Optimal control of a multiclass, flexible queueing system

We consider a general class of queueing systems with multiple job types and a flexible service facility. The arrival times and sizes of incoming jobs are random, and correlations among the sizes of arriving job types are allowed. By choosing among a finite set of configurations, the facility can dynamically control the rates at which it serves the various job types. We define system work at any given time as the minimum time required to process all jobs currently in the backlog. This quantity is determined by solving a linear program defined by the set of processing configurations. The problem we study is how to dynamically choose configurations to minimize the time average system work. Using bounds and heuristics, we analyze a class of service policies that is provably asymptotically optimal as system utilization approaches one, as well as a policy that in numerical studies performs near-optimally in moderate traffic. Our analysis also yields a closed-form expression for the optimal, average work in heavy traffic. This general problem has a number of applications in job shop and flexible manufacturing, in service organizations, and in the management of parallel processing and distributed database systems.