The MX/G/1 queue with queue length dependent service times. (2001)

• Record Type: Journal Article
• Authors: Choi, Bong Dae; Kim, Yeong Cheol; Shin, Yang Woo; Pearce, Charles E. M.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 14:Number 4(2001)
• Page Start: 399
• Page End: 419
• Publication Date: 2001
• Subjects: MX/G/1 queue -- queue length dependent service time -- transient queue length distribution -- waiting time distribution; 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/S104895330100034X
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : We deal with the M X / G / 1 queue where service times depend on the queue length at the service initiation. By using Markov renewal theory, we derive the queue length distribution at departure epochs. We also obtain the transient queue length distribution at time t and its limiting distribution and the virtual waiting time distribution. The numerical results for transient mean queue length and queue length distributions are given.