Equilibrium theory for the queueing system M/M/c with asynchronous vacations

This paper considers the M/M/c queue with asynchronous vacations. We give a detailed analysis for the multiple vacation model and the single vacation models. The distributions of the stable queue length and the waiting time are obtained. The emphasis is upon obtaining the conditional stochastic decomposition of stationary queue length and waiting time conditioned by the event (J = c), where the event (J = c) denotes that all of the c servers are busy.