Functional properties of throughput in tandem lines with unreliable servers and finite buffers

optimization;queueing theory;production

Sample-path solutions for simulation optimization problems and stochastic variational inequalities

inequality;simulation;optimization

Sample-Path Optimization of Buffer Allocations in a Tandem Queue - Part I:Theoretical Issues

This is the first of two papers dealing with the optimal bu er allocation problem in tandem manufacturing lines with unreliable machines.We address the theoretical issues that arise when using sample-path optimization, a simulation-based optimization method, to solve this problem.Sample-path optimization is a recent method to optimize performance functions of stochastic systems.By exploiting the fact that the performance function we want to optimize is the almost sure limit of a sequence of random functions, it overcomes some of the di culties from which variants of stochastic approximation methods su er.We provide a mathematical framework that makes use of a function space construction to model the dependence of throughput on bu er capacities and maximum ow rates of machines.Using this framework we prove various structural properties of throughput and show how these properties, along with a niceness condition on the steady-state, can be used to prove that the sample-path optimization method converges almost surely when applied to the bu er allocation problem.Among the properties established, monotonicity in bu er capacities and in ma- chine ow rates are especially important.Although monotonicity results of this nature have appeared in the literature for discrete tandem lines, as far as we are aware the kind of analysis we present here has not yet been done for continuous tandem lines.