Single-server queues with spatially distributed arrivals View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1994-03

AUTHORS

Dirk P. Kroese, Volker Schmidt

ABSTRACT

Consider a queueing system where customers arrive at a circle according to a homogeneous Poisson process. After choosing their positions on the circle, according to a uniform distribution, they wait for a single server who travels on the circle. The server's movement is modelled by a Brownian motion with drift. Whenever the server encounters a customer, he stops and serves this customer. The service times are independent, but arbitrarily distributed. The model generalizes the continuous cyclic polling system (the diffusion coefficient of the Brownian motion is zero in this case) and can be interpreted as a continuous version of a Markov polling system. Using Tweedie's lemma for positive recurrence of Markov chains with general state space, we show that the system is stable if and only if the traffic intensity is less than one. Moreover, we derive a stochastic decomposition result which leads to equilibrium equations for the stationary configuration of customers on the circle. Steady-state performance characteristics are determined, in particular the expected number of customers in the system as seen by a travelling server and at an arbitrary point in time. More... »

PAGES

317-345

References to SciGraph publications

  • 1989. Waiting Times in Polling Systems with Markovian Server Routing in MESSUNG, MODELLIERUNG UND BEWERTUNG VON RECHENSYSTEMEN UND NETZEN
  • 1992-03. Stability of token passing rings in QUEUEING SYSTEMS
  • 1987-06. Polling and greedy servers on a line in QUEUEING SYSTEMS
  • 1978-12. A splitting technique for Harris recurrent Markov chains in PROBABILITY THEORY AND RELATED FIELDS
  • 1994-03. Rate conservation laws: A survey in QUEUEING SYSTEMS
  • 1993-12. Polling systems and multitype branching processes in QUEUEING SYSTEMS
  • 1992-03. Stability, monotonicity and invariant quantities in general polling systems in QUEUEING SYSTEMS
  • 1993-10. Queueing systems on a circle in NONE
  • 1993-02. Cyclic Bernoulli polling in NONE
  • 1994-03. Monotonicity and stability of periodic polling models in QUEUEING SYSTEMS
  • Journal

    TITLE

    Queueing Systems

    ISSUE

    1-2

    VOLUME

    17

    Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01158698

    DOI

    http://dx.doi.org/10.1007/bf01158698

    DIMENSIONS

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