### Hanyi Chen (University of Edinburgh)

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

*Wednesday 25 March 2015 at 15.00, JCMB 6206*

##### Abstract

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 analysing the stability of
these systems and derive the probability distribution of the number of matches
up to some finite time given the number of arrivals. 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. 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.

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