Routing policies for a partially observable two-server queueing system

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 α 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 which queue the next X job should join. Y jobs (fraction 1−α) are non-observable and non-controllable. They randomly join a queue according to some static routing probability. We address the following main research questions: 1) what penetration level α is needed for effective control, 2) which policy should be implemented at the router, and 3) what is the added value of having more system information (e.g., average service times)? An extensive simulation study reveals that for heavily loaded systems a low penetration level suffices and that the performance (in terms of the average sojourn time) of a simple policy that relies on little system information is close to w-JSQ (weighted join-the-shortestqueue policy) which is optimal in a fully controllable and observable system. The latter result is confirmed by the analysis of deterministic fluid models that approximate the stochastic evolution under large loads.