A Robust Server-Effort Policy for Fluid Processing Networks

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. C...

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Bibliographic Details
Published in:Proceedings of the IEEE Conference on Decision & Control pp. 5902 - 5909
Main Authors: Ship, Harold, Shindin, Evgeny, Boni, Odellia, Dattner, Itai
Format: Conference Proceeding
Language:English
Published: IEEE 06.12.2022
Subjects:
Fluids
Linear programming
Numerical models
Optimal control
Process control
Sequential analysis
Uncertainty
ISSN:2576-2370
Online Access:Get full text
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Summary: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.
ISSN:2576-2370
DOI:10.1109/CDC51059.2022.9992816