Thesis Defense :: Spatial Service Systems Modeled as Stochastic Integrals of Marked Point Processes

Event Details
  • Date/Time:
    • Thursday June 30, 2005
      11:00 am - 12:00 am
  • Location: Groseclose Building, Room 226A
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Contact
Barbara Christopher
Industrial and Systems Engineering
Contact Barbara Christopher
404.385.3102
Summaries

Summary Sentence: Thesis Defense :: Spatial Service Systems Modeled as Stochastic Integrals of Marked Point Processes

Full Summary: Thesis Defense :: Spatial Service Systems Modeled as Stochastic Integrals of Marked Point Processes

We characterize the equilibrium behavior of a class of stochastic particle systems, where particles (representing customers, jobs, animals, molecules, etc.) enter a space randomly through time, interact, and eventually leave. The results are useful for analyzing the dynamics of randomly evolving systems including spatial service systems, species populations, and chemical reactions. Such models with interactions arise in the study of species competitions and systems where customers compete for service (such as wireless networks).

The models we develop are space-time measure-valued Markov processes. Specifically, particles enter a space according to a space-time Poisson process and are assigned independent and identically distributed attributes. The attributes may determine their movement in the space, and whenever a new particle arrives, it randomly deletes particles from the system according to their attributes.

Our main result establishes that spatial Poisson processes are natural temporal limits for a large class of particle systems.
Other results include the probability distributions of the sojourn times of particles in the systems, and probabilities of numbers of customers in spatial polling systems without Poisson limits.

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H. Milton Stewart School of Industrial and Systems Engineering (ISYE)

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Status
  • Created By: Barbara Christopher
  • Workflow Status: Published
  • Created On: Oct 8, 2010 - 7:38am
  • Last Updated: Oct 7, 2016 - 9:52pm