Routing policies for a partially observable two-server queueing system

Abstract

We consider a queueing system controlled by decisions based on partial state information. The motivation for this work stems from road traffic, in which drivers may, or may not, be subscribed to a smartphone application for dynamic route planning. Our model consists of two queues with independent exponential service times, serving two types of jobs. Arrivals occur according to a Poisson process; a fraction alpha of the jobs (type X) is observable and controllable. At all times the number of X jobs in each queue and their individual positions are known. Upon its arrival a router decides wh