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An ergodic control problem for many-server multiclass queueing systems with cross-trained servers

Anup Biswas, Indian Institute of Science Education and Research-Pune


Abstract
A \(M/M/N+M\) queueing network is considered with \(d\) independent customer classes and \(d\) server pools in Halfin–Whitt regime. Class \(i\) customers has priority for service in pool \(i\) for \(i=1, \ldots, d\), and may access some other pool if the pool has an idle server and all the servers in pool \(i\) are busy. We formulate an ergodic control problem where the running cost is given by a non-negative convex function with polynomial growth. We show that the limiting controlled diffusion is modelled by an action space which depends on the state variable. We provide a complete analysis for the limiting ergodic control problem and establish asymptotic convergence of the value functions for the queueing model.

AMS 2000 subject classifications: Primary 93E20; Secondary 60H30, 35J60

Keywords: Multi-class Markovian queues, reneging/abandonment, Halfin-Whitt (QED) regime, heavy-traffic, long time-average control, scheduling control, stable Markov optimal control, Hamilton-Jacobi-Bellman equation, asymptotic optimality

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Biswas, Anup, An ergodic control problem for many-server multiclass queueing systems with cross-trained servers, Stochastic Systems, 7, (2017), 1-46 (electronic). DOI: 10.1214/15-SSY209.

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