Performance bounds and pathwise stability for generalized vacation and polling systems
成果类型：
Article
署名作者：
Altman, E; Foss, S; Riehl, E; Stidham, S
署名单位：
Inria; Universite Cote d'Azur; University of North Carolina; University of North Carolina Chapel Hill
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.46.1.137
发表日期：
1998
页码：
137-148
关键词：
摘要：
We consider a generalized Vacation or polling system, modeled as an input-output process operating over successive cycles, in which the service mechanism can be in an up mode (processing) or down mode (e.g., vacation, walking). Our primary motivation is polling systems, in which there are several queues and the server moves cyclically between them providing some service in each. Our basic assumption is that the amount of work that leaves the system in a cycle is no less than the amount present at the beginning of the cycle. This includes the standard gated and exhaustive policies for polling systems in which a cycle begins whenever the server arrives at some prespecified queue. The input and output processes satisfy model-dependent conditions: pathwise bounds on the average rate and the burstiness (Cruz bounds); existence of long-nm average rates; a pathwise generalized Law of the Iterated Logarithm; or exponentially or polynomially bounded tail probabilities of burstiness. In each model we show that these properties are inherited by performance measures such as the workload and output processes, and that the system is stable (in a model-dependent sense) if the input rate is smaller than the up-mode processing rate.