View of RELATIVE ANALYSIS OF FAIR QUEUING DEFICIT ROUND ROBIN SCHEDULING SCHEME THROUGH PROBABILISTIC DATA MODELING

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ACCENT JOURNAL OF ECONOMICS ECOLOGY & ENGINEERING

Peer Reviewed and Refereed Journal IMPACT FACTOR: 2.104 (INTERNATIONAL JOURNAL) UGC APPROVED NO. 48767

Vol.03, Issue 04, April 2018, Available Online: www.ajeee.co.in/index.php/AJEEE

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RELATIVE ANALYSIS OF FAIR QUEUING DEFICIT ROUND ROBIN SCHEDULING SCHEME THROUGH PROBABILISTIC DATA MODELING

Dr. Manish Vyas

Associate Professor, Acropolis Institute of Management Studies and Research, Indore [email protected]

Abstract - Accomplishment of processor usage in sensible manner is turn out to be one of the essential objectives in designing of network scheduler algorithms for the period of packet scheduling in transmission. In this paper, to provide efficient and appropriate fairness packet scheduling and circulation of reasonable bandwidth during data flow, an attempt is made by considering Dynamic Deficit Round Robin Packet Scheduling Schemes along with Fair Queuing. For analysis and simulation study Markov Chain approach is considered.

Keyword: Packet Scheduling, Fair Queuing, Data flow, Generalized Processor Sharing, Markov Chain Model

I. INTRODUCTION

To keep up quality of service in consistent manner, network scheduling has need of appropriate traffic handling during data flow. One of key component to uphold this is network scheduling algorithms, which select packets in such a way that processor utilization can be done in fair manner. By means of suitable network scheduler algorithm, data flow, communication bandwidth and packet flow etc. can streamline. During designing of network scheduler algorithms, key emphasis stands on enhanced processor utilization in fair manner. It makes an effort for minimization of packet delay, packet loss and uncontrolled transmission rate. There are numerous networks scheduling algorithms proposed to approximate generalized processor sharing to ensure that all connections share the link in a fair manner. Usually, a good scheduling algorithm have reasonable distribution of bandwidth which can balance high as well as low priority packets and can serve the queue in a predictable way. In this paper,an attempt is made for providing an efficient fair queuing with fragmentation scheduling for packet switched networks.Some extensive schemes from deficit round robin scheduling are derived to approximate generalized processor sharing. Their analysis and comparative study is performed under markov chain model.

2 LITERATURE REVIEW

An algorithm for efficient fair queuing using deficit round robin was presented for

queues in round robin manner. A quantum of service allocated to each queue and during transmission if a queue was not capable to send a packet in previous round because of its large packet size then leftovers from previous quantum is added in next quantum for subsequent round. Thus deficits are kept in record and shortchanged queues compensated in next round [7]. An analysis of deficit round robin scheduling for future aeronautical data link with performance study is suggested [1]. Modified deficit round robin scheduling is put forward for wireless networks for fair channel access to balance high priority and low priority uncompleted data flows. Proposed schemes are compared as per latency, bandwidth utilization and throughput for real time burst. [2] [12].A weighted fair queuing scheduling mechanism is projected based on fair distributed credit based scheduler for differentiated service networks [9].An extensive Deficit Round Robin scheduling scheme is put forward along withfair queuing as an isolation mechanism to approximate generalized processor sharing [3]. Dynamic roundrobin packet scheduling algorithms for multi-processing environments is designed, implementation, analyzed and simulated [4] [5].Performance analysis of modified deficit round robin schedulers are evaluated through routers on the basis of analytical and simulation study [6] [8]. Some extensive Deficit Round Robin scheduling scheme is derived to attain improved processor utilization with fair queuing and generalized processor sharing as isolation mechanism [11]. A

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router mechanism provided for Fair Queuing along with fair bandwidth allocation to all processes [13]. One scheduling algorithm is proposed for packet-switched networks with analyzed study [10].

3 SCHEME FORMATION OF WEIGHTED FAIR QUEUING DEFICIT ROUND ROBIN SCHEDULING

a) Subsequent Picking at Random Scheduling

Consider five scheduling queues as Q1, Q2, Q3, Q4 and Q5.Each queue is having certain number of packets in terms of processes for transmission. A fixed time quantum is decided for processing of queues.New packet can arrive in any of queues hence initial probabilities of packet transmission from queues will be pr1, pr2, pr3, pr4 and pr5 respectively such that Pr1 + Pr2 + Pr3 + Pr4 + Pr5 = 1.

This scheme is framed in such a manner that scheduler can pick any of queues initially and after carrying out assigned time quantum, it switches to any of next queue at random for packet transmission. For example if Q1 is picked initially then at next time quantum scheduler can pick any of Q2, Q3, Q4 or Q5. Similarly after Q3, any of Q4 or Q5 can be picked.

Scheduler continues likewise till all packets from each queue get transmitted.

If any queue is concluded, then it is send out of ready queue otherwise it leftovers till next allotted time quantum.

Unit step transition probability matrix for scheme will be

Now to obtain state probabilities that scheduler will be on process ‘Pi’ after ‘n^th’ time quantum so that Markov chain

model will be applied with an indicator function Lij(for i, j=1,2,3,4,5) as,

Lij = 0 when (i=1, j=2, 3, 4, 5), (i=2, j=3, 4, 5),(i=3, j=4, 5), (i=4, j=5), (i=5, j=1) Lij = 1 other wise

b) Afterward Alternate Picking Scheduling

In this scheme, packets for transmission can be chosen from alternate queues after completion of assigned time quantum. By keeping identical initial probability for all queues, scheduler can move in linear direction and can pick packets from any of two queues on alternate basis. For example if we consider five scheduling queues as Q1, Q2, Q3, Q4 and Q5 then in beginning if scheduler pick packet from Q1 then after completion of first time quantum, it can shift towards queue Q3 or Q5 for forwarding of packets from there.

Similarly after Q3, scheduler can move on the way to Q5 or Q2.

As scheduler can pick packet from any of queue in the beginning, hence initial probability for all queues will be same as previous scheme as pr1, pr2, pr3, pr4 and pr5.

Transition probability matrix unit wise for above scheme will be

Now to obtain state probabilities, Markov chain model will be applied with an indicator function Lij (for i, j=1, 2, 3, 4, 5) as Lij = 0 when (i=1, j=1, 2, 4), (i=2, j=2, 3, 5), (i=3, j=1, 3, 4), (i=4, j=2, 4, 5), (i=5, j=1, 3, 5)

Lij = 1 otherwise

Generalized expressions of state probabilities for n^th time quantum can be obtained as,

X⁽ⁿ⁾

X^{(n – 1)}

54 0 S 52 0

S 5 0

Q

0 43 0

S 41 0

4 S Q

S35 0 32 0

S 3 0

Q

24 0 S 0 21 0

2 S Q

S15 13 0

S 0 1 0

Q

Q5 Q4 Q3 Q2 Q1

X ^{( n)}

X^{(n – 1)}

0 0 0 0 S Q

S 0 0 0 0 Q

S S 0 0 0 Q

S S S 0 0 Q

S S S S 0 Q

Q Q Q Q Q

51 5

45 4

35 34 3

25 24 23 2

15 14 13 12 1

5 4 3 2 1

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4 SIMULATION STUDY

In this paper, Markov chain model is considered as a basis of simulation study.

For obtaining transition probabilities, probabilistic linear ordered data model a + d.i is taken where‘a’is origin and ‘d’is scale. ‘i’stands for processing queue whose values is according to row (i=1,2,…). Matrix will be as,

To make sure fairness throughout the network scheduling, different weightage is given in terms of priority so that generic processor sharing concepts can be applied. For that a fairness index

‘S’ is used. Itprovides equity to last value so that probabilities can be spread likewise among all processing queues. It is calculated by dividing last value to (n – 1), where ‘n’ is total number of processes.

To obtain state probabilities, markov chain model is applied on obtained transition probabilities.

Overall graphical pattern of subsequent picking at random scheduling scheme is

While that of graphical pattern of afterward alternate picking scheduling scheme is

5 CONCLUDING REMARK

In this paper, common context of fair queuing with generalized processor scheduling for network scheduler algorithms is deliberated. After analysis it can be inferred that subsequent picking at random scheduling is considerably observed in despite range of probabilities where probabilities of each processing queue are dispersed from other. Here queues Q1 and Q2 becomes steady after some time quantum with some gain from initial level. While that of Q3, Q4 and Q5

turn into balanced with some cutback as they were at the beginning.

Comprehensive processing pattern of this scheme appears to be deviating.

Meantime afterward alternate picking scheduling made attemptsto converge all processing queues into a similar range of execution probability. Inclusive behaviour of this scheme seems to be queue positioned where Q1 remains with almost unchanged probability while Q2 and Q5

become steady with slight increment and that of Q3 and Q4 with slight decrement.

Although each queue follows a steady pattern but all queues are executed in slight variant manner.

6 FUTURE ENHANCEMENT

If afterward alternate picking scheduling scheme is implemented with a revision such that execution probabilities of processing queues can be concluded under a matching range of probabilities then it can be supportive for fairness in network scheduling to achieve objective of generalized processor scheduling more specifically.

REFERENCES

1. Ayaz, S., Hoffmann, F., Germany, R.and Dresslerz, F. (2011): Analysis of Deficit Round Robin Scheduling for Future 22d.i)

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6d.i) + (4a - 1 3d.i + a 2d.i + a d.i + a a Q

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Aeronautical Data Link, IEEE 22nd International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC)

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Krishnamurthy, A. (2018): Approximating Fair Queueing on Reconfigurable Switches, In Proceedings of the ACM SIGCOMM Conference

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