From Markov Jump Processes to Spatial Queues

This volume aims to develop a unified theory of spatial queues that yields concrete results for the performance analysis of mobile communication networks. A particular objective is to develop the most natural generalization of existing concepts (eg, the BMAP) toward the needs of mobile communication networks. To these belong the spatial distribution of batch arrivals and users in the system as well as time-inhomogeneous (periodic) arrival intensities and user movements. One of the major recent challenges for the stochastic modelling of communication systems is the emergence of wireless networks, which are used by more and more subscribers. The main new feature of those, which is not covered by classical queuing theory, clearly is the importance of the user location within the area that is served by the base stations of the network. In the framework of queuing theory, this opens up the natural extension of classical queuing models towards queues with a structured space in which users are served. The book is intended to introduce this extension under the name of spatial queues. The main point of view and the general approach will be that of Markov jump processes.The author starts with a closer look into the theory, then presents new results for the theory of stochastic processes, as well as for classical queuing theory. Finally, he introduces the new concepts of spatial Markovian arrival processes and spatial queues.