Systems with Refusals

  • A. A. Borovkov
Part of the Applications of Mathematics book series (SMAP, volume 4)


A natural characterization of such systems is the number of occupied channels at either the time of arrival of the n-th customer (q n ), or at time t (q(t)). The variables q n and q(t) will be called, as before, the queue lengths. As already explained in the introduction, the operation of the (systems ‹G/m R ) is analogous to that of ‹G/m› but with the essential difference that here, q(0) ≤ m, and if q n = m at the moment of arrival of the n-th group of requests, then all requests of this group are refused and leave the system. If, however, q n < m, then those requests of the group are refused which remain after the idle channels have been filled. Thus, we have qnm and q(t) ≤ m here and the important parameters of the systems are the probabilities that a customer is refused.


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Copyright information

© Springer-Verlag New York Inc. 1976

Authors and Affiliations

  • A. A. Borovkov
    • 1
  1. 1.Akademie der Wissenschaften der UDSSRSibirische Abteilung Math InsistuteNovosibirskUSSR

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