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An ergodic control problem for many-server multiclass queueing systems with cross-trained servers. (English) Zbl 1382.93036

Summary: A Markovian 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.

MSC:

93E20 Optimal stochastic control
90B22 Queues and service in operations research
60K25 Queueing theory (aspects of probability theory)
60H30 Applications of stochastic analysis (to PDEs, etc.)
35J60 Nonlinear elliptic equations
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