Z-Iteration: Efficient Estimation of Instantaneous Measures
in Time-Dependent Multi-Class Systems
Z-Iteration: Efficient Estimation of Instantaneous Measures
in Time-Dependent Multi-Class Systems
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Date
1998-10-15
Authors
Matta, Ibrahim
Shankar, A. Udaya
Advisor
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Abstract
Multiple-class multiple-resource (MCMR) systems, where a class of
customers requires a 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 flow 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.
(Also cross-referenced as UMIACS-TR-94-116.1)