An Integral Equation Approach to the M/G/2 Queue

C. Knessl, B. J. Matkowsky, Z. Schuss and C. Tier
Additional contact information
C. Knessl: Northwestern University, Evanston, Illinois
B. J. Matkowsky: Northwestern University, Evanston, Illinois
Z. Schuss: Tel Aviv University, Tel Aviv, Israel
C. Tier: University of Illinois at Chicago, Chicago, Illinois

Operations Research, 1990, vol. 38, issue 3, 506-518

Abstract: We study the stationary distribution of the number of customers in M/G/2 queueing systems. The two servers are allowed to have different service time distributions. We include the elapsed service times of the customers presently served as supplementary variables and obtain the forward equations satisfied by the joint stationary distribution of the number of customers and the elapsed service times. Using a sequence of transformations, we reduce the problem of determining the marginal probabilities of the number of customers present to the solution of a pair of coupled integral equations. When the servers are identical, only a single integral equation must be solved. The solution of the integral equation(s), and with it the stationary distribution of the number of customers, is constructed for several specific service time densities (e.g., Erlang, hyperexponential, and deterministic).

Keywords: queues:; length; distribution; in; M/G/2 (search for similar items in EconPapers)
Date: 1990
References: Add references at CitEc
Citations: View citations in EconPapers (3)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.38.3.506 (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:3:p:506-518

Access Statistics for this article

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