Dynamic Scheduling for Markov Modulated Single-server Multiclass Queueing Systems in Heavy Traffic

TL;DR

This paper analyzes optimal scheduling policies for a single-server multiclass queueing system in heavy traffic with a Markov-modulated environment, demonstrating the asymptotic optimality of an averaged cμ-policy across different environmental change rates.

Contribution

It introduces a unified approach to derive asymptotically optimal scheduling policies in Markov-modulated heavy traffic queueing systems, extending classical policies to dynamic environments.

Findings

Averaged cμ-policy is asymptotically optimal in heavy traffic.

The analysis covers fast, fixed, and slow environment changes.

Functional limit theorems underpin the convergence results.

Abstract

This paper studies a scheduling control problem for a single-server multiclass queueing network in heavy traffic, operating in a changing environment. The changing environment is modeled as a finite state Markov process that modulates the arrival and service rates in the system. Various cases are considered: fast changing environment, fixed environment and slow changing environment. In each of the cases, using weak convergence analysis, in particular functional limit theorems for renewal processes and ergodic Markov processes, it is shown that an appropriate "averaged" version of the classical c\mu -policy (the priority policy that favors classes with higher values of the product of holding cost c and service rate \mu) is asymptotically optimal for an infinite horizon discounted cost criterion.