University of Texas at Arlington
The authors consider queuing systems with coupled processors, where the service rate at each queue varies depending on the set of queues in the system with non-zero queue lengths. In general, such queuing systems are very difficult to analyze and steady state queue length distributions are known only for two-queue systems. The coupled-processors model arises naturally in the study of several systems where a resource is shared by several classes of customers. They study the stochastic recursive equations that govern such systems, and obtain lower and upper bounds on the moments of the queue length by formulating a moments problem and solving a semidefinite relaxation of the original problem.