Z-iteration: Eecient Estimation of Instantaneous Measures in Time-dependent Multi-class Systems

Multiple-class multiple-resource (MCMR) systems, where each class of customers requires a particular set of resources, are common. These systems are often analyzed under steady-state conditions. We describe a simple numerical-analytical method, referred to as Z-iteration, to estimate instantaneous (and steady-state) probability measures of time-dependent systems. The key idea is to approximate the relationship between certain instantaneous measures by the relationship between their steady-state counterparts, and use this approximation to solve dynamic ow equations. We show the generality of the Z-iteration by applying it to an integrated communication network, a parallel database server, and a distributed batch system. Validations against exact numerical solutions and discrete-event simulations show the accuracy and computational advantages of the Z-iteration.