Abstract
The BMAP/G/1 queue is a field of intensive research since several years. We generalize the BMAP/G/1 queue by allowing the arrival process to depend on the state (level) of the queue, i.e., on the number of customers in the system. This will be called a BMAP/G/1 queueing system with level-dependent arrivals. A suitable arrival process is defined by nesting a countable number of BMAPs.
We give conditions for the level-dependent BMAP/G/1 queue to be stable, i.e., in equilibrium. By analysing the fundamental periods, which now depend on their starting level, we determine the stationary queue length at service completion times and at an arbitrary time.
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Hofmann, J. The BMAP/G/1 Queue with Level-Dependent Arrivals – An Overview. Telecommunication Systems 16, 347–359 (2001). https://doi.org/10.1023/A:1016662911145
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DOI: https://doi.org/10.1023/A:1016662911145