Complutense University Library

Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes

Artalejo, Jesús R. and Chakravarthy , S. R. (2006) Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes. Mathematical Problems In Engineering , 2006 (2). pp. 1-15. ISSN 1024-123X

[img] PDF
Restricted to Repository staff only until 31 December 2020.

556kB

Official URL: http://www.hindawi.com/journals/mpe/2006/053570/abs/

View download statistics for this eprint

==>>> Export to other formats

Abstract

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system.

Item Type:Article
Additional Information:J. R. Artalejo thanks the support received from the Research Project MTM 2005-01248. The research was conducted while S. R. Chakravarthy was visiting the Complutense University of Madrid, Madrid, Spain, and would like to thank the hospitality of the Department of Statistics and Operations Research.
Uncontrolled Keywords:Networks; Queues
Subjects:Sciences > Mathematics > Operations research
ID Code:15564
References:

V. V. Anisimov and J. R. Artalejo, Analysis of Markov multiserver retrial queues with negative arrivals, Queueing Systems. Theory and Applications 39 (2001), no. 2-3, 157–182.

J. R. Artalejo and S. R. Chakravarthy, Algorithmic analysis of the MAP/PH/1 retrial queue, submitted.

Computational analysis of the maximal queue length in the MAP/M/cretrial queue, submitted.

J. R. Artalejo, A. Economou, and A. Gomez-Corral, Applications of maximum queue length to call centers management, to appear in Computers & Operations Research.

S. R. Chakravarthy, The batch Markovian arrival process: A review and future work, Advances in Probability Theory and Stochastic Processes (A. Krishnamoorthy, N. Raju, and V. Ramaswami, eds.), Notable Publications, New Jersey, 2000, pp. 21–39.

D. J. Houck and W. S. Lai, Traffic modeling and analysis of hybrid fiber-coax systems, Computer Networks and ISDN Systems 30 (1998), no. 8, 821–834.

G. K. Janssens, The quasi-random input queueing system with repeated attempts as a model for a collision-avoidance star local area network, IEEE Transactions on Communications 45 (1997), no. 3, 360–364.

G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Pennsylvania; American Statistical Association, Virginia, 1999.

D. M. Lucantoni, New results on the single server queue with a batch Markovian arrival process, Communications in Statistics. Stochastic Models 7 (1991), no. 1, 1–46.

M. A. Marsan, G. de Carolis, E. Leonardi, R. Lo Cigno, and M. Meo, Efficient estimation of call blocking probabilities in cellular mobile telephony networks with customer retrials, IEEE Journal on Selected Areas in Communications 19 (2001), no. 2, 332–346.

M. F. Neuts, The distribution of the maximum length of a Poisson queue during a busy period, Operations Research 12 (1964), no. 2, 281–285.

Matrix-Geometric Solutions in StochasticModels: An Algorithmic Approach, Johns Hopkins Series in the Mathematical Sciences, vol. 2, Johns Hopkins University Press, Maryland, 1981.

Structured Stochastic Matrices of M/G/1 Type and Their Applications, Probability: Pure and Applied, vol. 5, Marcel Dekker, New York, 1989.

R. F. Serfozo, Extreme values of birth and death processes and queues, Stochastic Processes and their Applications 27 (1988), no. 2, 291–306.

H. Shimonishi, T. Takine, M. Murata, and H. Miyahara, Performance analysis of fast reservation protocol in ATM networks with arbitrary topologies, Performance Evaluation 27-28 (1996), 41–69.

P. Tran-Gia and M. Mandjes, Modeling of customer retrial phenomenon in cellular mobile networks, IEEE Journal on Selected Areas in Communications 15 (1997), no. 8, 1406–1414.

Deposited On:11 Jun 2012 07:42
Last Modified:06 Feb 2014 10:27

Repository Staff Only: item control page