An Analytic Approach to a General Class of G/G/s Queueing Systems

Dimitris Bertsimas
Additional contact information
Dimitris Bertsimas: Massachusetts Institute of Technology, Cambridge, Massachusetts

Operations Research, 1990, vol. 38, issue 1, 139-155

Abstract: We solve the queueing system C k /C m /s, where C k is the class of Coxian probability density functions (pdfs) of order k , which is a subset of the pdfs that have a rational Laplace transform. We formulate the model as a continuous-time, infinite-space Markov chain by generalizing the method of stages. By using a generating function technique, we solve an infinite system of partial difference equations and find closed-form expressions for the system-size, general-time, prearrival, post-departure probability distributions and the usual performance measures. In particular, we prove that the probability of n customers being in the system, when it is saturated is a linear combination of geometric terms. The closed-form expressions involve a solution of a system of nonlinear equations that involves only the Laplace transforms of the interarrival and service time distributions. We conjecture that this result holds for a more general model. Following these theoretical results we propose an exact algorithm for finding the system-size distribution and the system's performance measures. We examine special cases and apply this method for numerically solving the C 2 /C 2 /s and E k /C 2 /s queueing systems.

Keywords: queues: multichannel; Markovian queues (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (5)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.38.1.139 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:38:y:1990:i:1:p:139-155

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().