On many-server queues in heavy traffic

Details On many-server queues in heavy traffic On many-server queues in heavy traffic

2010-01-13

arxiv.org/abs/1001.2163v1

Annals of Applied Probability 2010, Vol. 20, No. 1, 129-195

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/09-AAP604 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Inst

Scientific paper

10.1214/09-AAP604

We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critical loading condition is assumed. Generally, the limit process does not have trajectories in the Skorohod space. We give conditions for the convergence to hold in the topology of compact convergence. Some new results for an infinite server are also provided.

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