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A. B. Clarke's Tandem Queue Revisited-Sojourn Times

Gómez Corral, Antonio and Escribano Martos, Manuel David (2008) A. B. Clarke's Tandem Queue Revisited-Sojourn Times. Stochastic Analysis and Applications, 26 (6). pp. 1111-1135. ISSN 0736-2994

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Abstract

In telecommunications, packets or units may complete their service in a different order from the one in which they enter the station. In order to reestablish the original order resequencing protocols need to be implemented. In this article, the focus is on a two-server resequencing system with heterogeneous servers and two buffers. One buffer has an infinite capacity to hold the incoming units. The other with a finite capacity is used to resequence the serviced units. This is to maintain the order of departure of the units according to the order of their arrivals. To analyze this resequencing model, we introduce an equivalent two-stage queueing system, namely A. B. Clarke's Tandem Queue, in which the arriving units receive service from only one server, and the units departing from the first stage may be temporally prevented from leaving by occupied service units at the second stage. Our interest is to study the resequencing delay and the sojourn time as times until absorption in suitably defined quasi-birth-and-death processes and continuous-time Markov chains.


Item Type:Article
Uncontrolled Keywords:Blocking; Resequencing; Sojourn times; Queueing
Subjects:Sciences > Mathematics > Stochastic processes
ID Code:15595
References:

Baccelli, F., and Makowski, A.M. 1989. Queueing models for systems with synchronization constraints. Proceedings of the IEEE 77:138–161.

Shacham, N., and Shin, B.C. 1992. A selective-repeat-ARQ protocol for parallel channels and its resequencing analysis. IEEE Transactions on Communications 40:773–782.

Shikama, T., Watanabe, T., and Mizuno, T. 2005. Delay analysis of the selective-repeat ARQ with the per flow resequencing. Proceedings of the IEEE International Conference on Communications 1:26–32.

Kamoun, F., Kleinrock, L., and Muntz, R. 1981. Queueing analysis of the reordering issue in a distributed database concurrency control mechanism. In Proceedings of the Second International Conference on Distributed Computing Systems. Versailles, France, April, 13–23.

Harrus, G., and Plateau, B. 1982. Queueing analysis of a reordering issue.IEEE Transactions on Software Engineering 8:113–123.

Baccelli, F., Gelenbe, E., and Plateau, B. 1984. An end-to-end approach to the resequencing problem. Journal of the Association for Computing Machinery 31:474–485.

Lien, Y.-C. 1985. Evaluation of the resequence delay in a Poisson queueing system with two heterogeneous servers. In Proceedings of the International Workshop on Computer Performance Evaluation. Tokyo, Japan, September,189–197.

Yum, T.S.P., and Ngai, T.Y. 1986. Resequencing of messages in communication networks. IEEE Transactions on Communications 34:143–149.

Chowdhury, S. 1991. An analysis of virtual circuits with parallel links.IEEE Transactions on Communications 39:1184–1188.

Iliadis, I., and Lien, Y.-C. 1988. Resequencing delay for a queueing system with two heterogeneous servers under a threshold-type scheduling. IEEE Transactions on Communications 36:692–702.

Gogate, N., and Panwar, S.S. 1994. On a resequencing model for high speed networks. In Proceedings of INFOCOM’94. Toronto, Canada, June,40–47.

Jean-Marie, A., and Gün, L. 1993. Parallel queues with resequencing.Journal of the Association for Computing Machinery 40:1188–1208.

Lucantoni, D.M., Meier-Hellstern, K.S., and Neuts, M.F. 1990. A singleserver queue with server vacations and a class of non-renewal arrival processes. Advances in Applied Probability 22:676–705.

Balsamo, S., de Nitto Personé, V., and Onvural, R. 2001. Analysis of Queueing Networks with Blocking. Kluwer Academic, Boston.

Perros, H.G. 1994. Queueing Networks with Blocking. Exact and Approximate Solutions. Oxford University Press, New York.

Neuts, M.F. 1994. Matrix-Geometric Solutions in Stochastic Models. An Algorithm Approach, 2nd ed. Dover Publications, New York.

Clarke, A.B. 1977. A two-server tandem queueing system with storage between servers. Mathematical Report no. 50. Western Michigan University, Kalamazoo.

Niu, Z., Liu, Y., and Lin, X. 1999. Two-link striping system in packetswitched networks. ACTA Electronica SINICA 27(6):83–87. (in Chinese)

Chakravarthy, S.R., Chukova, S., and Dimitrov, B. 1998. Analysis of MAP/M/2/K queueing model with infinite resequencing buffer.Performance Evaluation 31:211–228.

Chakravarthy, S.R., and Chukova, S. 2005. A finite capacity resequencing model with Markovian arrivals. Asia-Pacific Journal of Operational Research 22:409–443.

Dudin, A.N., and Chakravarthy, S.R. 2003. Multi-threshold control of the BMAP/SM/1/K queue with group services. Journal of Applied Mathematics and Stochastic Analysis 16:327–347.

Kazimirsky, A.V. 2006. Analysis of BMAP/G/1 queue with reservation of service. Stochastic Analysis and Applications 24:703–718.

Krishnamoorthy, A., Narayanan, V.C., Deepak, T.G., and Vineetha, P.2006. Control policies for inventory with service time. Stochastic Analysis and Applications 24:889–899.

Akar, N., and Sohraby, K. 1997. An invariant subspace approach in M/G/1 and G/M/1 type Markov chains. Stochastic Models 13:381–416.

Alfa, A.S., Sengupta, B., Takine, T., and Xue, J. 2002. A new algorithm for computing the rate matrix of GI/M/1 type Markov chains. In: Matrix-Analytic Methods. Theory and Applications. Latouche, G., Taylor, P., (eds.),World Scientific, Singapore, pp. 1–16.

Hunter, J.J. 1983. Mathematical Techniques of Applied Probability. Vol. 1.Discrete Time Models: Basic Theory. Academic Press, New York.

Gómez-Corral, A. 2004. Sojourn times in a two-stage queueing network with blocking. Naval Research Logistics 51:1068–1089.

Abate, J., and Whitt, W. 1995. Numerical inversion of Laplace transforms of probability distributions. ORSA Journal on Computing 7:36–43

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