|M.Sc Student||Rozenshmidt Lubov|
|Subject||On Priority Queues with Impatient Customers:|
Stationary and Time-Varying Analysis
|Department||Department of Industrial Engineering and Management||Supervisor||Professor Emeritus Avishai Mandelbaum|
|Full Thesis text|
We consider Markovian non-preemptive and preemptive priority queueing systems with impatient customers, under the assumption that service rates and abandonment rates are equal across customer types. For such systems in steady-state, we develop an algorithm for calculating the expected waiting time of any type.
We then assume that the number of servers is large, formally taking this number to infinity, which enables an asymptotic analysis in three operational regimes: an Efficiency-Driven (ED) regime, in which the focus is on servers' utilization (efficiency), a Quality-Driven (QD) regime, where the focus is on the quality of the service and a Quality-and-Efficiency-Driven (QED) regime, where efficiency is carefully balanced against service quality.
Our asymptotic analysis provides simplified expressions for some operational measures, e.g., the expected waiting time of any type. But, as importantly, it yields structural insight. For example, assuming that the offered load of the lowest priority is non-negligible, we show that preemption and non-preemption are essentially equivalent, as far as average waiting times are concerned. Moreover, the delayed customers of all classes other than the lowest priority wait, on average, the same time as in a queue without abandonment. (In other words, their service level is high enough to render their abandonment negligible.)
Stationary behavior turns out to provide important insights on the behavior of time-varying queues. Specifically, under an appropriate scale and time-varying staffing, the performance of time-varying versions of the above-mentioned systems is in fact stable in time. Moreover, this stable performance matches remarkably well the performance of naturally-corresponding steady-state systems. We demonstrate all that via simulating queues in which the arrival-rates are taken from four real call-centers.
More specifically, we first simulate call-center environments with a single customer type whose arrivals are described by an empirical function. After that, we present simulation results of queues with two customer types that arrive according to analytical functions. The conclusion of these experiments, as mentioned, is that in many cases, and under appropriate staffing, stationary models can be used to properly predict the performance of time-varying queues.
In our last chapter, the traditional heavy-traffic approximation for expected waiting time, based on the first two moments of the service-time distribution, is considered. We check this approximation by simulating queues with different service-time distributions and conclude that in the QED regime, such two-moment approximations are inaccurate.