Characterizing the departure process of a single server queue from the embedded Markov renewal process at departures

In the literature, performance analyses of numerous single server queues ar e done by analyzing the embedded Markov renewal processes at departures. In this paper, we characterize the departure processes for a large class of s uch queueing systems. Results obtained include the Laplace-Stieltjes transf orm (LST) of the stationary distribution function of interdeparture times a nd recursive formula for {c(n) drop the covariance between interdeparture t imes 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 {c(n)} can be computed through an explicit recursive formula. With this formula, we can c alculate {c(n)} very quickly, which provides deeper insight into the correl ation structure of the departure process compared to the previous research. Numerical examples show that increasing server irregularity (i.e., the ran domness of the service time distribution) destroys the short-range dependen ce of interdeparture times, while increasing system load strengthens both t he short-range and the long-range dependence of interdeparture times. These findings show that the correlation structure of the departure process is g reatly 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 ap plication to the performance analysis of a series of queues, and the result s appear to be accurate.