Maximum likelihood estimates and confidence intervals of an M/M/R/N queue with balking and heterogeneous servers

¹ Department of Applied Mathematics National Chung-Hsing University Taichung, 402, Taiwan, R.O.C.; khwang@amath.nchu.edu.tw.
² Department of Statistics National Taichung Institute of Technology Taichung 404, Taiwan, R.O.C.

Received: 24 October 2003
Revised: 15 January 2004

Abstract

This paper considers an M/M/R/N queue with heterogeneous servers in which customers balk (do not enter) with a constant probability (1 - b). We develop the maximum likelihood estimates of the parameters for the M/M/R/N queue with balking and heterogeneous servers. This is a generalization of the M/M/2 queue with heterogeneous servers (without balking), and the M/M/2/N queue with balking and heterogeneous servers in the literature. We also develop the confidence interval formula for the parameter ρ, the probability of empty system P₀, and the expected number of customers in the system E[N], of an M/M/R/N queue with balking and heterogeneous servers. The effects of varying b, N, and R on the confidence intervals of P₀ and E[N] are also investigated.