Title page for ETD etd-06132007-124519


Type of Document Dissertation
Author Menéndez Gómez, José Mar­ía
URN etd-06132007-124519
Title Computational Methods for Control of Queueing Models in Bounded Domains
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Day, Martin V. Committee Chair
Adjerid, Slimane Committee Member
Ball, Joseph A. Committee Member
Borggaard, Jeffrey T. Committee Member
Herdman, Terry L. Committee Member
Keywords
  • queueing networks
  • bounded domain
  • Markov chain approximations
  • weak convergence
  • Skorokhod problem
Date of Defense 2007-06-08
Availability unrestricted
Abstract
The study of stochastic queueing networks is quite important due to the many applications including transportation, telecommunication, and manufacturing industries. Since there is often no explicit solution to these types of control problems, numerical methods are needed. Following the method of Boué-Dupuis, we use a Dynamic Programming approach of optimization on a controlled Markov Chain that simulates the behavior of a fluid limit of the original process. The search for an optimal control in this case involves a Skorokhod problem to describe the dynamics on the boundary of closed, convex domain. Using relaxed stochastic controls we show that the approximating numerical solution converges to the actual solution as the size of the mesh in the discretized state space goes to zero, and illustrate with an example.

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