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Queueing Systems

, Volume 34, Issue 1–4, pp 1–35 | Cite as

Performance analysis of a slotted-ALOHA protocol on a capture channel with fading

  • Jeetendra Sant
  • Vinod Sharma
Article

Abstract

We consider the slotted ALOHA protocol on a channel with a capture effect. There are M < ∞ users each with an infinite buffer. If in a slot, i packets are transmitted, then the probability of a successful reception of a packet is qi. This model contains the CDMA protocols as special cases. We obtain sufficient rate conditions, which are close to necessary for stability of the system, when the arrival streams are stationary ergodic. Under the same rate conditions, for general regenerative arrival streams, we obtain the rates of convergence to stationarity, finiteness of stationary moments and various functional limit theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.

multiple access CDMA rates of convergence stability functional limit theorems transient analysis Markov-modulated capture channel 

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References

  1. [1].
    A.A. Borovkov, Stochastic Processes in Queueing Theory (Springer, New York, 1976).Google Scholar
  2. [2].
    A.A. Borovkov and S.A. Utev, Estimates for distribution of sums stopped at random times, Theory Probab. Appl. 38 (1993) 214–225.Google Scholar
  3. [3].
    A.E. Brand and A.H. Aghvami, Performance of a joint CDMA/PRMA protocol, IEEE J. Selected Areas Commun. 14(9) (1996) 1698–1706.Google Scholar
  4. [4].
    A. Brandt, P. Franken and B. Lisek, Stationary Stochastic Models (Wiley, New York, 1990).Google Scholar
  5. [5].
    I. Cidon, A. Khamisy and M. Sidi, On packet loss process in high speed networks, in: Proc. of IEEE INFOCOM (1992) pp. 0242–0251.Google Scholar
  6. [6].
    Code Division Multiple Access Networks III, IEEE J. Selected Areas Commun. (special issue) 14(8) (October 1996).Google Scholar
  7. [7].
    Code Division Multiple Access Networks IV, IEEE J. Selected Areas Commun. (special issue) 14(9) (December 1996).Google Scholar
  8. [8].
    J.N. Daigle, Y. Lee and M.N. Magalhaes, Discrete time queues with phase dependent arrivals, IEEE Trans. Commun. 42(2) (1994) 606–614.Google Scholar
  9. [9].
    G. Fayolle et al., Topics in the Constructive Theory of Countable Markov Chains (Cambridge Univ. Press, Cambridge, 1995).Google Scholar
  10. [10].
    P. Franken, D. Konig, U. Amdt and V. Schmidt, Queues and Point Processes (Wiley, New York, 1982).Google Scholar
  11. [11].
    N.D. Gangadhar, Analysis of discrete-time queues with applications to ATM based B-ISDNs, Master thesis, Department of EE, Indian Institute of Science, Bangalore, India (1994).Google Scholar
  12. [12].
    S. Ghez, S. Verdu and S.C. Schwartz, Stability properties of slotted ALOHA with multipacket reception capability, IEEE Trans. Automat. Control 33 (July 1988) 640–649.Google Scholar
  13. [13].
    S. Ghez, S. Verdu and S.C. Schwartz, Optimal decentralized control in the random access multipacket channel, IEEE Trans. Automat. Control 34 (November 1989) 1153–1163.Google Scholar
  14. [14].
    K.S. Gilhousen, I.M. Jacobs, R. Padovani, A.J. Viterbi, L.A. Weaver, Jr., and C.E. Wheatly, On the capacity of a cellular CDMA system, IEEE Trans. Vehicular Technology 40(2) (1991) 303–312.Google Scholar
  15. [15].
    A. Gut, Stopped Random Walks (Springer, New York, 1988).Google Scholar
  16. [16].
    B. Hajek, A. Krishna and R.O. LaMaire, On the capture probability for a large number of stations, in: Proc. of IEEE Vehicular Technology Conf. (1995) pp. 21–24.Google Scholar
  17. [17].
    V. Kalashnikov, Topics on Regenerative Processes (CRC Press, 1994).Google Scholar
  18. [18].
    J. Keilson, Markov Chain Models – Rarity and Exponentiality (Springer, New York, 1979).Google Scholar
  19. [19].
    A. Kumar and J. Holtzman, Comparative performance analysis of versions of TCP in a local network with a mobile radio link, in: Conf. on Signal Processing, Communications and Networking, Bangalore, Indian Institute of Science, India (1997) pp. 89–98.Google Scholar
  20. [20].
    W.C.Y. Lee, Overview of cellular CDMA, IEEE Trans. Vehicular Technology 40(2) (1991) 291–302.Google Scholar
  21. [21].
    N. Likhanov and B. Tsybakov, Analysis of an ATM buffer with self-similar (fractal) input traffic, in: Proc. of IEEE INFOCOM (1995) pp. 985–992.Google Scholar
  22. [22].
    T.-K. Liu et al., A general performance for mobile slotted ALOHA networks with capture, in: Proc. of IEEE Internat. Conf. on Communications (1995) pp. 1582–1586.Google Scholar
  23. [23].
    R.M. Loynes, The stability of a queue with non-independent inter-arrival and service times, Proc. Cambridge Philos. Soc. 58 (1962) 497–520.Google Scholar
  24. [24].
    V.A. Malyshev and M.V. Menshikov, Networks and dynamical systems, Adv. in Appl. Probab. 25 (1993) 140–175.Google Scholar
  25. [25].
    R.L. Pickholtz et al., Spread spectrum for mobile communications, IEEE Trans. Vehicular Technology 40(2) (1991) 313–322.Google Scholar
  26. [26].
    J. Sant and V. Sharma, Comparison of CDMA versus TDMA for packet transmission schemes in circuit-mode, in: Proc. of IEEE GLOBECOM (1998) pp. 3414–3419.Google Scholar
  27. [27].
    V. Sharma, Stability and continuity of slotted ALOHA with stationary nonindependent input traffic, J. Appl. Probab. 25 (1988) 797–807.Google Scholar
  28. [28].
    V. Sharma, Reliable estimation via simulation, Queueing Systems 19 (1995) 169–192.Google Scholar
  29. [29].
    V. Sharma, Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains, Adv. in Appl. Probab. 29 (1997) 1039–1059.Google Scholar
  30. [30].
    V. Sharma, Limit theorems for general regenerative discrete queues, to appear in Adv. Performance Evaluation.Google Scholar
  31. [31].
    V. Sharma and N.D. Gangadhar, Asymptotics for transient and stationary probabilities for finite and infinite buffer discrete time queues, Queueing Systems 26 (1997) 1–22.Google Scholar
  32. [32].
    V. Sharma and N.D. Gangadhar, Some algorithms for discrete time queues with finite capacity, Queueing Systems 25 (1997) 281–305.Google Scholar
  33. [33].
    V. Sharma and J. Sant, Performance analysis of a multiple access scheme on mobility-dependent nonstationary fading channels, in: 2nd Canadian Conf. on Broadband Research, Ottawa (1998).Google Scholar
  34. [34].
    W. Szezotka, Exponential approximation of waiting time and queue size for queues in heavy traffic, Adv. in Appl. Probab. 22 (1990) 230–240.Google Scholar
  35. [35].
    D. Towsley, The analysis of statistical multiplexer with nonindependent arrivals and errors, IEEE Trans. Commun. 28(1) (1980) 65–72.Google Scholar
  36. [36].
    H.S. Wang and N. Moayeri, Finite-state Markov channel – a useful model for radio communication channels, IEEE Trans. Vehicular Technology 44(1) (1995) 163–171.Google Scholar
  37. [37].
    I. Widjaja, M.F. Neuts and J. Li, Conditional overflow probability and profile curve for ATM congestion detection, in: Proc. of IEEE INFOCOM (1996) pp. 970–977.Google Scholar
  38. [38].
    N.D. Wilson, R. Ganesh, K. Joseph and D. Raychaudhuri, Packet CDMA versus dynamic TDMA for multiple access in an integrated voice/data PCN, IEEE J. Selected Areas Commun. 11(6) (1993) 870–884.Google Scholar
  39. [39].
    H. Zhou and R.H. Deng, A new capture model for mobile radio slotted ALOHA systems, in: Proc. of IEEE Vehicular Technology Conf. (1995) pp. 549–553.Google Scholar
  40. [40].
    M. Zorzi and R.R. Rao, Capture and retransmission control in mobile radio, IEEE J. Selected Areas Commun. 12 (1994) 1289–1298.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Jeetendra Sant
    • 1
  • Vinod Sharma
    • 2
  1. 1.Department of Electrical EngineeringIndian Institute of ScienceBangaloreIndia
  2. 2.Department of Electrical Communication EngineeringIndian Institute of ScienceBangaloreIndia

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