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

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