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DELAY IN A TANDEM QUEUEING MODEL WITH MOBILE QUEUES: AN ANALYTICAL APPROXIMATION

Published online by Cambridge University Press:  19 March 2014

Ahmad Al Hanbali ,
Roland de Haan ,
Richard J. Boucherie  and
Jan-Kees van Ommeren
Ahmad Al Hanbali
Affiliation:
Department of Industrial Engineering and Business Information Systems, IEBIS Group, School of Management and Governance, University of Twente, The Netherlands. E-mail: [email protected]
Roland de Haan
Affiliation:
Dep. of Applied Mathematics, SOR Group, University of Twente, The Netherlands. E-mail: [email protected], [email protected], [email protected]
Richard J. Boucherie
Affiliation:
Dep. of Applied Mathematics, SOR Group, University of Twente, The Netherlands. E-mail: [email protected], [email protected], [email protected]
Jan-Kees van Ommeren
Affiliation:
Dep. of Applied Mathematics, SOR Group, University of Twente, The Netherlands. E-mail: [email protected], [email protected], [email protected]
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Abstract

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In this paper, we analyze the end-to-end delay performance of a tandem queueing system with mobile queues. Due to state-space explosion, there is no hope for a numerical exact analysis for the joint-queue-length distribution. For this reason, we present an analytical approximation that is based on queue-length analysis. Through extensive numerical validation, we find that the queue-length approximation exhibits excellent performance for light traffic load.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 28 , Issue 3 , July 2014 , pp. 363 - 387
Copyright
Copyright © Cambridge University Press 2014 

References

1.Al Hanbali, A., de Haan, R., Boucherie, R.J. & van Ommeren, J.K. (2008). A tandem queueing model for delay analysis in disconnected ad hoc networks. Proc. ASMTA, LCNS 5055, Nicosia, Cyprus, pp. 189–205CrossRefGoogle Scholar
2.Al Hanbali, A., de Haan, R., Boucherie, R.J. & van Ommeren, J.K. (2012). Time-limited polling systems with batch arrivals and phase-type service times. Annals of Operations Research 198: 57–82Google Scholar
3.Al Hanbali, A., Mandjes, M., Nazarathy, Y. & Whitt, W. (2011). The asymptotic variance of departures in critically loaded queues. Advances in Applied Probability 43: 243–263Google Scholar
4.Borst, S., Boxma, O. & Combé, M. (1992). Collection of customers: a correlated M/G/1 queue. Performance Evaluation 20: 47–59CrossRefGoogle Scholar
5.Coffman, E.G., Fayolle, G. & Mitrani, I. (1988). Two queues with alternating service periods. In: Performance ’87: Proc. of the 12th IFIP WG 7.3 Int. Symp. Computer Performance Modelling, Measurement and Evaluation. pp. 227–239Google Scholar
6.de Haan, R., Al Hanbali, A., Boucherie, R.J. & van Ommeren, J.K. (2009). A transient analysis of polling systems operating under exponential time-limited service disciplines. Research Memorandum 1894, University of Twente, NetherlandsGoogle Scholar
7.de Haan, R., Boucherie, R.J. & van Ommeren, J.K. (2009). A polling model with an autonomous server. Queueing Systems 62: 279–308CrossRefGoogle Scholar
8.Delay Tolerant Networking Research Group, Web site: http://www.dtnrg.org.Google Scholar
9.Doshi, B. (1986). Queueing systems with vacations—a survey. Queueing Systems 1: 29–66Google Scholar
10.Eliazar, I. & Yechiali, U. (1998). Polling under the randomly-timed gated regime. Stochastic Models 14: 79–93CrossRefGoogle Scholar
11.Frigui, I. & Alfa, A. (1998). Analysis of a time-limited polling system. Computer Communications 21(6): 558–571CrossRefGoogle Scholar
12.Grossglauser, M. & Tse, D. (2002). Mobility increases the capacity of ad hoc wireless networks. IEEE Transactions on Networking 10: 477–486CrossRefGoogle Scholar
13.Leung, K. (1994). Cyclic-service systems with non-preemptive time-limited service. IEEE Transactions on Communications 42: 2521–2524CrossRefGoogle Scholar
14.Neuts, M. (1981). Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Baltimore: Johns Hopkins University PressGoogle Scholar
15.Katayama, T. (2001). Waiting time analysis for a queueing system with time-limited service and exponential timer. Naval Research Logistics 48: 638–651Google Scholar
16.van Ommeren, J.K. (1991). The discrete-time single-server queue. Queueing Systems 8: 279–294Google Scholar
17.van Vuuren, M., Adan, I. & Resing-Sassen, S. (2005). Performance analysis of multi-server tandem queues with finite buffers and blocking. OR Spectrum 27: 315–338CrossRefGoogle Scholar
18.Wang, C. & Wolff, R. (2005). Work-conserving tandem queues. Queueing Systems 49: 283–296Google Scholar
19.Zazanis, M. (1998). A Palm calculus approach to functional versions of Little's law. Stochastic Processes and their Applications 74: 195–201CrossRefGoogle Scholar