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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.
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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 

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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