Optimal assignment of jobs to processors under heavy traffic: bursty arrivals and requirements

The paper deals with the almost optimal assignment of jobs from several arriving random streams to one of a bank of processors. Owing to the difficulty of the general problem, a heavy traffic approach is used. The required work depends on the assigned processor. Several information structures (data on which the control is based) are considered. The assignment can be made on arrival or when the job is to be processed. There can be rather general nonlinear cost functions and other complications. Under reasonably general conditions, the optimal costs for the physical systems converge to the optimal cost for the heavy traffic limit problem, as the heavy traffic parameter goes to its limit. We focus on one case of bursty arrivals and work requirements (the bursts depending on randomly varying environmental factors).