Skip to main content
SpringerLink
Log in

Stability of multiple access communication networks

  • Queueing Models For Performance Analysis Of Computer And Communication Systems
  • Published:
Sadhana Aims and scope Submit manuscript

Abstract

The problem of stability of different multiple access schemes in computer networks is discussed. The results for the main multiple access schemes — slottedaloha, controlledaloha, csma, csma/cd, polling systems and collision resolution algorithms are surveyed. The techniques used for the stability of these systems have been emphasized.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Abramson N 1970 The ALOHA system — Another alternative for computer communications. InProc. Fall Joint Computer Conf. (Montvale, NJ: AFIPS Press) vol. 37, pp. 281–285

    Google Scholar 

  • Aldous D J 1987 Ultimate instability of exponential back-off protocol for acknowledgement based transmission control of random access communication channels.IEEE Trans. Inf. Theory IT-33: 219–223

    Article  MathSciNet  Google Scholar 

  • Bambos N, Walrand J 1989 On queues with periodic inputs.J. Appl. Probab. 26: 381–389

    Article  MATH  MathSciNet  Google Scholar 

  • Bertsekas D, Gallagher R 1987Data networks (Englewood Cliffs, NJ: Prentice-Hall)

    Google Scholar 

  • Beuerman S L, Coyle E J 1988 The delay characteristics of CSMA/CD networks.IEEE Trans. Commun. 36: 553–563

    Article  Google Scholar 

  • Bux W 1989 Token ring local area networks and their performance.Proc. IEEE 77: 238–256

    Article  Google Scholar 

  • Capetanakis J I 1979 Tree algorithm for packet broadcast channels.IEEE Trans. Inf. Theory IT-25: 505–515

    Article  MathSciNet  Google Scholar 

  • Cidon I, Sidi M 1986 Conflict multiplicity estimation and batch resolution algorithms.INFOCOM’86: (New York: IEEE Press) pp. 197–203

    Google Scholar 

  • Clare L P 1986 Delay analysis of stable slotted ALOHA systems.INFOCOM’86 (New York: IEEE Press) pp. 10–19

    Google Scholar 

  • Cottrell M, Claude Fort J, Malgouyres G 1983 Large deviations and rare events in the study of stochastic algorithms.IEEE Trans. Autom. Control AC-28: 907–920

    Article  Google Scholar 

  • Coyle E J, Liu B 1985 A matrix representation of CSMA/CD networks.IEEE Trans. Commun. COM-33: 53–64

    Article  MathSciNet  Google Scholar 

  • Cunningham G A, Medith J S 1988 Distributed retransmission controls for slotted nonpersistent and virtual time CSMA.IEEE Trans. Commun. 36: 685–691

    Article  Google Scholar 

  • de Moraes L F M 1990 Priority scheduling in multiple access communication. Instochastic analysis of computer & communication systems (ed.) H Takagi (Amsterdam: Elsevier Science Publishers)

    Google Scholar 

  • Eisenberg M 1972 Queues with periodic service and changeover time.Oper. Res. 20: 440–451

    MATH  MathSciNet  Google Scholar 

  • Gallagher R G 1978 Conflict resolution in random access broadcast networks. InProc. AFOSR Workshop on Commun. Theory Appl. pp. 74–76

  • Georgiopoulos M, Merakos L, Papatani-Kazakos P 1986 High performance asynchronous limited sensing algorithms for CSMA and CSMA/CD channels. InLocal area and multiple access networks (ed.) R L Pickholtz (Rockville, MD: Computer Science Press) pp. 185–214

    Google Scholar 

  • Ghez S, Verdu S, Schwartz S C 1989 Optimal decentralized control in the random access multipacket channelIEEE Trans. Autom. Control 34: 1153–1163

    Article  MATH  MathSciNet  Google Scholar 

  • Goodman J, Greenberg A G, Madras N, March P 1988 Stability of binary exponential backoff.J. Assoc. Comput. Mach. 35: 579–602

    MathSciNet  Google Scholar 

  • Hajek B 1982 Hitting time and occupation time bounds implied by drift analysis with applications.Adv. Appl. Probab. 14: 502–525

    Article  MATH  MathSciNet  Google Scholar 

  • Hajek B 1985 Stochastic approximation methods for decentralized control of multiaccess communications.IEEE Trans. Inf. Theory IT-31: 176–184

    Article  MathSciNet  Google Scholar 

  • Hashida O 1972 Analysis of multiqueue.Rev. Elec. Commun. Lab. 20: 189–199

    Google Scholar 

  • Hastad J, Leighton T, Rogoff B 1987 Analysis of backoff protocols for multiple access channels.Proc. 19th Annu. ACM Symp. on Theory of Comput. pp. 241–243

  • Ibe O C, Chang X 1989 Stability conditions for multiqueue systems with cyclic service.IEEE Trans. Autom. Control 33: 102–103

    Article  Google Scholar 

  • IEEE Trans. Inf. Theory 1985 vol. IT-31, Special issue on Random-Access Communications

  • Jacquet P, Szpankowski W 1989 Ultimate characteristics of interval searching algorithms for distributed systems. InPerformance of distributed and parallel systems (eds) T Hasegawa, H Takagi, Y Takahashi (Amsterdam: Elsevier Science Publishers)

    Google Scholar 

  • Khasminskii R Z 1989 Some optimal algorithms of random multiple access.Theory Probab. Appl. 34: 454–463

    Article  MathSciNet  Google Scholar 

  • Kleinrock L, Tobagi F A 1975 Packet switching in radio channels: part I — Carrier sense multiple access models and their throughput — delay characteristics.IEEE Trans. Commun. Com-23: 1400–1416

    Article  Google Scholar 

  • Konheim A G, Meister B 1974 Waiting lines and times in a system with polling.J. Assoc. Comput. Mach. 21: 470–490

    MATH  MathSciNet  Google Scholar 

  • Kuehn P J 1979 Multiqueue systems with nonexhaustic cyclic service.Bell Syst. Tech. J. 58: 671–698

    Google Scholar 

  • Lim J T, Meerkov S M 1987 Theory of Markovian access to collision channels.IEEE Trans. Commun. COM-35: 1278–1288

    Article  Google Scholar 

  • Loynes R 1962 The stability of a queue with non-independent interarrival and service times.Proc. Cambridge Philos. Soc. 58: 497–520

    MATH  MathSciNet  Google Scholar 

  • Massey J L 1981 Collision resolution algorithms and random access communications. InMultiuser communications systems (ed.) G Longo (CISM courses and lectures No. 265) (New York: Springer)

    Google Scholar 

  • Medith J S, Lea C-T A 1983 Stability and optimization of the CSMA and CSMA/CD channels.IEEE Trans. Commun. COM-31: 763–774

    Article  Google Scholar 

  • Mehravari N 1984 TDMA in a random access environment, an overview.IEEE Commun. Mag. 22(11): 54–59

    Article  Google Scholar 

  • Merakos L, Kazakos D 1985 On the retransmission control policies in multiple access communication networks.IEEE Trans. Autom. Control. AC-30: 109–117

    Article  MathSciNet  Google Scholar 

  • Mosely J, Humblet P A 1985 A class of efficient contention resolution algorithms for multiple access.IEEE Trans. Commun. COM-33: 145–151

    Google Scholar 

  • Nelson R 1984 The stochastic cusp, swallowtail and hyperbolic umbilic catastrophes an manifest in a simple communications model.Performance’84 (Amsterdam: Elsevier Science Publishers)

    Google Scholar 

  • Neuts M F 1981 Matrix geometric solutions in stochastic models (Baltimore: Johns Hopkins Univ. Press)

    MATH  Google Scholar 

  • Onozato Y, Noguchi S 1985 On the thrashing cusp in slotted ALOHA systems.IEEE Trans. Commun. COM-33: 1171–1182

    Article  Google Scholar 

  • Pakes A G 1969 Some conditions for ergodicity and recurrence of Markov chains.Oper. Res. 117: 1059–1061

    MathSciNet  Google Scholar 

  • Paterakis M, Georgiadis L, Papatani-Kazakos P 1987 On the relation between the finite and the infinite population models for a class of RAA’s.IEEE Trans. Commun. COM-35: 1239–1240

    Article  Google Scholar 

  • Prathima B V 1991Stability and performance analysis of same multiple access and mobile cellular communication networks, MS thesis, Department of Electrical Engineering, Indian Institute of Science, Bangalore

    Google Scholar 

  • Rivest R L 1987 Network protocol by Bayesian broadcast.IEEE Trans. Inf. Theory IT-33: 323–328

    Article  Google Scholar 

  • Rolski T 1981Stationary random processes associated with point processes (New York: Springer-Verlag)

    MATH  Google Scholar 

  • Rosenkrantz W A, Towsley D 1983 On the instability of the slotted ALOHA multiaccess algorithm.IEEE Trans. Autom. Control AC-28: 994–996

    Article  Google Scholar 

  • Rubin I 1979 Message delay in FDMA and TDMA communication channels.IEEE Trans. Commun. COM-27: 516–536

    Google Scholar 

  • Rubin I 1983 Synchronous and channel sense asynchronous dynamic group-random-access scheme for multiple access communications.IEEE Trans. Commun. COM-31: 1063–1076

    Google Scholar 

  • Saadawi T N, Ephremides A 1981 Analysis, stability and optimization of slotted ALOHA with a finite number of buffered users.IEEE Trans. Autom. Control. 26: 680–689

    Article  Google Scholar 

  • Sachs S R 1988 Alternative local area network access protocols.IEEE Commun. Mag. 26(3): 25–44

    Article  Google Scholar 

  • Servi L D 1985 Capacity estimation of cyclic queues.IEEE Trans. Commun. COM-33: 279–282

    Article  Google Scholar 

  • Sharma V 1987 Stability analysis of slotted ALOHA with time varying input, NASA Tech. Report

  • Sharma V 1988 Stability and continuity for slotted ALOHA with stationary non-independent input traffic.J. Appl. Probab. 25: 797–807

    Article  MATH  MathSciNet  Google Scholar 

  • Swartz G B 1980 Polling in a loop system.J. Assoc. Comput. Mach. 27: 42–59

    MATH  MathSciNet  Google Scholar 

  • Szpankowski W 1986 Stability, bounds and approximation in asymmetric buffered ALOHA-type systems.Proc. 25th Conf. Decision and Control (New York: IEEE Press) pp. 1722–1727

    Google Scholar 

  • Takagi H 1986Analysis of polling systems (Cambridge, MA: MIT Press)

    Google Scholar 

  • Takagi H 1990 Queueing analysis of polling models: An update. InStochastic analysis of computer and communication systems (ed.) H Takagi (Amsterdam: Elsevier Science Publishers)

    Google Scholar 

  • Thomopoulos S C A 1988 A simple and versatile decentralized control for slotted ALOHA, reservation ALOHA and local area networks.IEEE Trans. Commun. 36: 662–674

    Article  Google Scholar 

  • Thomopoulos S C A, Sunder R 1987 Delay analysis of the controlled ALOHA: exact analysis and bounds.IEEE INFOCOM’87 (New York: IEEE Press) pp. 26–33

    Google Scholar 

  • Tobagi F A 1982 Distributions of packet delay and interdeparture time in slotted ALOHA and carrier sense multiple access.J. Assoc. Comput. Mach. 29: 907–922

    MATH  Google Scholar 

  • Tobagi F A, Hunt V B 1987 Performance analysis of carrier sense multiple access with collision detection. InAdvances in local area networks (ed.) Karl Kummerle, J O Limb, F A Tobagi (New York: IEEE Press)

    Google Scholar 

  • Tobagi F, Kleinrock L 1977 Packet switching in radio networks, Part IV. Stability considerations and dynamic control in carrier sense multiple access.IEEE Trans. Commun. COM-25: 1103–1120

    Article  Google Scholar 

  • Tsitsklis J N 1987 Analysis of a multiaccess control scheme.IEEE Trans. Autom. Control AC-32: 1017–1029

    Article  Google Scholar 

  • Tsybakov B S 1985 Survey of USSR contributions to random multiple access communications.IEEE Trans. Inf. Theory IT-31: 143–165

    Article  MathSciNet  Google Scholar 

  • Tsybakov B S, Mikhailov V A 1978 Free synchronous access of packets to a broadcast channel with feedback.Probl. Peredachi Inf. 14(4): 32–59

    MATH  MathSciNet  Google Scholar 

  • Tsybakov B S, Mikhailov V A 1979 Ergodicity of ALOHA system.Probl. Peredachi Inf. 15: 75–87

    MathSciNet  Google Scholar 

  • Tsybakov B S, Mihailov V A 1980 Random multiple access of packets: part and try algorithm.Probl. Peredachi Inf. 16: 65–79

    MATH  Google Scholar 

  • Zhdanov V S, Saksonov E A 1979 Conditions of existence of steady state modes in cyclic queueing systems.Avtom. Telemekh. (Engl. Transl.) 40: 176–184

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Electrical Engineering, Indian Institute of Science, 560 012, Bangalore, India

    Vinod Sharma

Authors
  1. Vinod Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

An error in the first draft of this paper was pointed out by the reviewer.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sharma, V. Stability of multiple access communication networks. Sadhana 15, 365–380 (1990). https://doi.org/10.1007/BF02811332

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02811332

Keywords

Search

Navigation