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

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.