Optimal control and scheduling in a multiclass queueing network: results and conjectures

Abstract

Dynamic scheduling and control in queuing networks are addressed. A two-station queuing network with two types of jobs is studied. Type 1 jobs visit stations, 1 and 2 in sequence, and type 2 jobs visit station 1 only. The problem is to control the (external) arrival processes and the service processes, as well as to schedule the server at station 1 among the two types of jobs. The objective is to minimize a discounted cost function over an infinite time horizon. The approach is based on stochastic intensity representation of point processes. The problem is divided into several cases, each corresponding to a certain parameter range. Optimal control and scheduling are derived for some cases. For the other cases, conjectures for the optimality of certain simple threshold policies are presented.<>