Stochastic bounds for heterogeneous-server queues with Erlang service times

This paper establishes stochastic bounds for the phasal departure times of a heterogeneous-server queue with a recurrent input and Erlang service times. The multi-server queue is bounded by a simple GI/E/I queue. When the shape parameters of the Erlang service-time distributions of different servers are the same, these relations yield two-sided bounds for customer waiting times and the queue length, which can in turn be used with known results for singleserver queues to obtain characterizations of steady-state distributions and heavy-traffic approximations. QUEUE; SERVICE SYSTEM; CONGESTION THEORY; MULTI-SERVER QUEUE; HETEROGENEOUS-SERVER QUEUE; QUEUE WITH ERLANG SERVICE TIMES; STOCHASTIC ORDERING OF QUEUES; STOCHASTIC BOUNDING RELATIONS FOR QUEUES; EXISTENCE THEOREMS FOR QUEUES; LIMIT THEOREMS FOR QUEUES; APPROXIMATIONS FOR QUEUES; QUEUES IN HEAVY TRAFFIC