-emptivelyThere are two different possibilities to schedule thetasks between the queues In fixed priority scheduling all thetasks from the higher priority queue are executed first Thelower priority tasks from the batch queue will not be executedunless the higher priority queue will be empty In this type ofscheduling there will be chances of occurrence of starvation[4]

However in the second type each queue gets a fixedamount of CPU time iteratively which is further distributedamongst its tasks In the above supposed case the readyqueue with 119899 is partitioned into 2 smaller ready subqueuesQ1 and Q2 where Q1 have the same priority tasks from 1to 119895 and Q2 have from 119869 + 1 to 119899 In preemptive priorityscheduling for the multiqueue technique all tasks from 1 to119895 in ready subqueue Q1 will be completed before any task isrun from ready subqueue Q2 through 119895 + 1 to 119899 Within thesubqueues the CPU may be allocated using any techniquesbut mainly the high priority Q1 using round robin and thelow priority queue that is Q2 using FCFSThere are differentstatic techniques available to share the CPU time across thesubqueues For example each subqueue can get the fractionof CPU time suppose that 100 seconds of CPU time can bepartitioned statically as 50 seconds among all the tasks or 80for Q1 or 20 for Q2 and so on [1]

Interactive queue

CPUBatch queue

Ready queueT5 T3

T3

T2

T2

T1

T1

T4T6Tn

Tn

middot middot middot middot middot middot

middot middot middot


Figure 1 Multilevel queue technique

As we have mentioned earlier there is very limitedliterature available for MLQ scheduling algorithm Shukla etal have presented aMLQ scheduling algorithmusingMarkovchainmodel [8]This scheduler can perform randomnumberof movements based on different processing states andwaiting states By adding queue priorities in the schedulingpolicy intelligently this system can perform better Nasser etal have introduced a new packet scheduling algorithm calleddynamic multilevel queue scheduling for wireless networks[9] Nasser et al proposed an algorithm in which the queuesizes can vary based on the application requirement [9] Shahet al have proposed multilevel hybrid scheduling algorithmfor optimum utilization of processors in grid environment[10] But any of this work did not consider uncertaintyand impreciseness of task For example the task with lowerpriority with small CPU time has always been assigned tolower level queues using these techniques but handling theimpreciseness dynamically rather than fixing the queues onthe basis of priority this task may be assigned to higherqueues and can improve the performance of scheduler

Professor Zadeh had designed a theory for dealing withimprecise data that provides the scope of further enhance-ments [11ndash14] Different scheduling algorithms are availablein literature using fuzzy set theory [15ndash17] Chahar andRahejahave explored this scope and introduced a fuzzy based MLQscheduling algorithm We are calling this algorithm FMLQscheduling algorithm [4] They have introduced a dynamicapproach to share the CPU time among different queuesand provided a fuzzy based solution over fixed amountof CPU time distribution Undoubtedly FMLQ schedulingalgorithm brought a solution for imprecise information andalso improved the performance of system Our present workexplores the scope of further enhancement in developmentof techniques dealing with uncertainty and impreciseness ina much better way Therefore this work uses the conceptof vague set theory which is an extended form of fuzzy settheory

The significant aspect of VMLQ scheduler is that itprovides a dynamic share of CPU time to queues It not onlyconsiders the prime factor of MLQ scheduling priority butalso considers the associated uncertainty and imprecisenessThe VMLQ scheduler improves the performance of systemover the MLQ scheduling and FMLQ scheduling algorithm

In the next section we will describe the core part of ourwork that is vague set theory

Applied Computational Intelligence and Soft Computing 3

3 Vague Set Theory

In 1965 Professor Zadeh has revolutionized the theory oflogics by introducing fuzzy set theory In fuzzy set theoryevery object has single degree of membership in between0 and 1 Let 119883 be the universe of discourse where 119883 =

1199091 1199092 119909

119899

Definition 1 (fuzzy set) A fuzzy set 119865 in 119883 is a set of orderedpairs 119909 120583

119865(119909) 119909 isin 119883 where 120583

119865(119909) is the degree of

membership of element 119909 in the set 119865 The larger the valueof 120583119865(119909)means is the more the element 119909 belongs to the set

119865 [11]

Well-known extensions of fuzzy set theory have beenproposed such as type-2 fuzzy sets having membershipfunctions that map from a set 119883 to a type-1 fuzzy set on theinterval [0 1] Such type-2 sets are 120593-fuzzy sets which mapfrom119883 to the set of closed intervals in [0 1] Such an interval-valued fuzzy set is characterized by a membership function120583119865(119909) 119909 isin 119883 which assigns to each element a grade of

membership over a continuous interval of real numbers in therange [0 1] instead of a single value It also assigns a grade ofmembership which is a subinterval of [0 1] to each elementThis subinterval keeps track of both evidences evidence forfavour and evidence for opposition Quinlan introduced twovalues 119905(119875) and 119891(119875) characterizing a proposition 119875 119905(119875) isthe greatest lower bound on the probability of 119875 derived fromthe evidence for119875 and119891(119875) is the greatest lower bound onsim119875

derived from the evidence against 119875In 1993 Professors Gau and Buehrer had extended

this single membership concept with the two member-ship concepts true-membership function 119905

119865(119909) and false-

membership function 119891119865(119909) to record the lower bounds on

120583119865(119909) They addressed the two membership degrees degree

of favour and degree of opposition individually rather thansingle membership value 120583

119865(119909) as in fuzzy set theory These

membership values even can process the two evidences atthe same timeThey had investigated that single membershipdegree cannot give more accuracy Gau and Buehrer haveintroduced the interval based theory that is vague settheory over single membership theory The two definedmembership functions are true-membership function 119905

119865and

false-membership function 119891119865which generalize the 120583

119865of

fuzzy set For forall119909 119905119865(119909) le 120583

119865(119909) le 119891

119865(119909) [18]

Definition 2 (vague set) A vague set 119881 in 119883 is characterizedby a true-membership function 119905

119881and a false-membership

function 119891119881

119905119881

119883 997888rarr [0 1] 119891119881

119883 997888rarr [0 1] (1)

where 119905119881(119909) is a lower bound on the grade of membership

of 119909 derived from the evidence for 119909 and 119891119881(119909) is a lower

bound on the negation of 119909 derived from the evidence against119909 There is a higher order check on the two independentmembership values that total amount cannot exceed 1 thatis 119905119881(119909) + 119891

119881(119909) le 1 Thus the grade of membership of 119909 in

the vague set119881 is bounded by a subinterval [119905119881(119909) 1minus119891

119881(119909)]

of [0 1] This indicates that if the fuzzy grade of membershipis 120583119865(119909) then 119905

119881(119909) le 120583

119865(119909) le 1 minus 119891

119881(119909) [18]

Definition 3 (vague value) The interval [119905119881(119909) 1 minus 119891

119881(119909)] is

called the ldquovague valuerdquo of 119909 in 119881 The vague set 119881 is writtenas

119860 = ⟨119909 [119905119881(119909) 119891

119881(119909)]⟩ 119909 isin 119883 (2)

Let us consider a vague value [06 08] in a vague set119881 Here119905119881

= 06 1 minus 119891119881

= 08 and 02 is the hesitated value that doesnot belong to either the true value or the false valueThe totalscope of these values is between 0 and 1 [19 20]

31 Deviation of Fuzzy Set towards Vague Set Let 119883 be auniverse of discourse suppose collection of static priority oftasks of OS Let119881 be a vague set of all ldquomediumpriority tasksrdquoof 119883 and let 119865 be a fuzzy set of all ldquomedium priority tasksrdquoof 119883 Suppose an expert e1 advises degree of membership120583119865(119909) for an object 119909 in fuzzy set 119865 by his expertise Whereas

at the other side another expert e2 advises two degreesof memberships 119905

119881(119909) and 119891

119881(119909) for the same object 119909 in

vague set 119881 by his expertise Both experts e1 and e2 havetheir limitation of sensing power assessment capability andworking ability with real life situations In case of fuzzyset 119865 there is no further check on degree of membership120583119865(119909) However an expert e2 advised degree of memberships

independently but can have a further check by maintainingthe constraint 119905

119881(119909) + 119891

119881(119909) le 1 [21]

4 Vague Logic Based MultilevelQueue CPU Scheduler

VMLQ scheduler has the capability of observing learningand holding information about ready tasks This learningpower makes the scheduler capable enough to responddynamically hence assigning different CPU time amongqueues at different situation Suppose at time 1199051 that theCPU time for Q1 is 65 and for Q2 is the remaining 35though at time 1199052 75 CPU time can be given to Q1 and theremaining 25 to Q2 Traditional scheduler assigns the fixedshare to queues [1] But our scheduler responds dynamicallydepending on the current state of ready queue VMLQscheduler performs mainly two tasks First it distributes theCPU time among different queues dynamically and adaptschanges with the variations in usage Second it resolvesthe starvation problem of lower priority tasks by makingdecisions using vague based multilevel queue schedulingalgorithm

VMLQ scheduler has two layers as shown in Figure 2Lower layer runs vague inference system and upper layer runsscheduling algorithm In the next sections we discuss theworking of these layers in detail

41 Vague Inference System for VMLQ Scheduler A vagueinference diagram expresses all the steps from vaguificationto devaguification [21] as shown in Figure 3 Vague inferencesystem (VIS) maps the crisp inputs into crisp outputs usingvague set theory [22] This mapping provides a base for the


Vague inference system

Vague based multilevel queue scheduling algorithm

DevaguificationVaguification Inference engine

Figure 2 2-layered architecture of VMLQ scheduler

N

Vaguification

Knowledge base

DevaguificationInference engine

Rule base

Crisp output(CPU share)

Crisp input

m

(P) Pmax and Pmin

tP fP

Figure 3 Vague inference system for VMLQ scheduler

decisions to bemadeWe considered a VIS for a uniprocessorsystem that supports 119873 number of tasks

Vaguification Vaguification is a mathematical procedurewhich determines the degree of belongingness of input inform of membership functions It takes the input V fromthe universe of discourse 119883 in crisp form and converts itinto appropriate vague data [119905

119881 1 minus 119891

119881] where 119905

119881represents

true-membership value and 119891119881represents false-membership

valueLet us assume universe of discourse 119875 = 119875

1 1198752 119875

119873

where an element of119875 is denoted by119875119894and represents the user

priority of 119894th taskIn the process of vaguification membership functions 119905

119875

and 119891119875which are defined in (3) are applied on crisp input

119875119894so that the degree of truth and degree of false forall119894 can be

determined It handles the impreciseness by considering themembership degree with respect tomaximum andminimumvalues of input so that imprecise value will be equallydispersed among all tasks Hence this does not affect the finaldecision Consider

forall119894 119905119875119894

=

119875max minus 119875119894

119875max + 119875min + 1

forall119894 119891119875119894

= sqrt(119875119894minus 119875min

119875max + 119875min + 1

)

(3)

The defined membership functions should follow the fouraxioms and all axioms are represented in Figure 4

Axiom 1 119905119875le 1

Axiom 2 119891119875

le 1

Axiom 3 0 le 119905119875le 1 minus 119891

119875le 1

Axiom 4 0 le 119905119875+ 119891119875le 1

Vague data forall119894 can be represented as

[119905119875119894 1 minus 119891

119875119894]

= [

119875max minus 119875119894

119875max + 119875min + 1

1 minus

119875119894minus 119875min

119875max + 119875min + 1

]

(4)

Knowledge Base It acts as the storage for the ready tasksAll the information associated with tasks like burst timeuser priorities arrival time maximum available priorityminimum available priority number of active tasks and soforth are stored in the system Consider

119875max = max 1198751 1198752 119875

119873

119875min = min 1198751 1198752 119875

119873

(5)

Rule Base Rule base mainly consists of if -then rules In ourrule base we have defined two rules based on the number oftasks ready in the system Consider

if 119873 lt 5 then 119878119894= 119873 lowast 10

if 119873 ge 5 then 119878119894= 119873 lowast 5

(6)

Vague Inference Engine It extracts the information forall119894 119905119875

and 1 minus 119891119875from the vaguification process and 119878 from rule

base After vaguifying the data system knows the degree offavour and degree of opposition Based on the degrees vagueinference engine evaluates the rules defined in rule baseAfterward based on the evaluation system computes the mas follows

forall119894 119898119894= 119878119894lowast (119905119875119894

+ 1 minus 119891119875119894) (7)

This phase results in fuzzy value which is assigned to eachtask The inference process should follow Axiom 5 Themultiple inputs can be passed to the inference process

Axiom 5 0 le 119898119894le 1

Devaguification The purpose of devaguification is to findthe crisp value of the outputGenerally the required outputis a single number However the vague inference engineproduces the multiple fuzzy values with respect to inputvariables Devaguification process converts the multiple out-put values into a single number Hence the task with themaximum fuzzy value 119898 is chosen for the output as shownin Figure 5

The crisp value for the output CPU share is computed bymultiplying the maximum fuzzy value by 100 as follows

CPUshare = 100 lowast max 1198981 1198982 119898

119873 (8)

42 Vague Based Multilevel Queue Scheduling Algorithm InVMLQ scheduling algorithm the ready queue is divided intotwo subqueues Q1 and Q2 as shown in Figure 6 Q1 is


1

0

tP

tP(x0)

x0

(a)

1

0

fPfP(x0)

x0

(b)

1

0

tP

x0

tP(x0)

1 minus fP(x0)

(c)

1

0x0

tP(x0) + fP(x0)

(d)

1

0

mn(x0)

m2(x0)

m1(x0)

x0

(e)

Figure 4 (a) Axiom 1 (b) Axiom 2 (c) Axiom 3 (d) Axiom 4 and (e) Axiom 5

holding interactive tasks whereas Q2 is holding backgroundtasks Since interactive tasks are the highest priority tasksamong all tasks [3] therefore this induces higher priority forQ1 overQ2The tasks are permanently assigned to each queueas in MLQ scheduling algorithm So task from Q1 cannot bemoved to Q2 and vice versa

The CPU time is shared dynamically among Q1 and Q2The CPU time for Q1 (Q1 time) is calculated using the vagueinference system as discussed in Section 41 The CPU time

for Q2 (Q2 time) is calculated using the CPU share of Q1The tasks of Q1 are dispatched with CPU only for Q1 timeHowever tasks from Q2 get the CPU only when eitherQ1 time becomes zero or Q1 becomes empty Both queueshave their own scheduling algorithm as both interactive andbackground tasks need different response

Each queue has its own scheduling algorithm becauseboth types of tasks have their different response time require-ments Interactive tasks in Q1 are scheduled using round


Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0

Figure 5 Task with maximum fuzzy value

Q1 RR

Task arrival Q2 FCFS

CPU share

Q1 time

Q2 time

Figure 6 Schematic view of proposed system

robin (RR) scheduling algorithm [23 24] it means that eachtask is dispatched to CPU only for given time quantum Afterthe expiry of each time quantum the current running taskwill preempt and the next task from Q1 will be scheduledwith CPU This process of switching CPU from one taskto another task is called context switch which is totally anoverhead for system since no useful work is performed bythe system during context switching [16] Sometimes bursttime of task is remaining in between 01 and 05 sec when timequantum expires which increases waiting time of task as wellas the number of context switches for system For reducingthe number of context switches VMLFQ scheduler will notpreempt the task if the remaining burst time of that task is lessthan 05 sec

VMLQ scheduler uses new first come first serve (NFCFS)scheduling algorithm for all tasks of Q2 NFCFS schedulingalgorithm schedules the task as soon as it arrives in thesystem However traditional FCFS scheduling algorithmschedules the next task only after completing the execution ofthe first task In interactive environment response time is themajor factor to measure performance of scheduler FCFS isnonpreemptive type of scheduling algorithmwhich increasesthe response time as well as waiting time for each task [1]whereas NFCFS is a preemptive scheduling algorithm whichimproves the response time as compared to FCFS

421 Algorithm

Step 1 Classify task into interactive and background tasksbased on burst time

Step 2 Assign IO bound tasks to Q1 and CPU bound tasksto Q2

N1 = number of tasks in Q1N2 = number of tasks in Q2

Step 3 Sort Q1 in ascending order based on burst time

Step 4 Calculate the percentage of CPU time allocation forQ1

Q1 time = CPUshare (using (8))

Step 5 Calculate the CPU time for Q2 (Q2 time)

Q2 time = 100 minus Q1 time)

Step 6 Schedule the tasks from Q1 using RR schedulingalgorithm

Time quantum (TQ) = Q1 timeN1

Step 7 If (Q1 time == 0 N1 == 0) then

schedule tasks from Q2 using NFCFS

Step 8 After each cycle repeat steps from 1 to 8 until (N2 ==0)

5 Simulation and Results

The performance metrics must be chosen carefully as theyreflect the characteristics of system The metrics chosen areas follows Response time is defined as the amount of time asystem takes to respond to the user input It is one of themostimportant factors in CPU scheduling algorithms Anothermetric which is considered in our work is waiting time whichis defined as the amount of time tasks wait in the readyqueue for CPU In our work total waiting time is the waitingtime of task in both higher priority queue and lower priorityqueue Next metric is turnaround time total time consumedby task from its submission to its completionThe last metricis normalized turnaround time relative delay of the task [1]The reduction in values of all these parameters representsimprovement in the performance of system We have imple-mented the proposed VIS-VMLQ using MatLab To comparethe performance of proposed algorithm with the traditionalMLQ and FMLQ the following procedure has been taken

For each 119873 isin [4 20] multiple sets of random taskswere considered Then these three algorithms were usedto schedule the tasks Results show that VMLQ approachperforms better than other approachesWe are presenting thethree scheduling algorithms MLQ FMLQ and VMLQ withthe help of sample task set [] as given in Table 1 Total 16 tasksare considered out of these 11 tasks are classified as inter-activeIO bound tasks and remaining 5 as backgroundCPUbound tasks IO bound tasks are represented by T and CPUbound tasks by C Assume all measures in seconds Supposeconstant CPU cycle time for each algorithm as 20 secondsThe scheduling sequence of each algorithm is illustrated withthe help of Gantt charts


T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)

Figure 7 (a) 1st cycle of CPU (MLQ) (b) 2nd cycle of CPU (MLQ) (c) 3rd cycle of CPU (MLQ) (d) 4th cycle of CPU (MLQ) (e) 5th cycleof CPU (MLQ) (f) 6th cycle of CPU (MLQ) (g) 7th cycle of CPU (MLQ) and (h) 8th cycle of CPU (MLQ)

Table 1 Sample task set

IO bound tasks CPU bound tasksTask Arrival time Priority Burst time Task Arrival time Priority Burst timeT1 0 9 8 C1 0 3 20T2 0 8 9 C2 0 2 25T3 0 7 5 C3 30 3 30T4 21 6 6 C4 35 2 35T5 25 5 7 C5 40 3 15T6 38 7 4T7 40 8 3T8 45 6 5T9 55 6 6T10 57 8 5T11 60 5 4

Figure 7 shows the scheduling sequence of task set givenin Table 1 for MLQ scheduling algorithmWith the MLQ thetasks from Q1 are scheduled using RR algorithm and fromQ2 using FCFS algorithm Let us consider the length of statictime quantum as 7 s As discussed in Section 2 assign fixed80 (16 s) CPU share to Q1 and the remaining 20 (4 s) toQ2 During first cycle the tasks T1 T2 and T3 are scheduleduntil 16 s and C1 is scheduled for 4 s as shown in Figure 7(a)

Till the end of the 2nd cycle tasks T1 T2 T3 and T4finish their execution as shown in Figure 7(b) Likewise thetasks from Q1 and Q2 are scheduled in the 3rd and 4th cycleas shown in Figures 7(c) and 7(d) After the 4th cycle Q1becomes empty Now the complete cycle of 20 s is assigned

to Q2 The scheduling sequence of Q2 tasks is shown inFigures 7(e) 7(f) 7(g) and 7(h) respectively

Figure 8 shows the schedule sequence with FMLQscheduling algorithm of the same task set After applyingFMLQ it returns the size of time quantum for first cycle as5 s and CPU share for Q1 as 65 (13 s) whereas the remaining35 (7 s) for Q2 The shortest task of Q1 is scheduled first toCPU as shown in Figure 8(a) Tasks from Q2 are scheduledas soon as they arrive in the queue hence C1 and C2 both arescheduled for 35 s each

During the 2nd cycle FMLQ gives the CPU share to Q1 as85 (14 s) and to Q2 as 15 (6 s) Each task in Q1 is scheduledfor 4 s time quantum forQ1 as shown in Figure 8(b)Whereas


T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)

Figure 8 (a) 1st cycle of CPU (FMLQ) (b) 2nd cycle of CPU (FMLQ) (c) 3rd cycle of CPU (FMLQ) (d) 4th cycle of CPU (FMLQ) (e)5th cycle of CPU (FMLQ) (f) 6th cycle of CPU (FMLQ) (g) 7th cycle of CPU (FMLQ) (h) 8th cycle of CPU (FMLQ) (i) 9th cycle of CPU(FMLQ) and (j) 10th cycle of CPU (FMLQ)

for the third and fourth cycle FMLQ returns size of timequantum forQ1 as 3 s and 4 s respectively Likewise it returnsthe CPU share as 70 and 80 respectively In FMLQ if theremaining burst time is less than or equal to 1 the task willnot preempt rather it finishes its execution as indicated inFigure 8(c)

Up to the third cycle all the CPU bound processes havearrived in Q2 and scheduled once to CPU In the fourthcycle task C1 has resumed its execution for 4 s as shown inFigure 8(d)

All the IO bound tasks have finished their execution upto the 5th cycle as shown in Figure 8(e) Afterwards the entireCPU share has been assigned to Q2 We can see the completescheduling from Figures 8(f)ndash8(j)

Figure 9 illustrates the scheduling order of each task usingVMLQ on the same task set For the first cycle VIS return70 (158 s) CPU share for Q1 as discussed in Section 4 and30 (42 s) for Q2 VMLQ algorithm return time quantumfor Q1 as 54 s Both tasks T1 and T2 are scheduled for 54 sas shown in Figure 9(a)

Task in Q2 is dispatched in the same way as discussed inFMLQ Both tasks C1 and C2 are scheduled for 21 s For the

second cycle VMLQ returns CPU share for Q1 as 69 (126 s)and time quantum as 32 s whereas it returns CPU share forQ2 as 31 as shown in Figure 9(b)

For the third cycle Q1 receives 153 s CPU time and Q2gets 47 s of CPU cycle as shown in Figure 9(c) The tasks T4and T5 have resumed and finished their execution Similarlythe CPU time has been computed for the 4th and 5th cyclefor Q1 as 139 s and 144 s respectively Up to the 4th cycle allthe tasks fromQ1 have dispatched oncewithCPUas shown inFigure 9(d)During the 5th cycleQ1 becomes empty as shownin Figure 9(e) From the 6th cycle onwards all the CPU timeis given to CPU bound tasks as shown in Figure 9(f)We haverepresented all cycles after the 5th one in a single Gantt chart

In addition to the distribution of CPU time amongQ1 andQ2 we are also interested in the performance improvementof the system So based on the above discussed Gantt chartswe have calculated the performance metrics response timewaiting time turnaround time and normalized turnaroundtime for all tasksThe respective outputs for all algorithms areshown in Figures 10 11 12 and 13 respectively

Then we compared the average waiting time averageresponse time and average normalized turnaround time for


Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)

Figure 9 (a) 1st cycle of CPU (VMLQ) (b) 2nd cycle of CPU (VMLQ) (c) 3rd cycle of CPU (VMLQ) (d) 4th cycle of CPU (VMLQ) (e)5th cycle of CPU (VMLQ) and (f) 6thndash10th cycles of CPU (VMLQ)

0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ

Figure 10 Response time (sample task set)

all three algorithms as shown in Figure 14 On 119909-axis ldquo1rdquorepresents MLQ scheduling algorithm ldquo2rdquo represents FMLQscheduling and ldquo3rdquo represents VMLQ scheduling algorithm

One can notice from Figure 14 that there is large dropoffin value of average response time from MLQ to FMLQ and

0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ

Figure 11 Waiting time (sample task set)

from FMLQ to VMLQ Dropoff represents the improvementin performance However there is slight deviation in averagewaiting time average turnaround time and average normal-ized turnaround time that is acceptable as response time is


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me

Figure 12 Turnaround time (sample task set)

0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me

Figure 13 Normalized turnaround time (sample task set)

the major considerable factor in multitasking or interactivesystems

We have repeated this process randomly over multipletasks set Furtherwe have calculated all permformancemeticsfor each task set Finally we have compared the results of allthree algorithms as shown in Figures 15 16 17 and 18

Result in Figures 15 16 17 and 18 indicates that VMLQhas an excellent performance over MLQ and FMLQ Amongall algorithms VMLQhas the lowest average response time Itis understandable that performance improvement in relationto response time can slightly increase the other factors includ-ing average waiting time and average normalized turnaround

0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT

Figure 14 Results (sample task set)

0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ

Figure 15 Average waiting time

time as we have discussed in our work VMLF schedulingalgorithm has better performance mainly by two reasons

The proposed architecture of VMLQ scheduler is veryeffective in highly dynamic environment where CPU timeis shared dynamically among multiple queues and furtheramong tasks in each queue It deals with impreciseness inmore better way as compared to fuzzy set theory In additionto sharing of CPU time decreased response time improvesthe starvation problem at the lower priority queues since atleast once the task has been scheduled to CPU as soon as itarrives to the system


0 5 10 15Number of cases

0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ

Figure 16 Average response time

0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ

Figure 17 Average turnaround time

6 Conclusion

The 2-layered architecture for VMLQ scheduler introducedin this paper offers solutions for the two basic problemsover classic MLQ algorithm and FMLQ algorithm Firstlyit is more appropriate for dynamical allocation of CPUtime among multiple queues because of its capability toapproximate the input parameters user priority and numberof tasks Further it improves the average response time ofsystem and consequently solves the starvation in the lowerpriority queues The proposed methodology implements thevague inference system using MatLab that takes the crispinput priority and converts it into vague data to handle

15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ

Figure 18 Average normalized turnaround time

the impreciseness of data Simulation results in Section 5demonstrate that this algorithm excellently improves theperformance of classic MLQ scheduling algorithm and theFMLQ scheduling algorithm In future VMLQ schedulingalgorithmcanbe extended formore partitions of ready queue

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

References

[1] A Silberschatz and P B Galvin Operating System ConceptsJohn Wiley amp Sons New Delhi India 6th edition 2008

[2] W Stallings Operating Systems Internal and Design PrinciplesPearson Education 6th edition 2006

[3] M V Panduranga Rao and K C Shet ldquoAnalysis of newmulti-level feedback queue scheduler for real time kernelrdquoInternational Journal of Computational Cognition vol 8 pp 5ndash16 2010

[4] V Chahar and S Raheja ldquoFuzzy based multilevel queuescheduling algorithmrdquo in Proceedings of the 2nd InternationalConference on Advances in Computing Communications andInformatics (ICACCI rsquo13) pp 115ndash120 August 2013

[5] S Lim and S-B Cho ldquoIntelligent OS process scheduling usingfuzzy inference with user modelsrdquo in New Trends in AppliedArtificial Intelligence vol 4570 of Lecture Notes in ComputerScience pp 725ndash734 Springer Berlin Germany 2007

[6] Kadhim and KM AI-AubidyDesign and Evaluation of a FuzzyBased CPU Scheduling Algorithm Springer Berlin Germany2011

[7] N Bin D Jianqiang X Guoliang L Hongning Y Riyue andW Quan ldquoA new operating system scheduling algorithmrdquo inAdvanced Research on Electronic Commerce Web Applicationand Communication vol 143 pp 92ndash96 Springer 2011


[8] D Shukla S Ojha and S Jain ldquoData model approach andMarkov Chain based analysis of multilevel queue schedulingrdquoJournal of Applied Computer Science Mathematics vol 8 no 4pp 50ndash56 2010

[9] N Nasser L Karim and T Taleb ldquoDynamic multilevel prioritypacket scheduling scheme for wireless sensor networkrdquo IEEETransactions on Wireless Communications vol 12 no 4 pp1448ndash1459 2013

[10] S N M Shah A K B Mahmood and A Oxley ldquoDynamicmultilevel dual queue scheduling algorithms for grid comput-ingrdquo in Software Engineering and Computer Systems vol 179 ofCommunications in Computer and Information Science pp 425ndash440 Springer Berlin Germany 2011

[11] L A Zadeh ldquoFuzzy setsrdquo Information and Control vol 8 no 3pp 338ndash353 1965

[12] L A Zadeh ldquoMaking computers think like peoplerdquo IEEESpectrum vol 8 pp 26ndash32 1983

[13] R E Bellman and L A Zadeh ldquoDecision making in a fuzzyenvironmentrdquo Management Science vol 17 no 4 pp 141ndash1641970

[14] L A Zadeh ldquoIs there a need for fuzzy logicrdquo InformationSciences vol 178 no 13 pp 2751ndash2779 2008

[15] A A Aburas and V Miho ldquoFuzzy logic based algorithm foruniprocessor schedulingrdquo in Proceedings of the Internation-al Conference on Computer and Communication Engineering(ICCCE rsquo08) pp 499ndash504 IEEE May 2008

[16] S Raheja R Dhadich and S Rajpal ldquoAn optimum timequantum using linguistic synthesis for round robin schedulingalgorithmrdquo International Journal of Soft Computing vol 3 no 1pp 57ndash66 2012

[17] A Rezaee A M Rahmani and S Adabi ldquoA fuzzy algorithm foradaptive multilevel queue management with QoS feedbackrdquo inProceedings of the International Conference onHigh PerformanceComputing and Simulation (HPCS rsquo11) pp 121ndash127 IEEE Istan-bul Turky July 2011

[18] W-L Gau and D J Buehrer ldquoVague setsrdquo IEEE Transactions onSystems Man and Cybernetics vol 23 no 2 pp 610ndash614 1993

[19] A Lu and W Ng Vague Sets or Intuitionistic Fuzzy Sets forHandling Vague Data Which One Is Bettervol 3716 of LectureNotes in Computer Science Springer 2005

[20] H Bustince and P Burillo ldquoVague sets are intuitionistic fuzzysetsrdquo Fuzzy Sets and Systems vol 79 no 3 pp 403ndash405 1996

[21] S Raheja and R Dhadich ldquoMany valued logics for modelingvaguenessrdquo International Journal of Computer Applications vol61 no 7 pp 35ndash39 2013

[22] S Raheja R Dhadich and S Rajpal ldquoDesigning of 2-stage CPUscheduler using vague logicrdquo Advances in Fuzzy Systems vol2014 Article ID 841976 10 pages 2014

[23] R J Matarneh ldquoSelf-adjustment time quantum in round Robinalgorithm depending on burst time of the now running pro-cessesrdquo American Journal of Applied Sciences vol 6 no 10 pp1531ndash1537 2009

[24] M Park H J Yoo J Chae and C-K Kim ldquoQuantum-basedfixed priority schedulingrdquo in Proceedings of the InternationalConference on Advanced Computer Theory and Engineering(ICACTE 08) pp 64ndash68 Phuket Thailand December 2008

Submit your manuscripts athttpwwwhindawicom

Computer Games Technology

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Distributed Sensor Networks


Advances in

FuzzySystems

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014


ReconfigurableComputing

Hindawi Publishing Corporation httpwwwhindawicom Volume 2014


Applied Computational Intelligence and Soft Computing

thinspAdvancesthinspinthinsp

Artificial Intelligence

HindawithinspPublishingthinspCorporationhttpwwwhindawicom Volumethinsp2014

Advances inSoftware EngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Electrical and Computer Engineering

Journal of

Journal of

Computer Networks and Communications


Hindawi Publishing Corporation

httpwwwhindawicom Volume 2014

Advances in

Multimedia


Biomedical Imaging


ArtificialNeural Systems

Advances in


RoboticsJournal of



Computational Intelligence and Neuroscience

Industrial EngineeringJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Human-ComputerInteraction

Advances in

Computer EngineeringAdvances in



algorithm With these two functions the VMLFQ schedulerimproves the response time of system as well which makesthe system more responsive

The paper is organized as follows Section 2 discusses theintroduction to MLQ scheduling algorithm and the relatedworkwithMLQ Section 3 gives the brief idea about the vagueset theory and how it is different from fuzzy set theory InSection 4 we introduce the 2-layered architecture of VMLQscheduler Section 5 describes the simulation and results indetail Finally Section 6 concludes the proposed work anddiscusses the future scope

2 Related Work

MLQ scheduling algorithm has been created where differ-ent tasks can be classified into different groups Schedulerorganized the ready queue of system into multiple separatequeues mainly for interactive and background tasks [5] Itis an extended form of priority scheduling where schedulerassigns each task permanently to one queue based on itspriority type of task andmemory size Each task has differentresponse time requirements and may have different schedul-ing needs Most operating systems including WindowsLinux and OS X support a form of multilevel queues [6]Let us consider two queues of two different types of tasksinteractive and batch tasks in which interactive tasks arehaving higher priorities over batch tasks In this type ofsystem scheduler schedules the tasks from those two queuesas shown in Figure 1

However each queue has its own scheduling algorithmusually interactive tasks run round robin scheduling tech-nique and batch tasks run first come first serve [7] Thesescheduling algorithms must be run between the queuesScheduler dispatches the tasks from the highest priorityqueue and executes that task either preemptively or nonpre-emptivelyThere are two different possibilities to schedule thetasks between the queues In fixed priority scheduling all thetasks from the higher priority queue are executed first Thelower priority tasks from the batch queue will not be executedunless the higher priority queue will be empty In this type ofscheduling there will be chances of occurrence of starvation[4]

However in the second type each queue gets a fixedamount of CPU time iteratively which is further distributedamongst its tasks In the above supposed case the readyqueue with 119899 is partitioned into 2 smaller ready subqueuesQ1 and Q2 where Q1 have the same priority tasks from 1to 119895 and Q2 have from 119869 + 1 to 119899 In preemptive priorityscheduling for the multiqueue technique all tasks from 1 to119895 in ready subqueue Q1 will be completed before any task isrun from ready subqueue Q2 through 119895 + 1 to 119899 Within thesubqueues the CPU may be allocated using any techniquesbut mainly the high priority Q1 using round robin and thelow priority queue that is Q2 using FCFSThere are differentstatic techniques available to share the CPU time across thesubqueues For example each subqueue can get the fractionof CPU time suppose that 100 seconds of CPU time can bepartitioned statically as 50 seconds among all the tasks or 80for Q1 or 20 for Q2 and so on [1]

Interactive queue

CPUBatch queue

Ready queueT5 T3

T3

T2

T2

T1

T1

T4T6Tn

Tn

middot middot middot middot middot middot



Figure 1 Multilevel queue technique

As we have mentioned earlier there is very limitedliterature available for MLQ scheduling algorithm Shukla etal have presented aMLQ scheduling algorithmusingMarkovchainmodel [8]This scheduler can perform randomnumberof movements based on different processing states andwaiting states By adding queue priorities in the schedulingpolicy intelligently this system can perform better Nasser etal have introduced a new packet scheduling algorithm calleddynamic multilevel queue scheduling for wireless networks[9] Nasser et al proposed an algorithm in which the queuesizes can vary based on the application requirement [9] Shahet al have proposed multilevel hybrid scheduling algorithmfor optimum utilization of processors in grid environment[10] But any of this work did not consider uncertaintyand impreciseness of task For example the task with lowerpriority with small CPU time has always been assigned tolower level queues using these techniques but handling theimpreciseness dynamically rather than fixing the queues onthe basis of priority this task may be assigned to higherqueues and can improve the performance of scheduler

Professor Zadeh had designed a theory for dealing withimprecise data that provides the scope of further enhance-ments [11ndash14] Different scheduling algorithms are availablein literature using fuzzy set theory [15ndash17] Chahar andRahejahave explored this scope and introduced a fuzzy based MLQscheduling algorithm We are calling this algorithm FMLQscheduling algorithm [4] They have introduced a dynamicapproach to share the CPU time among different queuesand provided a fuzzy based solution over fixed amountof CPU time distribution Undoubtedly FMLQ schedulingalgorithm brought a solution for imprecise information andalso improved the performance of system Our present workexplores the scope of further enhancement in developmentof techniques dealing with uncertainty and impreciseness ina much better way Therefore this work uses the conceptof vague set theory which is an extended form of fuzzy settheory

The significant aspect of VMLQ scheduler is that itprovides a dynamic share of CPU time to queues It not onlyconsiders the prime factor of MLQ scheduling priority butalso considers the associated uncertainty and imprecisenessThe VMLQ scheduler improves the performance of systemover the MLQ scheduling and FMLQ scheduling algorithm

In the next section we will describe the core part of ourwork that is vague set theory


3 Vague Set Theory


1199091 1199092 119909

119899


119865(119909) 119909 isin 119883 where 120583



119865 [11]





119865(119909) and false-






119865and


119865of


119865(119909) le 119891

119865(119909) [18]



function 119891119881

119905119881

119883 997888rarr [0 1] 119891119881

119883 997888rarr [0 1] (1)






119881(119909)]


119881(119909) le 120583

119865(119909) le 1 minus 119891

119881(119909) [18]


119881(119909)] is


119860 = ⟨119909 [119905119881(119909) 119891

119881(119909)]⟩ 119909 isin 119883 (2)


= 06 1 minus 119891119881




119881(119909) and 119891




119881(119909) + 119891

119881(119909) le 1 [21]










N

Vaguification

Knowledge base


Rule base


Crisp input

m

(P) Pmax and Pmin

tP fP




119881 1 minus 119891

119881] where 119905

119881represents



1 1198752 119875

119873



119875




forall119894 119905119875119894

=

119875max minus 119875119894

119875max + 119875min + 1

forall119894 119891119875119894

= sqrt(119875119894minus 119875min

119875max + 119875min + 1

)

(3)


Axiom 1 119905119875le 1

Axiom 2 119891119875

le 1

Axiom 3 0 le 119905119875le 1 minus 119891

119875le 1

Axiom 4 0 le 119905119875+ 119891119875le 1


[119905119875119894 1 minus 119891

119875119894]

= [

119875max minus 119875119894

119875max + 119875min + 1

1 minus

119875119894minus 119875min

119875max + 119875min + 1

]

(4)


119875max = max 1198751 1198752 119875

119873

119875min = min 1198751 1198752 119875

119873

(5)


if 119873 lt 5 then 119878119894= 119873 lowast 10

if 119873 ge 5 then 119878119894= 119873 lowast 5

(6)




forall119894 119898119894= 119878119894lowast (119905119875119894

+ 1 minus 119891119875119894) (7)


Axiom 5 0 le 119898119894le 1




119873 (8)



1

0

tP

tP(x0)

x0

(a)

1

0

fPfP(x0)

x0

(b)

1

0

tP

x0

tP(x0)

1 minus fP(x0)

(c)

1

0x0

tP(x0) + fP(x0)

(d)

1

0

mn(x0)

m2(x0)

m1(x0)

x0

(e)







Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0


Q1 RR


CPU share

Q1 time

Q2 time




421 Algorithm


















T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




3 Vague Set Theory


1199091 1199092 119909

119899


119865(119909) 119909 isin 119883 where 120583



119865 [11]





119865(119909) and false-






119865and


119865of


119865(119909) le 119891

119865(119909) [18]



function 119891119881

119905119881

119883 997888rarr [0 1] 119891119881

119883 997888rarr [0 1] (1)






119881(119909)]


119881(119909) le 120583

119865(119909) le 1 minus 119891

119881(119909) [18]


119881(119909)] is


119860 = ⟨119909 [119905119881(119909) 119891

119881(119909)]⟩ 119909 isin 119883 (2)


= 06 1 minus 119891119881




119881(119909) and 119891




119881(119909) + 119891

119881(119909) le 1 [21]










N

Vaguification

Knowledge base


Rule base


Crisp input

m

(P) Pmax and Pmin

tP fP




119881 1 minus 119891

119881] where 119905

119881represents



1 1198752 119875

119873



119875




forall119894 119905119875119894

=

119875max minus 119875119894

119875max + 119875min + 1

forall119894 119891119875119894

= sqrt(119875119894minus 119875min

119875max + 119875min + 1

)

(3)


Axiom 1 119905119875le 1

Axiom 2 119891119875

le 1

Axiom 3 0 le 119905119875le 1 minus 119891

119875le 1

Axiom 4 0 le 119905119875+ 119891119875le 1


[119905119875119894 1 minus 119891

119875119894]

= [

119875max minus 119875119894

119875max + 119875min + 1

1 minus

119875119894minus 119875min

119875max + 119875min + 1

]

(4)


119875max = max 1198751 1198752 119875

119873

119875min = min 1198751 1198752 119875

119873

(5)


if 119873 lt 5 then 119878119894= 119873 lowast 10

if 119873 ge 5 then 119878119894= 119873 lowast 5

(6)




forall119894 119898119894= 119878119894lowast (119905119875119894

+ 1 minus 119891119875119894) (7)


Axiom 5 0 le 119898119894le 1




119873 (8)



1

0

tP

tP(x0)

x0

(a)

1

0

fPfP(x0)

x0

(b)

1

0

tP

x0

tP(x0)

1 minus fP(x0)

(c)

1

0x0

tP(x0) + fP(x0)

(d)

1

0

mn(x0)

m2(x0)

m1(x0)

x0

(e)







Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0


Q1 RR


CPU share

Q1 time

Q2 time




421 Algorithm


















T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in








N

Vaguification

Knowledge base


Rule base


Crisp input

m

(P) Pmax and Pmin

tP fP




119881 1 minus 119891

119881] where 119905

119881represents



1 1198752 119875

119873



119875




forall119894 119905119875119894

=

119875max minus 119875119894

119875max + 119875min + 1

forall119894 119891119875119894

= sqrt(119875119894minus 119875min

119875max + 119875min + 1

)

(3)


Axiom 1 119905119875le 1

Axiom 2 119891119875

le 1

Axiom 3 0 le 119905119875le 1 minus 119891

119875le 1

Axiom 4 0 le 119905119875+ 119891119875le 1


[119905119875119894 1 minus 119891

119875119894]

= [

119875max minus 119875119894

119875max + 119875min + 1

1 minus

119875119894minus 119875min

119875max + 119875min + 1

]

(4)


119875max = max 1198751 1198752 119875

119873

119875min = min 1198751 1198752 119875

119873

(5)


if 119873 lt 5 then 119878119894= 119873 lowast 10

if 119873 ge 5 then 119878119894= 119873 lowast 5

(6)




forall119894 119898119894= 119878119894lowast (119905119875119894

+ 1 minus 119891119875119894) (7)


Axiom 5 0 le 119898119894le 1




119873 (8)



1

0

tP

tP(x0)

x0

(a)

1

0

fPfP(x0)

x0

(b)

1

0

tP

x0

tP(x0)

1 minus fP(x0)

(c)

1

0x0

tP(x0) + fP(x0)

(d)

1

0

mn(x0)

m2(x0)

m1(x0)

x0

(e)







Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0


Q1 RR


CPU share

Q1 time

Q2 time




421 Algorithm


















T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




1

0

tP

tP(x0)

x0

(a)

1

0

fPfP(x0)

x0

(b)

1

0

tP

x0

tP(x0)

1 minus fP(x0)

(c)

1

0x0

tP(x0) + fP(x0)

(d)

1

0

mn(x0)

m2(x0)

m1(x0)

x0

(e)







Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0


Q1 RR


CPU share

Q1 time

Q2 time




421 Algorithm


















T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Maximum value

1

0

mn(x0)

m2(x0)

m1(x0)

x0


Q1 RR


CPU share

Q1 time

Q2 time




421 Algorithm


















T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




T1 T2 T3

0 7 14 16

C1

16 20

Q1

Q2

(a)

T1 T2 T3 T4 T5

C1

2 0 21 23 26

36 40

32 36

Q1

Q2

(b)

T5 T6 T7

40 43 47 50

56 60

T8 T9

55 56

Q1

Q2 C1

(c)

T9 T10 T11

60 65 70 74

74 80

Q1

Q2 C1

(d)

C1 C2

80 82 100

Q2

(e)

C2 C3

100 107 120

Q2

(f)

C3 C4

120 137 140

Q2

(g)

C4 C5

140 172 187

Q2

(h)










T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




T3 T1 T2

0 5 10 13

C1

13 165

C2

20

Q1

Q2

(a)

T1 T2 T4

20 23 27 31

C3

37 40

T5 T2

35 37

C4

385

Q1

Q2

(b)

T4 T5 T7

40 42 45 48

C5

54 60

T6 T6

51 52

T8

54

Q2

Q1

(c)

T8 T11 T10

60 63 67 71

C1

76

T10 T9

72 76

80

Q2

Q1

(d)

80

T9

82

82

C1

945

C2

100

Q2

Q1

(e)

C3

140 160

C4

1445

Q2

(f)

C3

120 140

Q2

(g)

C3

140 160

C4

1445

Q2

(h)

C4

160 180

C5

178

Q2

(i)

C5

180 187

Q2

(j)












Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




Q1

Q2

T3 T1 T2

0 5 104 158

C1

158 179

C2

20

(a)

T1 T2 T4

20 226 262 294

C3

326 40

T5

326

C4

35

Q1

Q2

(b)

T4 T7 T5

40 428 458 496

C5

553 60

T6 T8

536 553

Q1

Q2

(c)

T8 T11 T10

60 633 693 706

C1

739

T9

739

80

Q1

Q2

(d)

T10

80 817

T9

C1 C2

844

844 962 100

Q1

Q2

(e)

C2 C3 C4

100 1191 1467 1767

C5

187

Q2

(f)


0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Resp

onse

tim

e

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 160

20

40

60

80

100

120

140

Number of tasks

Wai

ting

time

MLQFMLQVMLQ




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

0

50

100

150

Turn

arou

nd ti

me


0 2 4 6 8 10 12 14 16Number of tasks

MLQFMLQVMLQ

1

2

3

4

5

6

7

8

9

10

Nor

mal

ized

turn

arou

nd ti

me





0 1 2 3 40

10

20

30

40

50

60

Sample task set

AWTART

ATTANT


0 5 10 1525

30

35

40

45

50

55

60

65

70

75

Number of cases

Aver

age w

aitin

g tim

e

MLQFMLQVMLQ






0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in





0

10

20

30

40

50

60

Aver

age r

espo

nse t

ime

MLQFMLQVMLQ


0 5 10 1535

40

45

50

55

60

65

70

75

80

85

Number of cases

Aver

age t

urna

roun

d tim

e

MLQFMLQVMLQ


6 Conclusion


15

2

25

3

35

4

45

5

55

6

65

Aver

age n

orm

aliz

ed tu

rnar

ound

tim

e


MLQFMLQVMLQ





References

































Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in




























Advances in

FuzzySystems


Volume 2014












Journal of

Journal of





Advances in

Multimedia


Biomedical Imaging



Advances in


RoboticsJournal of










Advances in



2-layered architecture of vague logic based multilevel queue

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