An M/G/1-type queuing model with service times depending on queue length
Authors:
William J. Gray and Pu Wang
Meckinley Scott
Affiliation:
Dept. of Mathematics, University of Alabama, AL, USA
Department of Mathematics, Western Illinois University, Macomb, IL, USA
Abstract:
A study is made of an M/G/1-type queuing model in which customers receive one type of service until such time as, at the end of a service, the queue size is found to exceed a given value N, N ≥ 1. Then a second type of service is put into effect and remains in use until the queue size is reduced to a fixed value K, 0 ≤ K≤ N. Equations are derived for the stationary probabilities both at departure times and at general times. An algorithm is developed that allows the rapid computation of the mean queue length and some important probabilities.