2 research outputs found
Heavy-Traffic Optimality of a Stochastic Network under Utility-Maximizing Resource Control
We study a stochastic network that consists of a set of servers processing
multiple classes of jobs. Each class of jobs requires a concurrent occupancy of
several servers while being processed, and each server is shared among the job
classes in a head-of-the-line processor-sharing mechanism. The allocation of
the service capacities is a real-time control mechanism: in each network state,
the control is the solution to an optimization problem that maximizes a general
utility function. Whereas this resource control optimizes in a ``greedy''
fashion, with respect to each state, we establish its asymptotic optimality in
terms of (a) deriving the fluid and diffusion limits of the network under this
control, and (b) identifying a cost function that is minimized in the diffusion
limit, along with a characterization of the so-called fixed point state of the
network.Comment: 33 pages, 3 figure
Diffusion approximations for Kumar-Seidman network under a priority service discipline
Unlike for a single-class queueing network, diffusion approximations for a multiclass queueing network may not exist under the heavy traffic condition. In this paper, we derive a necessary and sufficient condition for the existence of the diffusion approximation for a four-class two-station multiclass queueing network (known as Kumar-Seidman network) under a priority service discipline