Hostname: page-component-745bb68f8f-v2bm5 Total loading time: 0 Render date: 2025-01-09T00:29:11.342Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic transient behaviour of the bulk service queue

Published online by Cambridge University Press:  09 April 2009

B. D. Craven
B. D. Craven
Affiliation:
Department of Mathematics, University of Melbourne
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Various authors have studied the transient behaviour of single-server queues. Notably, Takacs [13], [14] has analysed a queue with recurrent input and exponential service time distributions, Keilson and Kooharian [9], [10] and Finch [5] have considered a queue with general independent input and service times, Finch [6] has analysed a queue with non-recurrent input and Erlang service, and Jaiswal [8] has considered the bulk-service queue with Poisson input and Erlang service.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 3 , Issue 4 , November 1963 , pp. 503 - 512
Copyright
Copyright © Australian Mathematical Society 1963

References

[1]Bailey, N. T. J., On queueing problems with bulk service, J. Roy. Statist. Soc. B., 16 (1954), 80–86.Google Scholar
[2]Bailey, N. T. J., A continuous time treatment of a simple queue using generating functions, J. Roy. Statist. Soc. B, 16 (1954), 288–291.Google Scholar
[3]Bailey, N. T. J., Some further results in the non-equilibrium theory of a simple queue, J. Roy. Statist., Soc. B, 19 (1957) 326–333.Google Scholar
[4]Copson, E. T., Theory of functions of a complex variable, O.U.P. (1935).Google Scholar
[5]Finch, P. D., On the busy period in the queueing system GI/G/I, This Journal 2 (1961–1962) 217–228.Google Scholar
[6]Finch, P. D., The single-server queueing problem with non-recurrent input process and Erlang service time, this Journal (to appear).Google Scholar
[7]Gani, J., Problems in the probability theory of storage systems, J. Roy. Statist. Soc. B. 19 (1957), 181–206.Google Scholar
[8]Jaiswal, N. K., Time-dependent solution of the bulk service queueing problem, Opns. Res., 8 (1960), 773–781.CrossRefGoogle Scholar
[9]Keilson, J. and Kooharian, A., On time-dependent queueing processes, Ann. Math. Statist., 31 (1960), 104–112.CrossRefGoogle Scholar
[10]Keilson, J. and Kooharian, A., On the general time-dependent queue with a single server, Ann. Math. Statist., 33 (1962), 767–791.CrossRefGoogle Scholar
[11]Kendall, D. G., Some problems in the theory of queues, J. Roy. Statist. Soc. B, 13 (1951), 151–175.Google Scholar
[12]Lindley, D. V., The theory of queues with a single server, Proc. Camb. Phil. Soc., 48 (1952), 277–289.CrossRefGoogle Scholar
[13]Takacs, L., Transient behaviour of single-server queueing processes with recurrent input and exponentially distributed service times, Opns. Res., 8 (1960), 231–245.CrossRefGoogle Scholar
[14]Takacs, L., A single-server queue with recurrent input and exponentially distributed service times, Opns. Res., 10 (1962), 393–399.Google Scholar