HEAVY TRAFFIC CONVERGENCE OF A CONTROLLED, MULTICLASS QUEUING SYSTEM

This paper provides a rigorous proof of the connection between the opt imal sequencing problem for a two-station, two-customer-class queueing network and the problem of control of a multidimensional diffusion pr ocess, obtained as a heavy traffic limit of the queueing problem. In p articular, the diffusion problem, which is one of ''singular control'' of a Brownian motion, is used to develop policies which are shown to be asymptotically nearly optimal as the traffic intensity approaches o ne in the queueing network. The results are proved by a viscosity solu tion analysis of the related Hamilton-Jacobi-Bellman equations.