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

The probabilistic structure for the transient M/E,/2 queue is derived in discrete time, where El, denotes a k-Erlangdistribution. This queue has a twodimensional state-space. Expressions for the expected delay in queue are formulated in terms oftransition 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.