Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T16:51:45.632Z Has data issue: false hasContentIssue false
  • English
  • Français

The sojourn time distribution in an infinite server resequencing queue with dependent interarrival and service times

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Tijs Huisman  and
Richard J. Boucherie
Tijs Huisman*
Affiliation:
University of Amsterdam
Richard J. Boucherie*
Affiliation:
University of Amsterdam
*
∗ Current address: Railned BV, Department of Innovation, PO Box 2101, 3500 GC Utrecht, The Netherlands. Email address: t.huisman@railned.nl
∗∗ Current address: Stochastic Operations Research Group, Faculty of Mathematical Sciences, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands.
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider an infinite server resequencing queue, where arrivals are generated by jumps of a semi-Markov process and service times depend on the jumps of this process. The stationary distribution of the sojourn time, conditioned on the state of the semi-Markov process, is obtained both for the case of hyperexponential service times and for the case of a Markovian arrival process. For the general model, an accurate approximation is derived based on a discretisation of interarrival and service times.

Keywords

Resequencing queuesojourn time distributionsemi-Markovian arrival process

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Research Papers
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 590 - 603
Copyright
Copyright © Applied Probability Trust 2002 

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.)

References

[1]. Baccelli, F., Gelenbe, E., and Plateau, B. (1984). An end-to-end approach to the resequencing problem. J. Assoc. Comput. Mach. 31, 474–485.Google Scholar
[2]. Chowdhury, S. K. (1991). Distribution of the total delay of packets in virtual circuits. In Proc. IEEE Infocom ’91 (Bal Harbour, FL, 7–11 April 1991), IEEE, New York, pp. 911–918.Google Scholar
[3]. Dollard, J. D., and Friedman, C. N. (1979). Product Integration with Applications to Differential Equations (Encyclopedia Math. Appl. 10). Addison–Wesley, Reading, MA.Google Scholar
[4]. Harrus, G., and Plateau, B. (1982). Queueing analysis of a reordering queue. IEEE Trans. Software Eng. 8, 113–123.Google Scholar
[5]. Huisman, T., and Boucherie, R. J. (2001). Running times on railway sections with heterogeneous train traffic. Transportation Res. 35, 271–292.Google Scholar
[6]. Kamoun, F., Djerad, M. B., and Lann, G. L. (1982). Queueing analysis of the reordering issue in a distributed database concurrency control mechanism: a general case. In Proc. 3rd Internat. Conf. Distributed Computing Systems (Miami, FL, 18–22 October 1982), IEEE Computer Society Press, Los Alamitos, CA, pp. 447–452.Google Scholar
[7]. Kleinrock, L., Kamoun, F., and Muntz, R. (1981). Queueing analysis of the reordering queue in a distributed database concurrency control mechanism. In Proc. 2nd Internat. Conf. Distributed Computing Systems, IEEE Computer Society Press, Los Alamitos, CA, pp. 13–23.Google Scholar
[8]. Ren, J. F., Takahashi, Y., and Hasegawa, T. (1996). Analysis of impact of network delay on multiversion conservative timestamp algorithms in DDBS. Performance Evaluation 26, 21–50.Google Scholar
[9]. Zabreyko, P. P. et al. (1975). Integral Equations—A Reference Text. Noordhoff, Leyden.Google Scholar