ON THE JOINT DISTRIBUTION OF THE DEPARTURE INTERVALS IN AN M/G/1/N QUEUE

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  • Ishikawa Akihiko
    Fundamentals of Natural Science College of Humanities and Social Sciences Iwate University

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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 = O 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 lag k, 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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