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Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment
Authors:Anders Gorst-rasmussen  Martin B Hansen
Institution:1. Department of Mathematical Sciences , Aalborg University , Aalborg East, Denmark gorst@math.aau.dk;3. Department of Mathematical Sciences , Aalborg University , Aalborg East, Denmark
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
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