##### Department of Mathematics,

University of California San Diego

****************************

### Math 288 - Seminar In Probability & Statistics

## Amber L. Puha

#### California State University, San Marcos

## Asymptotically Optimal Policies for Many Server Queues with Reneging

##### Abstract:

The aim of this work (joint with Amy Ward [USC, Marshall School of Business]) is to determine fluid asymptotically optimal policies for many server queues with general reneging distributions. For exponential reneging distributions, it has been shown that static priority policies are optimal in a variety of settings, that include generally distributed interarrival and service times. Moreover, in these cases, the priority ranking is determined by a simple rule known as the c-mu-theta rule. For non-exponential reneging distributions, the story is more complex. We study reneging distributions with monotone hazard rates. For reneging distributions with bounded, nonincreasing hazard rates, we prove that static priority is not necessarily asymptotically optimal. We identify a new class of policies, which we are calling Random Buffer Selection and prove that these are asymptotically optimal in the fluid limit. We further identify a fluid approximation for the limiting cost as the optimal value of a certain optimization problem. For reneging distributions with nondecreasing hazard rates, our work suggests that static priority policies are in fact optimal, but the rule for determining the priority ranking seems more complex in general. It is work in progress to prove this.

Host: Bruce Driver

### June 1, 2017

### 10:00 AM

### AP&M 6402

****************************