Complex-analytic and matrix-analytic solutions for a queueing system with group service controlled by arrivals. (2000)

• Record Type: Journal Article
• Authors: Abolnikov, Lev; Dukhovny, Alexander
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 4(2000)
• Page Start: 415
• Page End: 427
• Publication Date: 2000
• Subjects: arrival-controlled systems -- complex-analytic method -- matrix-analytic method; 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/S1048953300000356
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : A bulk M / G / 1 system is considered that responds to large increases (decreases) of the queue during the service act by alternating between two service modes. The switching rule is based on two “up” and “down” thresholds for total arrivals over the service act. A necessary and sufficient condition for the ergodicity of a Markov chain embedded into the main queueing process is found. Both complex-analytic and matrix-analytic solutions are obtained for the steady-state distribution. Under the assumption of the same service time distribution in both modes, a combined complex-matrix-analytic method is introduced. The technique of “matrix unfolding” is used, which reduces the problem to a matrix iteration process with the block size much smaller than in the direct application of the matrix-analytic method.