Skip to main content
SpringerLink
Log in

Queuing Theory Applications to Communication Systems: Control of Traffic Flows and Load Balancing

  • Reference work entry
Springer Handbook of Engineering Statistics

Part of the book series: Springer Handbooks ((SHB))

Abstract

With the tremendous increase in traffic on modern communication systems, such as the World Wide Web, it has made it imperative that users of these systems have some understanding not only of how they are fabricated but also how packets, which traverse the links, are scheduled to their hosts in an efficient and reliable manner. In this chapter, we investigate the role that modern queueing theory plays in achieving this aim. We also provide up-to-date and in-depth knowledge of how queueing techniques have been applied to areas such as prioritizing traffic flows, load balancing and congestion control on the modern internet system.

The Introduction gives a synopsis of the key topics of application covered in this chapter, i.e. congestion control using finite buffer queueing models, load balancing and how reliable transmission is achieved using various transmission control protocols.

In Sect. 52.1, we provide a brief review of the key concepts of queueing theory, including a discussion of the performance metrics, scheduling algorithms and traffic variables underlying simple queues. A discussion of the continuous-time Markov chain is also presented, linking it with the lack of memory property of the exponential random variable and with simple Markovian queues.

A class of queues, known as multiple-priority dual queues (MPDQ), is introduced and analyzed in Sect. 52.2. This type of queues consists of a dual queue and incorporates differentiated classes of customers in order to improve their quality of service. Firstly, MPDQs are simulated under different scenarios and their performance compared using a variety of performance metrics. Secondly, a full analysis of MPDQs is then given using continuous-time Markov chain. Finally, we show how the expected waiting times of different classes of customers are derived for a MPDQ.

Section 52.3 describes current approaches to assigning tasks to a distributed system. It highlights the limitations of many task-assignment policies, especially when task sizes

have a heavy-tailed distribution. For these so called heavy-tailed workloads, several size-based load distribution policies are shown to perform much better than classical policies. Amongst these, the policies based on prioritizing traffic flows are shown to perform best of all.

Section 52.4 gives a detailed account of how the balance between maximizing throughput and congestion control is achieved in modern communication networks. This is mainly accomplished through the use of transmission control protocols and selective dropping of packets. It will be demonstrated that queueing theory is extensively applied in this area to model the phenomena of reliable transmission and congestion control.

The final section concludes with a brief discussion of further work in this area, an area which is growing at a rapid rate both in complexity and level of sophistication.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Institutional subscriptions

Abbreviations

ACK:

acknowledgment

AQM:

active queue management

CBFQ:

credit-based fair queueing

CBQ:

class-based queues

CDF:

cumulative distribution function

CS-CQ:

cycle stealing with central queue

CS-ID:

cycle stealing with immediate dispatch

DQ:

dual-queue

DQLT:

dual queue length threshold

DRR:

deficit round-robin

EWMA:

exponentially weighted moving average

FCFS:

first-come first-served

FTP:

file transfer protocol

HCF:

highest class first

HTTP:

hypertext transfer protocol

IETF:

internet engineering task force

LCF:

lowest class first

LIFO:

last-in first-out

LLF:

least loaded first

MPDQ:

multiple-priority dual queues

QoS:

quality of service

RED:

random early-detection queue

RIO:

RED in/out

SCFQ:

as self-clocked fair queueing

SIRO:

service in random order

TCP:

transmission control protocol

WRED:

weighted RED

WRR:

weighted round-robin

References

  1. A. K. Erlang: Solution of some probability problems of significance for automatic telephone exchanges, Elektroleknikeren 13, 5–13 (1917)

    Google Scholar 

  2. C. Palm: Intensitatsschwankungen im Fernsprechverkehr, Ericsson Technics 44, 1–89 (1943)

    MathSciNet  Google Scholar 

  3. M. A. Labrador, S. Banerjee: Enhancing application throughput by selective packet dropping, Proceedings of IEEE International Conference on Communications (ICC), Vancouver (1999) 1217-1222

    Google Scholar 

  4. W. Feng, D. D. Kandlur, D. Saha, K. G. Shin: Adaptive packet marking for maintaining end-to-end throughput in a differentiated services internet, IEEE/ACM Trans. Network. 7(5), 685–697 (1999)

    Article  Google Scholar 

  5. S. G. Golestani: A self-clocked fair queueing scheme for broadband applications, Proceedings of the IEEE Infocom, Toronto (1994) 636-646

    Google Scholar 

  6. K. T. Chan, B. Bensaou, D. H. K. Tsang: Credit-based fair queueing (CBFQ), IEEE Electron. Lett. 33(7), 584–585 (1997)

    Article  Google Scholar 

  7. J. Jang, S. Shim, B. Shin: Analysis of DQLT scheduling for an ATM mMultiplexer, IEEE Commun. Lett. 1(4), 175–177 (1997)

    Article  Google Scholar 

  8. J. Wang, L. Yonatan: Managing Performance using Weighted Round Robin, IEEE Symposium on Computers and Communications 1, 785–792 (2000)

    Google Scholar 

  9. D. Hayes, M. Rumsewicz, L. Andrew: Quality of service driven packet scheduling disciplines for real-time applications: looking beyond fairness, IEEE Infocom 1999 1, 405–412 (1999)

    Google Scholar 

  10. M. Shreedhar, G. Varghese: Efficient fair queuing using Deficit Round Robin, IEEE/ACM Trans. Network. 4(3), 375–385 (1996)

    Article  Google Scholar 

  11. R. Ranasinghe, L. Andrew, D. Hayes, D. Everitt: Scheduling disciplines for multimedia WLANs: Embedded round robin and wireless dual queue, Proc. IEEE Int. Conf. Commun. (ICC), ed. by K.-P. Estola, Helsinki (2001) 1243-1248

    Google Scholar 

  12. A. Bedford, P. Zeephongsekul: On a dual queueing system with preemptive priority service discipline, Eur. J. Oper. Res. 161, 224–239 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  13. T. Saaty: Elements of Queueing Theory with Applications. (Dover, New York 1961)

    Google Scholar 

  14. S. Asmussen: Applied Probability and Queues (Springer, Berlin Heidelberg New York 2003)

    MATH  Google Scholar 

  15. A. Allen: Probability, Statistics and Queueing Theory: With Computer Science Applications (Academic, New York 1990)

    MATH  Google Scholar 

  16. D. Gross, C. Harris: Fundamentals of Queueing Theory (Wiley, New York 1998)

    MATH  Google Scholar 

  17. N. Jaiswal: Priority Queues (Academic, New York 1968)

    MATH  Google Scholar 

  18. F. Kelly: Reversibility and Stochastic Networks (Wiley, New York 1979)

    MATH  Google Scholar 

  19. L. Kleinrock: Queueing Systems 1: Theory (Wiley, New York 1975)

    Google Scholar 

  20. L. Kleinrock: Queueing Systems 2: Computer Applications (Wiley, New York 1975)

    Google Scholar 

  21. M. L. Chaudhry, J. G. C. Templeton: A First Course in Bulk Queues (Wiley, Canada 1983)

    MATH  Google Scholar 

  22. D. Kendall: Stochastic processes occurring in the theory of queues and their analysis by the method of the embedded Markov chain, Ann. Math. Stat. 24, 338–354 (1953)

    Article  MathSciNet  MATH  Google Scholar 

  23. J. D. C. Little: A simple proof of L = λW, Oper. Res. 9, 383–387 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  24. K. L. Chung: Markov Chains with Stationary Transition Probabilities (Springer, Berlin Heidelberg New York 1960)

    MATH  Google Scholar 

  25. W. D. Kelton, R. P. Sadowski, D. A. Sadowski: Simulation with Arena, 2nd edn. (McGraw–Hill, New York 2002) p. 2

    Google Scholar 

  26. P. Zeephongsekul, A. Bedford: Waiting time analysis of the multiple dual queue with a preemptive priority service discipline, Eur. J. Oper. Res. (2006) (In press)

    Google Scholar 

  27. P. Zeephongsekul, A. Bedford: Analysis of the non-preemptive Multiple Priority Dual Queue, Department of Mathematics and Statistics Research Report 2 (2004)

    Google Scholar 

  28. M. Neuts: Matrix-Geometric Solutions in Stochastic Models, An Algorithmic Approach (John Hopkins Univ. Press, Baltimore 1981)

    MATH  Google Scholar 

  29. D. Wagner, U. Krieger: Analysis of a finite buffer with non-preemptive priority scheduling, Commun Stat.-Stoch. Models 15, 345–365 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  30. R. Wolff: Poisson arrivals see time averages, Oper. Res. 30, 223–231 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  31. M. Crovella, M. Taqqu, A. Bestavros: Heavy-Tailed Probability Distributions in the World Wide Web (Chapman Hall, New York 1998)

    Google Scholar 

  32. M. Crovella, A. Bestavros: Self-similarity in World Wide Web traffic: evidence and possible causes, IEEE/ACM Trans. Network. 5(6), 835–846 (1997)

    Article  Google Scholar 

  33. G. Irlam(1993): Available at http://www.base.com/gordoni/ufs93.html

    Google Scholar 

  34. M. Harchol-Balter, A. Downey: Exploiting process lifetime distributions for dynamic load balancing, ACM Trans. Comp. Sys. 15(3), 253–285 (1997)

    Article  Google Scholar 

  35. M. Arlitt, T. Jin: Workload characterization of the 1998 world cup web site, IEEE Network 14, 30–37 (2000)

    Article  Google Scholar 

  36. A. Iyengar, M. Squillante, L. Zhang: Analysis and characterization of large scale web server access patterns and performance, World Wide Web 2, 85–100 (1999)

    Article  Google Scholar 

  37. M. Harchol-Balter: Task assignment with unknown duration, J. ACM 49(2), 260–288 (2002)

    Article  MathSciNet  Google Scholar 

  38. M. Harchol-Balter, M. Crovella, C. Murta: On choosing a task assignment policy for a distributed server system, J. Parallel Distrib. Comput. 59(2), 204–228 (1999)

    Article  Google Scholar 

  39. A. Silberschatz, P. Galvin: Operating System Concepts, 5th edn. (Addison–Wesley, Reading 1998)

    MATH  Google Scholar 

  40. M. Crovella, M. Harchol-Balter, C. Murta: Task assignment in a distributed system: improving performance by unbalancing load, Proceedings of ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems, Madison, USA 1998, ed. by S. Leutenegger (ACM Press, New York 1998) 268–269

    Google Scholar 

  41. M. Harchol-Balter, C. Li, T. Osogami, A. Scheller-Wolf, M. Squillante: Task assignment with cycle stealing under central queue, International Conference on Distributed Computing Systems (ICDCSʼ03) 23, 628–637 (2003)

    Google Scholar 

  42. R. W. Weber: On the optimal assignment of customers to parallel servers, J. Appl. Probab. 15, 826–834 (1978)

    Article  MathSciNet  Google Scholar 

  43. R. D. Nelson, T. K. Philips: An approximation for the mean response time for shortest queue routing with general interarrival and service times, Perform. Eval. Rev. 7(1), 181–189 (1978)

    Google Scholar 

  44. S. Sozaki, R. Ross: Approximations in finite capacity multiserver queues with Poisson arrivals, J. Appl. Probab. 13, 826–834 (1978)

    Google Scholar 

  45. B. Schroder, M. Harchol-Balter: Evaluation of task assignmentpolicies for supercomputing servers. The case for load unbalancing and fairness, 9th IEEE Symposium on High Performance Distributed Computing , 211–220 (2000)

    Google Scholar 

  46. J. Broberg, Z. Tari, P. Zeephongsekul: Task assignment based on prioritising traffic flows, Lect. Notes Comp. Sci. 3544, 415–430 (2005)

    Article  Google Scholar 

  47. N. Cardwell, S. Savage, T. Anderson: Modelling TCP latency, Proc. IEEE Infocom, Isreal 2000, ed. by M. Sidi (IEEE, USA 2000) 1742–1751

    Google Scholar 

  48. T. Lakshman, U. Madhow: The performance of TCP/IP for networks with high bandwidth-delay products and random loss, IEEE/ACM Trans. Network. 5(3), 336–350 (1997)

    Article  Google Scholar 

  49. A. Kumar: A comparative performance analysis of versions of TCP in a local network with a lossy link, IEEE/ACM Trans. Network. 6(4), 485–498 (1998)

    Article  Google Scholar 

  50. J. Padhye, D. Firouiu, D. Towsley, J. Kurose: Modeling TCP reno performance: a simple model and its empirical validation, IEEE/ACM Trans. Network. 8(2), 133–145 (2000)

    Article  Google Scholar 

  51. C. Casetti, M. Meo: A new approach to model the stationary behaviour of TCP connections, IEEE Infocom 1999 1, 367–375 (2000)

    Google Scholar 

  52. P. Dimopoulos, P. Zeephongsekul, Z. Tari: Modeling the burstiness of TCP, Proceedings of the IEEE International Symposium on Modelling, Analysis and Simulation of Computer and Telecomunication Systems, Netherlands 2004, ed. by D. DeGroot, P. Harrison (IEEE, USA 2004) 175–183

    Google Scholar 

  53. S. Floyd, V. Jacobson: Random early detection gateways for congestion avoidance, IEEE/ACM Trans. Network. 1(4), 397–413 (1993)

    Article  Google Scholar 

  54. S. Floyd, V. Jacobson: Link-sharing and resource management models for packet networks, IEEE/ACM Trans. Network. 3(4), 365–386 (1995)

    Article  Google Scholar 

  55. Weighted random early detection, Tech. Rep. (CISCO Corp., USA 2003)

    Google Scholar 

  56. D. Clark, W. Fang: Explicit allocation of best-effort packet delivery service, IEEE/ACM Trans. Network. 6(4), 362–373 (1998)

    Article  Google Scholar 

  57. P. Dimopoulos, P. Zeephongsekul, Z. Tari: Reducing the user perceived delay of interactive TCP connections using a dynamic priority approach, Proceedings of the 14th International Conference on Computer Communications and Networks (ICCCN), USA 2005, ed. by E. K. Park (IEEE, USA 2005) 421–427

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology University, GPO Box 2467V, 3000, Melbourne, Victoria, Australia

    Panlop Zeephongsekul

  2. School of Mathematical and Geospatial Sciences, Royal Melbourne Institute of Technology University, Bundoora East Campus, Plenty Rd, 3083, Bundoora, Victoria, Australia

    Anthony Bedford

  3. School of Computer Science & Information Technology, Royal Melbourne Institute of Technology University, GPO Box 2476V, 3001, Melbourne, Victoria, Australia

    James Broberg

  4. Computer Science and IT, Royal Melbourne Institute of Technology University, 376-392 Swanston Street, 3001, Melbourne, Australia

    Peter Dimopoulos

  5. School of Computer Science and Information Technology, Royal Melbourne Institute of Technology University, GPO Box 2476V, 3001, Melbourne, Victoria, Australia

    Zahir Tari

Authors
  1. Panlop Zeephongsekul
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Anthony Bedford
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. James Broberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peter Dimopoulos
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Zahir Tari
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Panlop Zeephongsekul , Anthony Bedford , Peter Dimopoulos or Zahir Tari .

Editor information

Editors and Affiliations

  1. Department of Industrial and Systems Engineering, Rutgers the State University of New Jersey, 96 Frelinghuysen Road, 08854, Piscataway, NJ, USA

    Hoang Pham Prof.

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag

About this entry

Cite this entry

Zeephongsekul, P., Bedford, A., Broberg, J., Dimopoulos, P., Tari, Z. (2006). Queuing Theory Applications to Communication Systems: Control of Traffic Flows and Load Balancing. In: Pham, H. (eds) Springer Handbook of Engineering Statistics. Springer Handbooks. Springer, London. https://doi.org/10.1007/978-1-84628-288-1_52

Download citation

  • DOI: https://doi.org/10.1007/978-1-84628-288-1_52

  • Publisher Name: Springer, London

  • Print ISBN: 978-1-85233-806-0

  • Online ISBN: 978-1-84628-288-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation