An MX/GI/1/N queue with close-down and vacation times. (1999)

• Record Type: Journal Article
• Authors: Frey, Andreas; Takahashi, Yoshitaka
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 12:Number 1(1999)
• Page Start: 63
• Page End: 83
• Publication Date: 1999
• Subjects: MX/GI/1/N type queue -- finite capacity -- close-down time -- server vacation -- exhaustive -- queue length -- acceptance strategy -- loss probability -- waiting time; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953399000064
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : An M X / G I / 1 / N finite capacity queue with close-down time, vacation time and exhaustive service discipline is considered under the partial batch acceptance strategy as well as under the whole batch acceptance strategy. Applying the supplementary variable technique the queue length distribution at an arbitrary instant and at a departure epoch is obtained under both strategies, where no assumption on the batch size distribution is made. The loss probabilities and the Laplace-Stieltjes transforms of the waiting time distribution of the first customer and of an arbitrary customer of a batch are also given. Numerical examples give some insight into the behavior of the system.