The transient behavior of the M/Ek/2 queue and steady-state simulation

Abstract The probabilistic structure for the transient M / E k /2 queue is derived in discrete time, where E k denotes a k -Erlang distribution. This queue has a two-dimensional state-space. Expressions for the expected delay in queue are formulated in terms of transition probabilities. Results are numerically evaluated for a few cases. The convergence behavior is similar to that seen in previous work on queues with one-dimensional state spaces. The implications for initialization of steady-state simulations are discussed.