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University of Bradford Ethesis Performance Modelling and Analysis of Weighted Fair Queueing for Scheduling in Communication Networks. An investigation into the Development of New Scheduling Algorithms for Weighted Fair Queueing System with Finite Buffer. Item Type Thesis Authors Alsawaai, Amina S.M. Rights <a rel="license" href="http://creativecommons.org/licenses/ by-nc-nd/3.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by- nc-nd/3.0/88x31.png" /></a><br />The University of Bradford theses are licenced under a <a rel="license" href="http:// creativecommons.org/licenses/by-nc-nd/3.0/">Creative Commons Licence</a>. Download date 26/09/2021 15:01:09 Link to Item http://hdl.handle.net/10454/4877 University of Bradford eThesis This thesis is hosted in Bradford Scholars – The University of Bradford Open Access repository. Visit the repository for full metadata or to contact the repository team © University of Bradford. This work is licenced for reuse under a Creative Commons Licence. Performance Modelling and Analysis of Weighted Fair Queueing for Scheduling in Communication Networks An investigation into the Development of New Scheduling Algorithms for Weighted Fair Queueing System with Finite Buffer Amina Said Mohammed Alsawaai Submitted for the Degree of Doctor of Philosophy Department of Computing School of Computing, Informatics and Media University of Bradford 2010 Abstract Analytical modelling and characterization of Weighted Fair Queueing (WFQ) have re- cently received considerable attention by several researches since WFQ offers the min- imum delay and optimal fairness guarantee. However, all previous work on WFQ has focused on developing approximations of the scheduler with an infinite buffer because of supposed scalability problems in the WFQ computation. The main aims of this thesis are to study WFQ system, by providing an analytical WFQ model which is a theoretical construct based on a form of processor sharing for finite capacity. Furthermore, the solutions for classes with Poisson arrivals and exponential service are derived and verified against global balance solution. This thesis shows that the analytical models proposed can give very good results un- der particular conditions which are very close to WFQ algorithms, where accuracy of the models is verified by simulations of WFQ model. Simulations were performed with QNAP-2 simulator. In addition, the thesis presents several performance studies signify- ing the power of the proposed analytical model in providing an accurate delay bounds to a large number of classes. These results are not able to cover all unsolved issues in the WFQ system. They represent a starting point for the research activities that the Author will conduct in the future. The author believes that the most promising research activities exist in the scheduler method to provide statistical guarantees to multi-class services. The author is convinced that alternative software, for example, on the three class model buffer case, is able to satisfy the large number of buffer because of the software limitation in this thesis. While they can be a good topic for long-term research, the short-medium term will show an increasing interest in the modification of the WFQ models to provide differentiated services. Dedicated to my parents, my husband and my lovely son ... keep inspiring me! 1 Acknowledgements My deep thanks, from beginning to end, goes to God, who created me, helps me and has given me the ability to reach this stage. I would especially like to express my sincere gratitude and appreciation to my project supervisors Prof. Irfan Awan and Dr. Rod Fretwell for their helpful guidance, advice and valuable comments. Without their help, I would not have been able to complete my project. I would also like to extend my deep gratitude to the Computing department who provided me the needed knowledge to undertake this study. I would like also to thank the members of the Computing Department: Miss Rona Wilson and Mrs. Bev Yates. I give loving thanks to my husband, Hussain Ali, my lovely son, Ali, and my mother. It would not have been possible to complete my PhD research without their encouragement and support throughout my personal life and career. My gratitude also goes to all my friends Dr. Iman Alansari, Rasha Osman, Ibtihal Nafea, Rasha Fares, Hamda Al.Shihi and Ruqayya Abdulrahman and colleagues who supported me in my personal life and career. I am greatly indebted to the Ministry of Higher Edu- cation for providing me the opportunity and encouragement to obtain a higher degree in my field. Last, I wish to extend my heartfelt to my father and my family, who encouraged and continued supporting me until the end. i Publications 1. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, "Validation of Analytical Model of WFQ System ", proceedings of 26rd Annual UK Performance Engineering Work- shop (UKPEW2010). July 08-09, Warwick University, UK, pp. 1-8, 2010. 2. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, "Performance of weighted fair queu- ing system with multi-class jobs", proceedings of 24th IEEE International Confer- ence on Advanced Information Networking and Applications, pp. 50-57, 2010. 3. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, "Performance Evaluation of Weighted Fair Queuing System Using Matrix Geometric Method", proceedings of Interna- tional Conferences on Networking (IFIP2009) Lecture Notes in Computer Science, vol. 5550/2009, pp.66-78, 2009. 4. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, "Analysis of the weighted fair queu- ing system with two classes of customers with finite buffer", proceedings of 2009 International Conference on Advanced Information Networking and Applications Workshops, pp. 218-223, 2009. 5. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, Stationary queue length distribution for M/M/1/K queue with preemptive priorities . proceedings of 23rd Annual UK Performance Engineering Workshop (UKPEW2007). July 09-10, Edge Hill Uni- versity, UK, pp. 1-5, 2007. 6. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, Stationary queue length distribution for M/M/1/K queue with non-preemptive priorities. proceedings of 8th Annual Postgraduate Symposium on the Convergence of Telecommunication, Networking and Broadcasting (PG NET 2007). June 28 -29, School of Computing and Mathe- matical Sciences, John Morse University, Liverpool, UK, pp. 15-20, 2007 . ii 7. Amina Al-Sawaai, Irfan Awan, Rod Fretwell, "Stationary queue length distribution for M/M/1/K queue with non-preemptive and preemptive priorities", proceedings of 8th Informatics Workshop for Research Student, 28 June, School of Informatics, University of Bradford, UK, pp. 25-32, 2007. iii List of Symbols K Number of classes λi Arrival rate of class-i µi Service rate of class-i 1 Mean service time of class-i µi N Number of jobs in the system ni Number of jobs in the class-i wi Weight of class-i ~π0 : : : ~πN Steady state probabilities Li Mean queue length of class-i Si Mean response time of class-i λeffectivei The rate of jobs not dropped of class-i Ti Throughput of class-i QN j=2Rj Product rate matrices of N jobs in K class iv List of Abbreviations FIFO First In First Out PS Processor Sharing RR Round Robin WRR Weighted Round Robin GPS Generalized Processor Sharing QoS Quality of Service QBD Quasi Birth Death FQ Fair Queueing SFF Smallest Finish-time First SSF Smallest Start-time First WFQ Weighted Fair Queueing CBWFQ Class Based Weighted Fair Queueing SCFQ Self-Clocking Fair Queueing SFQ Start-time Fair Queueing VC Virtual Clock WF2Q Worst-case Fair Queueing v Contents List of Figuresx List of Tables1 1 Introduction2 1.1 Introduction . .2 1.2 Motivation . .3 1.3 Aims and Objectives . .4 1.4 Research Methodology . .5 1.5 Thesis Organization . .6 2 Literature Review7 2.1 Introduction . .7 2.2 Review of Scheduling Disciplines for Fair Queueing . .8 CONTENTS 2.2.1 Processor-Sharing (PS) . .8 2.2.2 Generalized Processor Sharing (GPS) . .9 2.2.3 Application of GPS in a Packet System . 10 2.2.4 Approximating GPS . 11 2.2.4.1 Weighted Round-Robin (WRR) . 11 2.2.4.2 Weighted Fair Queueing (WFQ) . 13 2.2.4.3 Enhancements to WFQ . 15 2.3 Related Research Work . 17 2.4 Summary . 21 3 Mathematical Model 22 3.1 Introduction . 22 3.2 Simulation Model . 23 3.3 K-Class Queueing Mathematical Model . 23 3.4 Analysis . 24 3.4.1 State Equilibrium Equations . 26 3.5 The Analytical Solution . 27 3.5.1 Computation of the Rate Matrices . 28 3.5.2 Stationary Probabilities . 30 vii CONTENTS 3.6 Application of the Solution Method to Queues with More Complex Ar- rival and Service Process . 33 3.7 Derivations of Performance Metrics . 34 3.7.1 Mean Queue Length . 35 3.7.2 Mean Response Time . 36 3.7.3 Throughput . 37 3.7.4 Job Loss . 38 3.7.5 Jitter . 38 3.8 Summary . 39 4 Numerical Results 40 4.1 Introduction . 40 4.2 Two-class Model . 41 4.2.1 Case 1 ................................ 45 4.2.2 Case 2 ................................ 51 4.2.3 Case 3 ................................ 56 4.2.4 Case 4 ................................ 60 4.2.5 Case 5 ................................ 64 4.3 Three-class Model . 66 4.3.1 Case 1 ................................ 69 viii CONTENTS 4.3.2 Case 2 ................................ 71 4.3.3 Case 3 ................................ 73 4.4 Summary . 74 5 Conclusions and Future Work 75 5.1 Summary . 75 5.2 Future Work . 77 References 79 Appendices 85 Appendix A Two Class Model 86 A.1 Analytical Model Description . 86 A.2 Steady State Probability Calculation of Two-Class Model . 89 Appendix B Three Class Model 91 B.1 Analytical Model Description . 91 B.2 Steady State Probability Calculation for Three-Class Model . 94 ix List of Figures 2.1 Round Robin (Fair Queueing) .
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