Hostname: page-component-89b8bd64d-x2lbr Total loading time: 0 Render date: 2026-05-05T11:18:50.693Z Has data issue: false hasContentIssue false
  • English
  • Français

Loss Probability of a Burst Arrival Finite Queue with Synchronized Service

Published online by Cambridge University Press:  27 July 2009

Masakiyo Miyazawa
Masakiyo Miyazawa
Affiliation:
Department of Information SciencesScience University of Tokyo Chiba, Japan
Get access Rights & Permissions [Opens in a new window]

Abstract

We are concerned with a burst arrival single-server queue, where arrivals of cells in a burst are synchronized with a constant service time. The main concern is with the loss probability of cells for the queue with a finite buffer. We analyze an embedded Markov chain at departure instants of cells and get a kind of lumpability for its state space. Based on these results, this paper proposes a computation algorithm for its stationary distribution and the loss probability. Closed formulas are obtained for the first two moments of the numbers of cells and active bursts when the buffer size is infinite.

Information

Type
Articles
Information
Probability in the Engineering and Informational Sciences , Volume 6 , Issue 2 , April 1992 , pp. 201 - 216
Copyright
Copyright © Cambridge University Press 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Brandt, A., Brandt, M., & Sulanke, H. (1990). A single server model for packetwise transmission of messages. Queueing System 6: 287–310.CrossRefGoogle Scholar
Cohen, J.W. (1974). Superimposed renewal processes and storage with gradual input. Stochastic Processes and Their Applications 2: 31–58.CrossRefGoogle Scholar
Franken, P., König, D., Arndt, U., & Schmidt, V. (1982). Queues and point processes. New York: John Wiley & Sons.Google Scholar
Hashida, O. & Fujiki, M. (1973). Queueing models for buffer memory in store.and.forward systems. Proceedings of ITC 7 Stockholm 323/1-323/7.Google Scholar
Kosten, L. (1974). Stochastic theory of a multi-entry buffer (1). Delft Progress Report 1: 10–18.Google Scholar
Miyazawa, M. (1985). The intensity conservation law for queues with randomly changed service rate. Journal of Applied Probability 22: 408–418.CrossRefGoogle Scholar
Miyazawa, M. (1989). Comparison of the loss probability of the GIx/GI/l/k queues with a common traffic intensity. Journal of the Operations Research Society of Japan 32: 505–516.Google Scholar
Miyazawa, M. (1990). Complementary generating functions for Mx/GI/l/k and Gl/My/l/k queues and their applications to the comparison of loss probabilities. Journal of Applied Probability 27: 684–692.CrossRefGoogle Scholar
Miyazawa, M. & Shanthikumar, J.G. (1991). Monotonicity of the loss probabilities of single server finite queues to convex order of arrival or service processes. Probability in the Engineering and Informational Sciences 5: 43–52.CrossRefGoogle Scholar
Pan, H., Okazaki, H., & Kino, I. (1991). Analysis of a gradual input model for bursty traffic in ATM. ITC 13 Copenhagen 795–800.Google Scholar
Rosberg, Z. (1981). A note on the ergodicity of Markov chains. Journal of Applied Probability 18: 112–121.CrossRefGoogle Scholar
Sigman, K. & Yamazaki, G. (1992). Fluid models with burst arrivals: A sample path analysis. Probability in the Engineering and Informational Sciences 6: 17–27.CrossRefGoogle Scholar