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Some limit theorems for regenerative queues

Sharma, Vinod (1998) Some limit theorems for regenerative queues. In: Queueing Systems, 30 (3-4). pp. 341-363.

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Official URL: http://portal.acm.org/citation.cfm?id=598038


We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.

Item Type: Journal Article
Publication: Queueing Systems
Publisher: Springer
Additional Information: Copyright of this article belongs to Springer.
Keywords: regenerative queues;rates of convergence;functional limit theorems;continuity.
Department/Centre: Division of Electrical Sciences > Electrical Engineering
Date Deposited: 11 Dec 2009 11:36
Last Modified: 11 Dec 2009 11:36
URI: http://eprints.iisc.ac.in/id/eprint/19245

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