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Quasi loss probability and quasi throughput of the system M/M/1/N→/M/1/1

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Abstract

We consider the two stage tandem queueing systems with finite waiting room capacity. The interdeparture intervals, that is output, from the first stage form the input to the second stage. In general, the interdeparture intervals from the first stage are not mutually independent. Nevertheless, we compute the value of the loss probability for the second stage assuming as if the output from the first stage has i.i.d.. We call the value “quasi-loss probability”. In the same dense, we compute the quasi-throughput from the second stage. We guess the quasi-values may be available as a good approximation to the true values. In a viewpoint of above statement, we investigate these values of the loss probability and the throughput for the system M/M/1/N→/M/1/1.

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Article
This paper discusses a stationary departure process from the M/G/1/N queue. Using a Markov renewal process, we examine the joint density function f k of the k-successive departure intervals. In Section 2, we discuss the covariance of departure intervals. The departure intervals are statistically independent in case of N=0 or N=1, but not in case of N=2 or N=3. In Section 3, f k in the M/M/1/N is shown to be a symmetric function of arrival and service rates, and we find that cov{d 1 ,d k } is not dependent on lagk, for k≤N+1. Further, we prove that the covariance of departure intervals in the dual (reversed) system is equal to one in the original system, for any lag k.
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