Computational Methods for Control of Queueing Models in Bounded Domains

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.

Name thesis:degree_name

Ph. D.

Level thesis:degree_level

doctoral

Discipline thesis:degree_discipline

Mathematics

Department dc:contributor.department

Mathematics

Grantor dc:publisher

Virginia Tech

Year dc:date.issued

2007

Author dc:creator

• Menéndez Gómez, José Mar­ía

Chair dc:contributor.committeechair

• Day, Martin V.

Committee members dc:contributor.committeemember

• Borggaard, Jeffrey T.
• Ball, Joseph A.
• Herdman, Terry L.
• Adjerid, Slimane

• queueing networks
• bounded domain
• Markov chain approximations
• weak convergence
• Skorokhod problem

Statement dc:rights

• In Copyright

Licence dc:rights.uri

• http://rightsstatements.org/vocab/InC/1.0/

Dc Identifier Other

etd-06132007-124519

OAI identifier oai:identifier

oai:vtechworks.lib.vt.edu:10919/28036