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

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.