Title: Some results on queueing systems in the presence of catastrophes
Speaker: Antonio Di Crescenzo, University of Salerno, Italy
Date: Friday, May 28, 2004 11:00am
Location: DIMACS Center, CoRE Bldg, Room 431, Rutgers University, Busch Campus, Piscataway, NJ
In recent years attention has been focused on certain extensions of queueing systems that include the effect of catastrophes. This consists of adding to standard assumptions the hypothesis that the number of customers is istantly reset to zero at certain random times.
In this talk the analysis of the M/M/1 queue in the presence of catastrophes is presented. It is shown that the transient probabilities can be obtained by a non-conventional straightforward method, and can be expressed as the sum of the steady-state probabilities and of a time-dependent term. Various results on the busy period and on the catastrophe waiting time are also given. A heavy-traffic approximation for the M/M/1 queueing model is then proposed. This turns out to be a Wiener-type process with jumps. The approximating busy period density for the continuous process is obtained and the goodness of the approximation is discussed.
Some of the above results are finally extended to more general families of birth-death processes,including the time-non-homogeneous M/M/1 and the M/M/infinity queueing systems with catastrophes.