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

TL;DR

This paper analyzes an ergodic control problem for large-scale multiclass queueing systems with cross-trained servers, providing a comprehensive limit diffusion model and convergence results in the Halfin-Whitt regime.

Contribution

It introduces a novel ergodic control framework for multiclass queueing networks with cross-trained servers and establishes asymptotic convergence of the value functions.

Findings

Limiting controlled diffusion model with state-dependent action space

Complete analysis of the ergodic control problem

Asymptotic convergence of queueing model's value functions

Abstract

AM/M/N+Mqueueingnetworkisconsideredwithdindependentcustomerclasses and d server pools in Halfin-Whitt regime. Class i customers has priority for service in pool i for i = 1, . . . , 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 modeled 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