Title: Analysis of a two-node task-splitting feedback tandem queue with infinite buffers by functional equation

Authors: Aliakbar Montazer Haghighi, Dimitar P. Mishev

Addresses: Department of Mathematics, Prairie View A&M University, PO Box 519 – MS2225, Prairie View, Texas 77446 0519, USA. ' Department of Mathematics, Prairie View A&M University, PO Box 519 – MS2225, Prairie View, Texas 77446 0519, USA

Abstract: In this article, a two-node single-processor Markovian tandem queueing system with task splitting and feedback is considered. Each node has an infinite buffer before it and, thus, no blocking is possible in the system. Splitting feature is added to the model considered and it makes it a novel tandem queue. The functional equation developed from the generating function applied to the system of difference equations is solved using Riemann-Hilbert problem. The mean of the stationary queue length at each node is found. An algorithm is given for computation of performance measures. Using approximation, a numerical example is offered to illustrate the workability of the algorithm.

Keywords: task splitting; feedback; functional equations; infinite buffers; tandem queueing systems; performance measures.

DOI: 10.1504/IJMOR.2009.022884

International Journal of Mathematics in Operational Research, 2009 Vol.1 No.1/2, pp.246 - 277

Published online: 31 Jan 2009 *

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