Analysis of discrete-time multiserver queueing models with constant service times. (English) Zbl 0814.90030

Summary: A discrete-time multiserver queueing model is analyzed. The model allows for an arbitrary number of servers, arbitrary-length constant service times, and general independent arrivals. As a result of the analysis, an explicit expression is obtained for the generating function of the queue length, which easily allows the derivation of such performance measures as the moments and the tail distribution of the queue length. Application areas of the model include ATM switching elements, circuit-switched TDMA systems and traffic concentrators.


90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
Full Text: DOI


[1] Bruneel, H., A general model for the behaviour of infinite buffers with periodic service opportunities, Eur. J. Oper. Res., 16, 98-106 (1984) · Zbl 0531.90037
[2] Bruneel, H., On statistical multiplexers with randomly changing input characteristics, Comput. Oper. Res., 14, 481-487 (1986)
[3] Bruneel, H., Performance of discrete-time queueing systems, Comput. Oper. Res., 20, 303-320 (1993) · Zbl 0771.60074
[4] Bruneel, H.; Kim, B. G., Discrete-Time Models for Communication Systems Including ATM (1993), Kluwer Academic Publishers: Kluwer Academic Publishers Boston
[5] Devault, M.; Servel, M.; Cochennec, J.-Y., The Prelude experiment: assessments and future prospects, IEEE J. Selected Areas Commun., SAC-6, 1528-1537 (1988)
[6] Gravey, A.; Louvion, J.-R.; Boyer, P., On the Geo/D/1 and Geo/D/1/n queues, Performance Evaluation, 11, 117-125 (1990)
[7] Hayes, J. F., Modeling and Analysis of Computer Communications Networks (1984), Plenum Press: Plenum Press New York
[8] Henrion, M. A.; Schrodi, K. J.; Boettle, D.; De Somer, M.; Dieudonne, M., Switching network architecture for ATM based broadband communications, (Proc. ISS’90, Vol. V (1990)), 1-8, Stockholm
[9] Kleinrock, L., (Queueing Systems, Vol. I: Theory (1975), Wiley: Wiley New York) · Zbl 0334.60045
[10] Kobayashi, H.; Konheim, A., Queueing models for computer communications system analysis, IEEE Trans. Commun., COM-25, 2-29 (1977) · Zbl 0365.68064
[11] Rubin, I., Access-control disciplines for multi-access communication channels: Reservation and TDMA schemes, IEEE Trans. Inform. Theory, IT-25, 516-536 (1979) · Zbl 0422.94022
[12] Rubin, I.; Zhang̀, Z., Message delay and queue-size analysis for circuit-switched TDMA systems, IEEE Trans. Commun., COM-39, 905-914 (1991) · Zbl 0739.94006
[13] Schormans, J. A.; Scharf, E. M.; Pitts, J. M., Analysis of telecommunications switch model (Geo/D/1) with the priorities, Electronics Lett., 26, 325-326 (1990)
[14] Towsley, D.; Wolf, J. K., On the statistical analysis of queue lengths and waiting times for statistical multiplexers with ARQ retransmission schemes, IEEE Trans. Commun., COM-27, 693-702 (1979) · Zbl 0397.94005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.