## Center for Applied Mathematics Colloquium

In most queueing models it is assumed that the primitive processes (arrival, service, abandonment, etc.) are independent. However, data shows that the service time of a customer may depend on that customer’s patience, or on her delay in queue. In this talk I will discuss the impacts that such a dependency has on key performance measures (waiting times, queue length, proportion of abandonment and throughput), and on optimal capacity decisions. In particular, I will first consider a system with a single pool of many statistically-homogeneous agents serving one class of statistically-identical customers whose service requirements and patience times are dependent random variables. Since the assumed dependence renders exact analysis intractable, we develop a deterministic (fluid) approximation which is characterized via the entire joint distribution of the service and patience times. To evaluate the impacts of the dependence, we employ bivariate dependence orders, and provide structural results which facilitate revenue optimization when a staffing cost is incurred. Time permitting; I will also discuss an alternative model, in which the service times depend on the delay in queue, and how the two different models can be related and approximated via a unified fluid model. (Joint work with Allen Wu and Achal Bassamboo, Northwestern University)