Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment

Abstract

Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about waiting time and patience distributions in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated waiting times. Assuming a regenerative structure 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. A small simulation study and a real data example are presented.

Keywords:

• Dependent survival data
• Empirical process
• Queues with abandon-ment
• Regenerative sequence
• Tele-queues

Mathematics Subject Classification:

• 90B22
• 62G09

Acknowledgments

The research is supported by the Danish Natural Science Research Council, grant 272-06-0442, “Point Process Modelling and Statistical Inference”. We would like to thank Professor Avishai Mandelbaum, Industrial Engineering and Management, Technion, Israel for providing access to the call center data.