The departure process of an N/G/1 queue
Performance Evaluation
The Markov-modulated Poisson process (MMPP) cookbook
Performance Evaluation
Departure Processes of BMAP/G/1 Queues
Queueing Systems: Theory and Applications
Characterizing output processes of Em /Ek/1 queues
Mathematical and Computer Modelling: An International Journal
Departure process analysis of the multi-type MMAP[K]/PH[K]/1 FCFS queue
Performance Evaluation
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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 {c}_{n} ≡ 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 c_{ n} can be computed through an explicit recursive formula. With this formula, we can calculate c_{ n} 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.