Monitoring of stochastic particle systems: Analysis and optimization

I. Eliazar*, U. Yechiali

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Consider a system to which particles with random lifetimes flow stochastically. The system is monitored at discrete time epochs following a renewal process. When the system is detected non-empty (upon monitoring), a service procedure is initiated - clearing the system off particles. Once the service procedure is concluded, the system's evolution regenerates. Particles may represent customers or jobs in a queueing system, contaminants in a physical system, hazardous chemical or biological agents in an environmental system, standing buy/sell orders at a brokerage center, etc. This class of stochastic systems is modeled and analyzed. We (i) derive the joint transform of the time-to-first-detection and the number of particles present in the system at that epoch, and compute their statistics; (ii) define and calculate various path-functionals and performance measures of the system; and, (iii) study the issue of optimal monitoring schemes.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalStochastic Models
Issue number1
StatePublished - Jan 2008


  • Discrete-time monitoring
  • Optimal monitoring
  • Queueing theory
  • Stochastic particle systems


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