×

Using factorization in analyzing D-BMAP/G/1 queues. (English) Zbl 1102.60080

A queueing model with discrete-time batch Markovian arrival process (D-BMAP) is considered. If there are no customers to serve the server waits until the queue reaches the first threshold (builup period), and then a setup period is started. The server begins to serve customeres (busy period) if the queue size is greater than or equal to the second (higher) threshold. It is shown (the factorization property) that only generation function (GF) of the (steady-state) queue size at arbitrary slot boundary during an idle period is required to derive GFs of the queue size at an arbitrary slot and the queue size at a departure instant. Based on the factorization property, the queue-size distribution (and the mean queue size) is derived effectively by avoiding many complicated classical procedures.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDFBibTeX XMLCite
Full Text: DOI EuDML