Stability with Uniform Bounds for On-line Dial-a-Ride Problems under Reasonable Load

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Krumke, Sven O. ; Rambau, Jörg:
Stability with Uniform Bounds for On-line Dial-a-Ride Problems under Reasonable Load.
In: Johansson, Rolf ; Rantzer, Anders (Hrsg.): Distributed Decision Making and Control. - London : Springer , 2012 . - pp. 387-412 . - (Lecture Notes in Control and Information Sciences ; 417 )
ISBN 978-1-447-12264-7

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Abstract in another language

In continuously running logistic systems (like in-house pallet transportation systems), finite buffer capacities usually require controls that can achieve uniformly bounded waiting queues (strong stability). Standard stochastic traffic assumptions (arrival rates below service rates) cannot, in general, guarantee these strong stability requirements, no matter which control policy is used. So, the worstcase traffic notion of reasonable load was introduced, originally for the analysis of the on-line 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 nonreasonable request sets renders the system overloaded, requiring capacity 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 naïve reoptimization, however, can in general achieve neither bounded flow times nor strong stability. 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 naïve reoptimization fails.