On the transient behavior of the Erlang loss model: Heavy usage asymptotics

On the transient behavior of the Erlang loss model: Heavy usage asymptotics

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Article ID: iaor19932448
Country: United States
Volume: 53
Issue: 2
Start Page Number: 555
End Page Number: 599
Publication Date: Apr 1993
Journal: SIAM Journal On Control and Optimization
Authors: ,
Keywords: Erlang loss
Abstract:

The Erlang loss model, which is the M/M/m/m queue is considered. Asymptotic expansions are constructed for systemswith a large number of servers (m>>1) and a large arrival rate that is O(m). Fromulas are given for the probability pn(t) that n servers are occupied at time t. Several cases are treated of initial conditions and several regions in the (n,t) plane. The approximations are constructed by using singular perturbation techniques such as the ray method, boundary layer theory, and the method of matched asymptotic expansions.

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