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.
|Title of host publication||2022 IEEE 61st Conference on Decision and Control, CDC 2022|
|Publisher||Institute of Electrical and Electronics Engineers Inc.|
|Number of pages||8|
|State||Published - 2022|
|Event||61st IEEE Conference on Decision and Control, CDC 2022 - Cancun, Mexico|
Duration: 6 Dec 2022 → 9 Dec 2022
|Name||Proceedings of the IEEE Conference on Decision and Control|
|Conference||61st IEEE Conference on Decision and Control, CDC 2022|
|Period||6/12/22 → 9/12/22|
Bibliographical notePublisher Copyright:
© 2022 IEEE.
ASJC Scopus subject areas
- Control and Systems Engineering
- Modeling and Simulation
- Control and Optimization