Exponential families and regression in the Monte Carlo study of queues and random walks. (English) Zbl 0716.62082

Asmussen, Søren

Ann. Stat. 18, No. 4, 1851-1867 (1990).

Summary: An importance sampling method studied by D. Siegmund [ibid. 4, 673- 684 (1976; Zbl 0353.62044)] and the author [Stochastic Processes Appl. 20, 213-229 (1985; Zbl 0574.60095)] in the case of waiting time probabilities is extended to the mean and other functionals. The ideas involve exponential families of queues and control variates (regression), and it is found both from theory and practice that the method is dramatically better than standard tools like regenerative simulation or sample-mean estimation, not least under heavy traffic conditions.

MSC:

62M05	Markov processes: estimation; hidden Markov models
65C05	Monte Carlo methods
62J05	Linear regression; mixed models

Keywords:

variance reduction; regression; random walk; importance sampling method; waiting time probabilities; exponential families of queues; control variates; regenerative simulation; sample-mean estimation; heavy traffic conditions

Citations:

Zbl 0353.62044; Zbl 0574.60095