Complete Solution of a Markov Modulated Tandem Fluid Queueing Model of a Voice Network

This paper presents a complete pathwise computational transient solution of a stochastic fluid tandem queueing network model for a communication network carrying voice traffic. The three state Markov modulated voice source input is considered as a special case of a PieceWise Constant Rate (PWCR) class of inputs. Employing a uniform sampling, an exact iterative algorithm for computing the queueing processes in finite buffered fluid queues with PWCR inputs is presented. The PWCR processes are shown to form a closed class for describing all the queueing processes of tandem queueing networks which leads to the complete solutions for a tandem network with PWCR input. Numerical solution of the tandem network of two queues with a three-state Markov modulated model of a voice source and a parametric study of its time average behaviour is carried out.