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About the Sojourn Time Process in Multiphase Queueing Systems

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  • S. Minkevičius

    (Institute of Mathematics and Informatics)

  • S. Steišūnas

    (Institute of Mathematics and Informatics)

Abstract

Multiphase queueing systems (MQS) (tandem queues, queues in series) are of special interest both in theory and in practical applications (packet switch structures, cellular mobile networks, message switching systems, retransmission of video images, asembly lines, etc.). In this paper, we deal with approximations of MQS and present a heavy traffic limit theorems for the sojourn time of a customer in MQS. Functional limit theorems are proved for the customer sojourn time – an important probability characteristic of the queueing system under conditions of heavy traffic.

Suggested Citation

  • S. Minkevičius & S. Steišūnas, 2006. "About the Sojourn Time Process in Multiphase Queueing Systems," Methodology and Computing in Applied Probability, Springer, vol. 8(2), pages 293-302, June.
    • Handle: RePEc:spr:metcap:v:8:y:2006:i:2:d:10.1007_s11009-006-8553-x
    DOI: 10.1007/s11009-006-8553-x
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    References listed on IDEAS

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    1. Martin I. Reiman & Burton Simon & J. Stanford Willie, 1992. "Simterpolation: A Simulation based Interpolation Approximation for Queueing Systems," Operations Research, INFORMS, vol. 40(4), pages 706-723, August.
    2. O. J. Boxma & Q. Deng, 2000. "Asymptotic behaviour of the tandem queueing system with identical service times at both queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 52(2), pages 307-323, November.
    3. Martin I. Reiman & Lawrence M. Wein, 1999. "Heavy Traffic Analysis of Polling Systems in Tandem," Operations Research, INFORMS, vol. 47(4), pages 524-534, August.
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