On a GI/M/c Queue with Bounded Waiting Times

We derive the asymptotic distribution of the remaining load, virtual waiting time and actual waiting time for a multiserver queueing system with exponentially distributed service times and bounded waiting times. Interarrival distributions are Coxian, with m stages. This model has application to telephone exchange operations and to perishable inventory. The explicit derivation of the distributions involves determining the eigenvalues of m-dimensional matrices and solving linear equations in m unknowns. We give a few numerical illustrations.