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August, 1993 Queues in Series in Light Traffic
B. Blaszczyszyn, T. Rolski
Ann. Appl. Probab. 3(3): 881-896 (August, 1993). DOI: 10.1214/aoap/1177005370


We study light traffic approximations for queues in series with renewal arrivals and i.i.d. service time vectors. Formulae for limits of functions of the waiting time at different stations based on single customer effect are obtained for two approaches: dilation and thinning of the arrival process. Interdeparture times from a station possess a one-dependence property in light traffic. This paper complements previous studies of Daley and Rolski and also Asmussen's approach to light traffic limits applied to the cases considered.


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B. Blaszczyszyn. T. Rolski. "Queues in Series in Light Traffic." Ann. Appl. Probab. 3 (3) 881 - 896, August, 1993.


Published: August, 1993
First available in Project Euclid: 19 April 2007

zbMATH: 0781.60081
MathSciNet: MR1233632
Digital Object Identifier: 10.1214/aoap/1177005370

Primary: 60K25

Keywords: $\gamma$-dilation , $\pi$-thinning , $GI/G/1 \rightarrow \cdots \rightarrow G/1$ queue , asymptotically conditionally equivalent families , asymptotically one-dependent family , interdeparture times , Light traffic , single customer effect , waiting time

Rights: Copyright © 1993 Institute of Mathematical Statistics


Vol.3 • No. 3 • August, 1993
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