Heavy-traffic limits for waiting times in many-server queues with abandonment

By Rishi Talreja, Ward Whitt. 2008

60 citations recorded by the source corpus.

We establish heavy-traffic stochastic-process limits for waiting times in many-server queues with customer abandonment. If the system is asymptotically critically loaded, as in the quality-and-efficiency-driven (QED) regime, then a bounding argument shows that the abandonment does not affect waiting-time processes. If instead the system is overloaded, as in the efficiency-driven (ED) regime, following Mandelbaum et al. [Proceedings of the Thirty-Seventh Annual Allerton Conference on Communication, Control and Computing (1999) 1095--1104], we treat customer abandonment by studying the limiting behavior of the queueing models with arrivals turned off at some time $t$. Then, the waiting time of an infinitely patient customer arriving at time $t$ is the additional time it takes for the queue to empty. To prove stochastic-process limits for virtual waiting times, we establish a two-parameter version of Puhalskii's invariance principle for first passage times. That, in turn, involves proving that two-parameter versions of the composition and inverse mappings appropriately preserve convergence.

Subfields: Electrical and Electronic Engineering, Management Information Systems, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9679898f8042116ab94e338472be4a376937ad2c

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In Management Information Systems

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  2. Tolga Tezcan
  3. Shuangchi He

In Statistics and Probability

  1. J. Dai
  2. Tolga Tezcan
  3. Shuangchi He

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