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Spatial Queues with Infinitely Many Servers

In: From Markov Jump Processes to Spatial Queues

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  • Lothar Breuer

    (University of Trier, Department of Computer Science)

Abstract

Spatial Queues with infinitely many servers arise naturally as models for the planning process of mobile communication networks. A very useful concept has been developed by Çinlar [44], partly on the basis of Massey and Whitt [84]. This assumes single arrivals distributed in time as a non-homogeneous Poisson process. Every arrival chooses a position in space according to a (time-dependent) distribution on the space and independent of all other users. Since the arrival process is a multi-dimensional Poisson process on the product space of time and arrival space, the queue process is Poisson as well, and the mean measures can be computed in a straightforward manner. This yields a nice solution to the queue process.

Suggested Citation

  • Lothar Breuer, 2003. "Spatial Queues with Infinitely Many Servers," Springer Books, in: From Markov Jump Processes to Spatial Queues, chapter 0, pages 119-138, Springer.
    • Handle: RePEc:spr:sprchp:978-94-010-0239-4_9
    DOI: 10.1007/978-94-010-0239-4_9
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