PALS Seminar Series

(Performance Analysis of Logistic Systems)

ABSTRACTS

Josh Reed (New York University)

A Fair Policy for the Servers in the G/GI/N Queue with Multiple Server Pools

We consider the G/GI/N queue with multiple server pools, each possessing a pool-specific service time distribution. We then consider the class of non-idling routing policies referred to as u-greedy policies. These policies route incoming customers to the server pool with the longest weighted cumulative idle time. Our first set of results demonstrate that asymptotically in the Halfin-Whitt regime and under any u-greedy policy, the diffusion scaled cumulative idle time processes of each of the server pools are held in fixed proportion to one another. We next move on to providing a heavy-traffic limit theorem for the process keeping tracking of the total number of customers in the system. Our limit may be characterized as the solution to a stochastic convolution equation.
As a first step to proving our main results, we also show that under any non-idling policy and under appropriate initial conditions, the fluid scaled total number of customers in the system and in each server pool is asymptotically constant. This is joint work with Yair Shaki.

Last updated 22-05-13
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