Comparing ordered-entry queues with heterogeneous servers

We study a queueing system with m exponential servers with distinct service rates. Jobs arrive at the system following an arbitrary point process. Arrived jobs receive service at the first unoccupied server (if any) according to an entry order π, which is a permutation of the integers 1, 2,..., m. The system has a finite buffer capacity. When the buffer limit is reached, arrivals will be blocked. Blocked jobs will either be lost or come back as New arrivals after a random travel time. We are concerned with the dynamic stochastic behavior of the system under different entry orders. A partial ordering is established among entry orders, and is shown to result in some quite strong orderings among the associated stochastic processes that reflect the congestion and the service characteristics of the system. The results developed here complement existing comparison results for queues with homogeneous servers, and can be applied to aid the design of conveyor and communication systems. © 1987 J.C. Baltzer AG, Scientific Publishing Company.