A Finite Capacity Queueing Model with Primary and Secondary Jobs

Document Type

Article

Publication Date

1989

Publication Title

Computers and Industrial Engineering

Abstract

We consider a queueing model consisting of a primary buffer of capacity K and a secondary buffer of capacity N. Upon completion of the primary service, customers enter the secondary buffer for one additional service with probability p, 0 ⩽ p ⩽ 1, or leave the system with probability q = 1 − p. The server exhaustively processes the jobs from the secondary buffer whenever the primary buffer becomes empty or the secondary buffer fills up. The service times of the primary customers are assumed to follow a phase type distribution and those of the secondary jobs follow an exponential distribution with parameter μ2. Customers arrive to the system according to a homogeneous Poisson process of rate λ. Using Markov chain theory, we discuss numerically stable algorithms to compute various steady-state system performance measures such as throughput, the fraction of time the server is busy, the fraction of time a primary customer is blocked, the fraction of time new customers are lost, expected numbers of customers waiting in the primary and secondary buffers. A number of numerical examples are presented.

Volume

16

Issue

1

First Page

97

Last Page

108

DOI

10.1016/0360-8352(89)90012-0

ISSN

ISSN: 0360-8352

Comments

This research was supported in part by Grant Nr. ECS-8601203 from the National Science Foundation.

Rights

© 1989 Elsevier Ltd.

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