Characterizing the departure process of a single server queue from the embedded Markov renewal process at departures |
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Authors: | Yeh Ping-Cheng Chang Jin-Fu |
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Institution: | (1) Department of Electrical Engineering, National Taiwan University, Taipei, Taiwan |
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Abstract: | In the literature, performance analyses of numerous single server queues are done by analyzing the embedded Markov renewal
processes at departures. In this paper, we characterize the departure processes for a large class of such queueing systems.
Results obtained include the Laplace–Stieltjes transform (LST) of the stationary distribution function of interdeparture times
and recursive formula for {cn ≡ the covariance between interdeparture times of lag n}. Departure processes of queues are difficult to characterize and for queues other than M/G/1 this is the first time that
{cn} can be computed through an explicit recursive formula. With this formula, we can calculate {cn} very quickly, which provides deeper insight into the correlation structure of the departure process compared to the previous
research. Numerical examples show that increasing server irregularity (i.e., the randomness of the service time distribution)
destroys the short-range dependence of interdeparture times, while increasing system load strengthens both the short-range
and the long-range dependence of interdeparture times. These findings show that the correlation structure of the departure
process is greatly affected by server regularity and system load. Our results can also be applied to the performance analysis
of a series of queues. We give an application to the performance analysis of a series of queues, and the results appear to
be accurate.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | departure process M/G/1 type correlation structure covariance structure |
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