UC Berkeley

In queueing theory, the phenomenon that customers get impatient and renege from the system when the waiting time exceeds their tolerance is called customer abandonments. For those abandoning customers, they may go back to the service system after some time. This is called customer retrials. In the modern design of service systems, the impact of customer abandonments and retrials on the system performance and queueing dynamics has been realized. In this thesis, we aim to characterize the stationary properties for queueing systems with both customer abandonments and retrials. We also apply some of those properties in a revenue management problem for queueing systems with customer abandonments.

First, we study a multi-server queueing system with both customer abandonments and retrials. By using RTA (retrials see time average) approximation, we characterize the stationary properties of such a queueing system. We also justify the appropriateness of RTA approximation in this model both theoretically and numerically.

Then, we extend the study to incorporate negative customers and unreliable servers. Two different models are considered. One is a multi-server retrial queueing system with both regular customers and negative customers. The other is a single-server retrial queue

with negative customers and server interruptions. Closed-form expressions of some relevant performance measurements for both models are obtained.

For the last, we apply some of our findings in queues with abandonments and retrials to a revenue management problem for a queueing system with customer abandonments. By using a mechanism design framework, we identify the optimal price-lead time manus and scheduling policies for different scenarios.