Departure Processes of BMAP/G/1 Queues

Abstract

A unified approach is applied to analyze the departure processes of finite/infinite BMAP/G/1 queueing systems for both vacationless and vacation arrangements via characterizing the moments, the z-transform of the scaled autocovariance function of interdeparture times CP(z), and lag n (n≥1) covariance of interdeparture times. From a structural point of view, knowing departure process helps one to understand the impact of service mechanisms on arrivals. Through numerical experiments, we investigate and discuss how the departure statistics are affected by service and vacation distributions as well as the system capacity. From a practical perspective, output process analysis serves to bridge the nodal performance and connectionwise performance. Our results can be then used to facilitate connection- or networkwise performance analysis in the current high-speed networks.