Light-Traffic Analysis for Queues with Spatially Distributed Arrivals

Light-Traffic Analysis for Queues with Spatially Distributed Arrivals

We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is "greedy," in the sense that he always moves (with const...

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Veröffentlicht in:Mathematics of Operations Research. - Institute for Operations Research and the Management Sciences. - 21(1996), 1, Seite 135-157
1. Verfasser: Kroese, Dirk P. (VerfasserIn)
Weitere Verfasser: Schmidt, Volker
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 1996
Zugriff auf das übergeordnete Werk:Mathematics of Operations Research
Schlagworte:Queueing theory Continuous polling system Greedy server Poisson arrivals Light-traffic derivative Taylor-expansion Queue length Workload General stationary input Business mehr... Applied sciences Mathematics Biological sciences
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520 |a We consider the following continuous polling system: Customers arrive according to a homogeneous Poisson process (or a more general stationary point process) and wait on a circle in order to be served by a single server. The server is "greedy," in the sense that he always moves (with constant speed) towards the nearest customer. The customers are served according to an arbitrary service time distribution, in the order in which they are encountered by the server. First-order and second-order Taylor-expansions are found for the expected configuration of customers, for the mean queue length, and for expectation and distribution function of the workload. It is shown that under light traffic conditions the greedy server works more efficiently than the cyclically polling server. 
540 |a Copyright 1996 Institute for Operations Research and the Management Sciences 
650 4 |a Queueing theory 
650 4 |a Continuous polling system 
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650 4 |a Poisson arrivals 
650 4 |a Light-traffic derivative 
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650 4 |a Queue length 
650 4 |a Workload 
650 4 |a General stationary input 
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650 4 |a Mathematics  |x Pure mathematics  |x Probability theory  |x Random variables  |x Stochastic processes  |x Poisson process 
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650 4 |a Applied sciences  |x Engineering  |x Transportation  |x Traffic 
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700 1 |a Schmidt, Volker  |e verfasserin  |4 aut 
773 0 8 |i Enthalten in  |t Mathematics of Operations Research  |d Institute for Operations Research and the Management Sciences  |g 21(1996), 1, Seite 135-157  |w (DE-627)320435318  |w (DE-600)2004273-5  |x 15265471  |7 nnns 
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952 |d 21  |j 1996  |e 1  |h 135-157