Joint routing and scheduling control in a two-class network with a flexible server

In this study we analyze a queueing model with a Gurvich structure. In such a network, the controller may route incoming jobs to different classes, but they are routed to the same server. This structure, although it falls into the general class of stochastic processing networks, is somewhat unconventional. We focus on a single-server two-class version of a Gurvich network in this paper. For a Poisson arrival stream and exponential service rates, we develop a Markov decision process representation of the system and prove structural results on optimal routing and scheduling controls. We show that the optimal policy uses \(c\mu \) scheduling and switching curve routing. We also investigate the fluid model and perturbation expansions thereof, which are useful in deriving near-optimal policies in the original network.