Stability of Open Multiclass Queueing Networks via Fluid Models

This paper surveys recent work on the stability of open multiclass queueing networks via fluid models. We recapitulate the stability result of Dai [8]. To facilitate study of the converse of the stability result, we distinguish between the notion of fluid limit and that of fluid solution. We define the stability region of a service discipline and the global stabil-ity region of a network. Examples show that piecewise linear Lyapunov functions are powerful tools in determining stability regions. Stability, queueing networks, fluid models, scheduling, performance analysis, Harris recurrence, heavy traffic, Brownian models.

Scheduling Manufacturing Systems Of Re-Entrant Lines

Re-entrant lines are manufacturing systems where parts may return more than once to the same machine, for repeated stages of processing. Examples of such systems are semiconductor manufacturing plants. We consider the problems of scheduling such systems to reduce manufacturing lead times, variations in the manufacturing lead times, or holding costs. We assume a deterministic model, which allows for bursty arrivals. We show how one may design scheduling policies to help in meeting these objectives. To reduce the mean or variance of manufacturing lead time, we design a class of scheduling policies called Fluctuation Smoothing policies. To reduce the holding costs in systems with set--up times, we introduce the class of Clear--A--Fraction scheduling policies. We study the stability and performance of these scheduling policies. We illustrate how scheduling policies can be unstable in that the levels of the buffers become unbounded. However, we show that all Least Slack policies, including..