On the joint distribution of the departure intervals in an M/G/1/N queue

On the joint distribution of the departure intervals in an M/G/1/N queue

0.00 Avg rating0 Votes
Article ID: iaor19921957
Country: Japan
Volume: 34
Issue: 4
Start Page Number: 422
End Page Number: 435
Publication Date: Dec 1991
Journal: Journal of the Operations Research Society of Japan
Authors:
Keywords: statistics: distributions
Abstract:

This paper discussed a stationary departure process from the M/G/1/N queue. Using a Markov renewal process, it examines the joint density function fk of the k-successive departure intervals. In Section 2, the paper discusses 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, fk in the M/M/1/N is shown to be a symmetric function of arrival and service rates, and it is found that cov(d1,dk) is not dependent on lagk, for k•N+1. Further, the paper proves that the covariance of departure intervals in the dual (reversed) system is equal to one in the original system, for any lagk.

Reviews

Required fields are marked *. Your email address will not be published.