A routing problem in a simple queueing system with non-classical information structure

The following routing problem in a queueing system with non-classical information structure is investigated in discrete time. A service system consists of two service stations and two controllers; one controller is affiliated with each station. Each station has an infinite size buffer. The service stations provide the same service with identical Bernoulli(μ) service time distributions and identical holding costs. Customers requiring service arrive at one of the service stations. The processes describing the two arrival streams are independent Bernoulli (λ). At any time, a controller can route one of the waiting customers in its own service station to the other service station. Each controller knows perfectly the workload in its own station. Furthermore, it observes perfectly the arrival stream to its own station as well as the arrivals due to customers routed from the other service station. The structure of the controllers' routing policies that minimize the total expected holding cost is determined. Under certain conditions on the initial workload at each station, the controllers' optimal routing policies are explicitly determined.