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In a quasi-birth–death (QBD) queue, the level forward and level backward transitions of a QBD-type Markov chain are interpreted as customer arrivals and services. In the generalized QBD queue considered in this paper, arrivals and services can occur in matrix-geometrically distributed batches. This paper presents the queue length and sojourn time analysis of generalized QBD queues. It is shown that,...
Markov Fluid Queues (MFQs) are the continuous counterparts of quasi birth–death processes, where infinitesimally small jobs (fluid drops) are arriving and are being served according to rates modulated by a continuous time Markov chain. The fluid drops are served according to the First-Come–First-Served (FCFS) discipline. The queue length process of MFQs can be analyzed by efficient numerical methods...
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