Stability with uniform bounds for online dial-a-ride problems under reasonable load

In continuously running logistic systems (like in-house pallet transportation systems), finite buffer capacities usually require controls achieving uniformly bounded waiting queues (strong stability). Standard stochastic traffic assumptions (arrival rates below service rates) can, in general, not guarantee these strong stability requirements, no matter which control. Therefore, the worst-case traffic notion of reasonable load was introduced, originally for the analysis of the Online-Dial-a-Ride In continuously running logistic systems (like in-house pallet transportation systems), finite buffer capacities usually require controls achieving uniformly bounded waiting queues (strong stability). Standard stochastic traffic assumptions (arrival rates below service rates) can, in general, not guarantee these strong stability requirements, no matter which control. Therefore, the worst-case traffic notion of reasonable load was introduced, originally for the analysis of the Online-Dial-a-Ride Problem. A set of requests is reasonable if the requests that are presented in a sufficiently large time period can be served in a time period of at most the same length. The rationale behind this concept is that the occurrence of non-reasonable request sets renders the system overloaded, and capacity should be extended. For reasonable load, there are control policies that can guarantee uniformly bounded flow times, leading to strong stability in many cases. Control policies based on naive eoptimization, however, can in general achieve neither bounded flow times nor strong ability. In this chapter, we review the concept and examples for reasonable load. Moreover, we present new control policies achieving strong stability as well as new elementary examples of request sets where naive reoptimization fails.show moreshow less

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Metadaten
Institutes:Mathematik
Author: Sven O. Krumke, Jörg Rambau
Contributing Corporation:Fachbereich Mathematik, TU Kaiserslautern
Year of Completion:2011
SWD-Keyword:Dynamische Optimierung
Tag:online dial-a-ride; online optimization; performance guarantees; reasonable load
Dewey Decimal Classification:510 Mathematik
MSC-Classification:68W27 Online algorithms
90C27 Combinatorial optimization
URN:urn:nbn:de:bvb:703-opus-8672
Source:Chapter 17 of "Distributed Decision Making and Control", Springer Verlag, to appear 2011.
Document Type:Preprint
Language:English
Date of Publication (online):31.05.2011