A Finite Capacity GI/PH/1 Queue with Group Services
Document Type
Article
Publication Date
4-1-1992
Publication Title
Naval Research Logistics
Abstract
We consider a finite‐capacity single‐server queue in which arrivals occur one at a time, according to a renewal process. The successive service times are mutually independent and have a common phase‐type distribution. The customers are served in groups of size at least L, a preassigned threshold value. Explicit analytic expressions for the steady‐state queue‐length densities at arrivals and at arbitrary time points, and the throughput of the system are obtained. The Laplace‐Stieltjes transform of the stationary waiting‐time distribution of an admitted customer at points of arrivals is computed. It is shown to be of phase type when the arrival process is also of phase type. Efficient algorithmic procedures for the steady‐state analysis of the model are presented. These procedures are used in arriving at an optimal value for L that minimizes the mean waiting time of an admitted customer. A conjecture on the nature of the mean waiting time is proposed.
Volume
39
Issue
3
First Page
345
Last Page
357
DOI
10.1002/1520-6750(199204)39:3<345::AID-NAV3220390305>3.0.CO;2-V
ISSN
Online ISSN:1520-6750
Rights
© 1992 Wiley Periodicals, Inc., A Wiley Company
Recommended Citation
Chakravarthy, Srinivas R., "A Finite Capacity GI/PH/1 Queue with Group Services" (1992). Industrial & Manufacturing Engineering Publications. 88.
https://digitalcommons.kettering.edu/industrialmanuf_eng_facultypubs/88
