Simple Solutions for a Class of Periodic Queues

In the present paper, the periodic BMAP/M-t/c queue is analyzed. This queue. has a periodic BMAP arrival process, which is defined in this paper, and exponential service time distributions with service rates varying periodically in time. The transient distribution and several formulae for its efficient computation are derived. Furthermore, a stability condition in terms of arrival and service rates is proven, and for the case of stability the asymptotic distribution is given explicitly. A special class of periodic BMAP/M-t/c queues, which allows to reduce the complexity of computations to the level of homogeneous queues, is separated. The obtained results are applied to the spatial SMAP/M-t/(c)/(c) variant of the queue, too. This variant is very useful as a model for mobile communication networks.