Stochastic bounds for heterogeneous-server queues with Erlang service times
- 1 December 1974
- journal article
- research article
- Published by Cambridge University Press (CUP) in Journal of Applied Probability
- Vol. 11 (04) , 785-796
- https://doi.org/10.1017/s0021900200118212
Abstract
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/1 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 single-server queues to obtain characterizations of steady-state distributions and heavy-traffic approximations.Keywords
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