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Harsha Honnappa: New Insights on Queues in Random Environments

Time: Mon 2021-03-22 15.15 - 16.15

Location: Zoom, meeting ID: 621 4469 8204

Participating: Harsha Honnappa, Purdue

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Abstract

Queueing systems are often subject to clear nonstationarities that arise a as a consequence of diurnal, seasonal or stochastic effects, with the latter emerging as a consequence of being subject to a random environment. The modeling and performance analysis of queues in random environments, in particular, has attracted significant interest in the recent literature. In this talk I will present recent work on approximating performance metrics of infinite server queueing systems that are fed by arrival processes with stochastic arrival intensities that fluctuate rapidly. This setting includes Cox processes, as well as self-excited models such as the Hawkes process. At the outset, it is clear that computing performance metrics in this setting cannot be achieved in closed form, raising the question of how to compute approximations. In particular, one is confronted by the question of whether to use an annealed setting (where the performance measures are “averaged” or “annealed” over the random environment) or a quenched setting (where the performance measures are conditioned on the random environment). I will present our on-going work studying both settings establishing asymptotic approximations in three flavors: as asymptotic “refinements”, fluid-scale limits and diffusive-scale limits of performance measures. In the case of infinite server queues driven by Cox processes, our results show that there exists a parameter regime where the quenched limits exist (and coincide with the annealed limits) and a complementary regime where they may not, suggesting that the quenched analysis, though seemingly more robust and simpler to carry out, should be used with caution.

This is based on joint work with Peter W. Glynn, Zeyu Zheng at Stanford University and Samy Tindel, Aaron Nung-Kwan Yip and Yiran Liu at Purdue University.

Zoom notes: This meeting ID – 621 4469 8204 – will be the recurring meeting for the Statistics and Probability Seminar.