Heavy Traffic Convergence of a Controlled, Multiclass Queueing System
- 1 November 1996
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Control and Optimization
- Vol. 34 (6) , 2133-2171
- https://doi.org/10.1137/s0363012994265882
Abstract
This paper provides a rigorous proof of the connection between the optimal sequencing problem for a two-station, two-customer-class queueing network and the problem of control of a multidimensional diffusion process, obtained as a heavy traffic limit of the queueing problem. In particular, 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 one in the queueing network. The results are proved by a viscosity solution analysis of the related Hamilton--Jacobi--Bellman equations.Keywords
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