Complete Computational Solution of Multi-Class Fluid Queueing Communication Network Models with Piecewise Constant Rate Inputs

Abstract

This paper develops an explicit characterization and computation of the queueing processes associated with finite buffered multiclass fluid queues and their tandem networks under strict priority and with PieceWise Constant Rate (PWCR) inputs which arise in the performance analysis of communication networks. Analytical and exact computational solutions are developed for accepted arrival, fluid level and departure processes which allow solutions for all other queueing processes. A decomposition of the multiclass queue into a hierarchical sequence of single class queues, termed Virtual Queues, is established and the solutions of each class of the original queue are computed from those of the Virtual Queues taking into account the loosely coupled dynamics of these Virtual Queues. A uniform time sampling sequence, dynamically constructed from the input rate change instances and the boundary hitting times, is employed to develop the iterative transient sample path solutions of all the queueing processes. The processes of a multiclass queue with PWCR inputs are shown to be PWCR processes. The computational solution is extended to tandem networks of multiclass queues in which a class can have different static priorities along its path. The developed algorithm is applied to solve a tandem communication network with three-state Markov modulated voice source inputs. A parametric study of the voice network in terms of long-term time-averaged behaviour of its queueing processes is carried out.