A Robust Server-Effort Policy for Fluid Processing Networks

• Main Authors: Ship, Harold, Shindin, Evgeny, Boni, Odellia, Dattner, Itai
• Format: Journal Article
• Language: English
• Published: 10-07-2022
• Subjects: Mathematics - Optimization and Control
• DOI: 10.48550/arxiv.2207.04472

Multi-Class Processing Networks describe a set of servers that perform
multiple classes of jobs on different items. A useful and tractable way to find
an optimal control for such a network is to approximate it by a fluid model,
resulting in a Separated Continuous Linear Programming (SCLP) problem. Clearly,
arrival and service rates in such systems suffer from inherent uncertainty. A
recent study addressed this issue by formulating a Robust Counterpart for SCLP
models with budgeted uncertainty which provides a solution in terms of
processing rates. This solution is transformed into a sequencing policy.
However, in cases where servers can process several jobs simultaneously, a
sequencing policy cannot be implemented. In this paper, we propose to use in
these cases a a resource allocation policy, namely, the proportion of server
effort per class. We formulate Robust Counterparts of both processing rates and
server-effort uncertain models for four types of uncertainty sets: box,
budgeted, one-sided budgeted, and polyhedral. We prove that server-effort model
provides a better robust solution than any algebraic transformation of the
robust solution of the processing rates model. Finally, to get a grasp of how
much our new model improves over the processing rates robust model, we provide
results of some numerical experiments.