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Direct martingale arguments for stability: The M/G/1 case. (English) Zbl 0568.60091

Using martingale arguments the authors give direct proofs of the stability properties of the M/G/1 queueing system operating under a non- preemptive work-conserving queueing discipline which is not based on service times.
Reviewer: E.A.van Doorn

MSC:

60K25 Queueing theory (aspects of probability theory)
60G42 Martingales with discrete parameter
90B22 Queues and service in operations research
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References:

[1] Baccelli, F.; Makowski, A. M., Generating martingales for \(M| G\)|1 queues in random environment (1985), in preparation · Zbl 0568.60091
[2] Baccelli, F., Generating martingales and Wald’s formulas for two-queue networks (1985), in preparation
[3] Baras, J. S.; Dorsey, A. J.; Makowski, A. M., Discrete-time competing queues with geometric service requirements: stability, parameter estimation and adaptive control, SIAM J. Control Optim. (1984), submitted
[4] Kleinrock, L., (Queueing Systems, Volume 1: Theory (1975), Wiley: Wiley New York) · Zbl 0334.60045
[5] Kleinrock, L., (Queueing Systems, Volume 11: Computer Applications (1976), Wiley: Wiley New York) · Zbl 0361.60082
[6] Neveu, J., Discrete-Parameter Martingales (1975), North-Holland: North-Holland Amsterdam, English Translation · Zbl 0345.60026
[7] Takacs, L., Introduction to the Theory of Queues (1962), Oxford University Press: Oxford University Press London · Zbl 0118.13503
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