Artalejo, Jesús R. and Chakravarthy , S. R. (2006) Algorithmic Analysis of the MAP/PH/1 Retrial Queue. Top, 14 (2). pp. 293-332. ISSN 1134-5764
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In this paper the distribution of the maximum number of customers in a retrial orbit for a single server queue with Markovian arrival process and phase type services is studied. Efficient algorithm for computing the probability distribution and some interesting numerical examples are presented.
|Additional Information:||The authors thank an anonymous referee for his/her constructive comments on an earlier version of the paper. The first author thanks the support received from the research project MTM2005-01248. This research was conducted while the second author 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:||Markovian arrival process, retrial, busy period, queueing, maximal queue length, phase type distribution, and algorithmic probability|
|Subjects:||Sciences > Mathematics > Operations research|
Artalejo J.R. and Falin G.I. (2002). Standard and Retrial Queueing Systems: A Comparative Analysis.Revista Matematica Complutense 15, 101–129.
Artalejo J.R., Economou A. and Lopez-Herrero M.J. (2007). Algorithmic Analysis of the Maximum Queue Length in a Busy Period for theM/M/c Retrial Queue.INFORMS Journal on Computing (to appear).
Artalejo J.R. and Chakravarthy S.R. (2007). Maximal Queue Length in a Busy Period of aMAP/M/c Retrial Queue.Applied Mathematics and Computation (to appear).
Bini D. and Meini B. (1995). On Cyclic Reduction Applied to a Class of Toeplitz Matrices Arising in Queueing Problems. In: Stewart W.J. (ed.),Computations with Markov Chains. Kluwer Academic Publishers, 21–38.
Breuer L, Dudin A.N. and Klimenok V.I. (2002). A RetrialBM AP/PH/N System.Queueing Systems 40, 433–457.
Bright L.W. and Taylor P.G. (1995). Calculating the Equilibrium Distribution in Level Dependent Quasi-Birth-and-Death Process.Stochastic Models 11, 497–525.
Chakravarthy S.R. (2001). The Batch Markovian Arrival Process: A Review and Future Work. In: Krishnamoorthy A., Raju N. and Ramaswami V. (eds.),Advances in Probability Theory and Stochastic Processes. Notable Publications Inc. 21–39.
Chakravarthy S.R. (2006). A Multi-Server Retrial Queueing Model with Markovian Arrivals and Multiple Thresholds.Asia-Pocific Journal of Operational Research (to appear).
Chakravarthy S.R. and Dubin A.N. (2002). A Multi-Server Retrial Queue withBMAP Arrivals and Group Services.Queueing Systems 42, 5–31.
Chakravarthy S.R. and Dudin A.N. (2003). Analysis of a Retrial Queuing Model withMAP Arrivals and Two Types of Customers.Mathematical and Computer Modelling 37, 343–363.
Chakravarthy S.R., Krishnamoorthy A. and Joshua V.C. (2006). Analysis of a Multi-Server Queue with Search of Customers from the Orbit.Performance Evaluation 63, 776–798 (to appear).
Choi B.D. and Chang Y. (1999).MAP 1 , MAP 2 /M/c with Retrial Queue with the Retrial Group of Finite Capacity and Geometric Loss.Mathematical and Computer Modelling 30, 99–113.
Choi B.D., Chang Y. and Kim B. (1999).MAP 1 , MAP 2 /M/c Retrial Queue with Guard Channels and its Application to Cellular Networks.TOP 7, 231–248.
Diamond J.E. and Alfa A.S. (1995). Matrix Analytic Methods forM/PH/1 Retrial Queues.Stochastic Models 11, 447–470.
Diamond J.E. and Alfa A.S., (1998). TheMAP/PH/1 Retrial Queue.Stochastic Models 14, 1151–1177.
Diamond J.E. and Alfa A.S., (1999a). Approximation Method forM/PH/1 Retrial Queues with Phase Type Inter-Retrail Times.European Journal of Operational Research 113, 620–631.
Diamond J.E. and Alfa A.S., (1999b). Matrix Analytic Methods for a Multi-Server Retrial Queue with Buffer.TOP 7, 249–266.
Dudin A. and Klimenok V. (1999). Queueing SystemBM AP/G/1 with Repeated Calls.Mathematical and Computer Modelling 30, 115–128.
Dudin A. and Klimenok V. (2000). A RetrialBMAP/SM/1 System with Linear Repeated Requests.Queueing Systems 34, 47–66.
Falin G.I. (1983). Calculation of Probability Characteristics of a Multiline System with Repeated Calls.Moscow University Computational Mathematics and Cybernetics 1, 43–49.
Falin G.I. and Templeton J.G.C. (1997).Retrial Queues. Chapman and Hall.
Gomez-Corral A. (2001). On Extreme Values of Orbit Lengths in M/G/1 Queues with Constant Retrial Rate.OR Spectrum 23, 395–409.
Gomez-Corral A. (2006). A Bibliographical Guide to the Analysis of Retrial Queues Through Matrix Analytic Techniques.Annals of Operations Research 141, 163–191.
Latouche G. and Ramaswami V. (1993). A Logarithmic Reduction Algorithm for Quasi-Birth-and-Death Processes.Journal of Applied Probability 30, 650–674.
Lopez-Herrero M.J. and Neuts M.F. (2002). The Distribution of the Maximum Orbit Size of anM/G/1 Retrial Queue During a Busy Period. In: Artalejo J.R. and Krishnamoorthy A. (eds.),Advances in Stochastic Modelling. Notable Publications Inc., 219–231.
Lucantoni D.M. (1991). New Results on the Single Server Queue with a Batch Markovian Arrival Process.Stochastic Models 7, 1–46.
Marcus M. and Minc H. (1964).A Survey of Matrix Theory and Matrix Inequalities. Allyn and Bacon.
Neuts M.F. (1964). The Distribution of the Maximum Length of a Poisson Queue During a Busy Period.Operations Research 12, 281–285.
Neuts M.F. (1989).Structured Stochastic Matrices of M/G/1 type and their Applications. Marcel Dekker.
Neuts M.F. (1992). Models Based on the Markovian Arrival Process.IEICE Transactions on Communications E 75B, 1255–1265.
Neuts M.F. (1995).Algorithmic Probability: A Collection of Problems. Chapman and Hall.
Neuts M.F. and Rao B.M. (1990). Numerical Investigation of a Multiserver Retrial Model.Queueing Systems 7, 169–190.
Serfozo R.F. (1988). Extreme Values of Birth and Death Processes and Queues.Stochastic Processes and their Applications 27, 291–306.
Shin Y.W. (2004). Multi-Server Retrial Queue with Negative Customers and Disasters. Proceedings of the Fifth International Workshop on Retrial Queues, TMRC, Korea University, Seoul, 53–60.
|Deposited On:||07 Jun 2012 07:59|
|Last Modified:||06 Feb 2014 10:26|
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