Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment

Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about the waiting time and patience distribution in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated successive waiting times. Assuming a regenerative structure of the sequence of offered waiting times, we establish asymptotic properties of estimators of limiting distribution functions and derived functionals. We discuss construction of bootstrap confidence intervals and statistical tests, including a simple bootstrap two-sample test for comparing patience distributions. The methods are exemplified in a small simulation study, and a real data example is given involving comparison of patience distributions for two customer classes in a call center.