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 which queue the next X job should join. Y jobs (fraction p_Y) 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 alpha 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-shortest- queue 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.
Additional Metadata
Keywords partial control, partial observability, routing policies, join the shorter queue
MSC Queueing theory (msc 60K25), Markov and semi-Markov decision processes (msc 90C40), Queueing theory (msc 60K25)
THEME Logistics (theme 3), Information (theme 2)
Editor A. Busic , M. Gribaudo , P. Reinecke
Conference International Conference on Performance Evaluation Methodologies and Tools
Citation
Ellens, W, Kovacs, P, van den Berg, J.L, & Núñez Queija, R. (2015). Routing policies for a partially observable two-server queueing system. In A Busic, M Gribaudo, & P Reinecke (Eds.), .