Buke, Burak

Antal, Tibor

Rasonyi, Miklos

Chen, Hanyi

Engineering and Physical Sciences Research Council (EPSRC)

2015-09-11T14:47:32Z

2015-09-11T14:47:32Z

2015-11-26

In this work we introduce a novel queueing model with two classes of users in which, instead of accessing a resource, users wait in the system to match with a candidate from the other class. The users are selective and the matchings occur probabilistically. This new model is useful for analysing the traffic in web portals that match people who provide a service with people who demand the same service, e.g. employment portals, matrimonial and dating sites and rental portals. We first provide a Markov chain model for these systems and derive the probability distribution of the number of matches up to some finite time given the number of arrivals. We then prove that if no control mechanism is employed these systems are unstable for any set of parameters. We suggest four different classes of control policies to assure stability and conduct analysis on performance measures under the control policies. Contrary to the intuition that the rejection rate should decrease as the users become more likely to be matched, we show that for certain control policies the rejection rate is insensitive to the matching probability. Even more surprisingly, we show that for reasonable policies the rejection rate may be an increasing function of the matching probability. We also prove insensitivity results related to the average queue lengths and waiting times. Further, to gain more insight into the behaviour of probabilistic matching systems, we propose approximation methods based on fluid and diffusion limits using different scalings. We analyse the basic properties of these approximations and show that some performance measures are insensitive to the matching probability agreeing with the results found by the exact analysis. Finally we study the optimal control and revenue management for the systems with the objective of profit maximization. We formulate mathematical models for both unobservable and observable systems. For an unobservable system we suggest a deterministic optimal control, while for an observable system we develop an optimal myopic state dependent pricing.

http://hdl.handle.net/1842/10570

en

The University of Edinburgh

B. Buke and H. Chen. Stabilizing policies for probabilistic matching systems. Queueing Systems, 80:35-69, June 2015.

H. Chen and M. Z. Frank. State dependent pricing with a queue. IIE Transactions, pages 847-860, 2007.

H. Chen and D. D. Yao. Fundamentals of Queuing Networks, Performance, Asymptotics, and Optimization. Springer, New York, 2001.

matching systems

stability

admission control policies

rejection rates

fluid approximation

diffusion approximation

optimal control

Probabilistic matching systems: stability, fluid and diffusion approximations and optimal control

Thesis or Dissertation

Doctoral

PhD Doctor of Philosophy