Algorithmic Analysis of the Maximum Queue Length in a Busy Period for the M/M/c Retrial Queue

This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue. Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities. By reducing to the single-serv...

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Bibliographic Details
Published in:INFORMS journal on computing 2007-12, Vol.19 (1), p.121-126
Main Authors: Artalejo, Jesus R, Economou, Antonis, Lopez-Herrero, M. J
Format: Article
Language:English
Subjects:
Algorithms
Analysis
busy period
continuous-time Markov chain
Linear programming
M/M/c
Markov analysis
Markov processes
maximum orbit size
Queues (Computers)
Queuing theory
retrial queue
Studies
tridiagonal linear system
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Summary:This paper deals with the maximum number of customers in orbit (and in the system) during a busy period for the M/M/c retrial queue. Determining the distribution for the maximum number of customers in orbit is reduced to computation of certain absorption probabilities. By reducing to the single-server case we arrive at a closed analytic formula. For the multi-server case we develop an efficient algorithmic procedure for computation of this distribution by exploiting the special block-tridiagonal structure of the system. Numerical results illustrate the efficiency of the method and reveal interesting facts concerning the behavior of the M/M/c retrial queue.
ISSN:1091-9856
1526-5528
1091-9856
DOI:10.1287/ijoc.1050.0156