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October 2003 The attractiveness of the fixed points of a $\cdot/GI/1$ queue
Balaji Prabhakar
Ann. Probab. 31(4): 2237-2269 (October 2003). DOI: 10.1214/aop/1068646384


We consider an infinite tandem of first-come-first-served queues. The service times have unit mean, and are independent and identically distributed across queues and customers. Let $\bI$ be a stationary and ergodic interarrival sequence with marginals of mean $\tau>1$, and suppose it is independent of all service times. The process $\bI$ is said to be a fixed point for the first, and hence for each, queue if the corresponding interdeparture sequence is distributed as $\bI$. Assuming that such a fixed point exists, we show that it is the distributional limit of passing an arbitrary stationary and ergodic interarrival process of mean $\tau$ through the infinite queueing tandem.


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Balaji Prabhakar. "The attractiveness of the fixed points of a $\cdot/GI/1$ queue." Ann. Probab. 31 (4) 2237 - 2269, October 2003.


Published: October 2003
First available in Project Euclid: 12 November 2003

zbMATH: 1057.60090
MathSciNet: MR2016618
Digital Object Identifier: 10.1214/aop/1068646384

Primary: 60K25 , 82B43 , 82C22

Keywords: Couplings , Fixed points , Queueing networks , weak convergence

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • October 2003
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