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Investigation of the Mθ/G/1/m system with service regime switchings and threshold blocking of the input flow

  • Articles from the Russian Journal Informatsionnye Protsessy
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Abstract

The Mθ/G/1/m queueing system with the group arrival of customers, switchings of service regimes, and threshold blocking of the flow of customers is studied. The input flow is blocked if, at the instant of the successive customer service start, the number of customers in the system exceeds specified threshold level h. If, at instant t of the customer service start, number of customers in the system ξ(t) satisfies the condition \(h_i < \xi (t) \leqslant h_{i + 1} (i = \overline {1,r} )\), then the service time for this customer corresponds to distribution function F i (t). At 1 ≤ ξ(t) ≤ h = h 1, the service time for a customer is distributed according to law F(t) (basic service time). The Laplace transforms for the distribution of the number of customers in the system on the busy period and for the distribution function of the busy period are found, the mean length of the busy period (including the case m = ∞) is determined and formulas for the ergodic distribution of the number of customers in the system (including the case m = ∞) are obtained. An effective algorithm for calculation of the ergodic distribution is proposed. The recurrence relations of the algorithm are not explicitly dependent on m.

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Authors
  1. K. Yu. Zhernovyi
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Original Russian Text © K.Yu. Zhernovyi, 2010, published in Informatsionnye Protsessy, 2010, Vol. 10, No. 2, pp. 159–180.

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Zhernovyi, K.Y. Investigation of the Mθ/G/1/m system with service regime switchings and threshold blocking of the input flow. J. Commun. Technol. Electron. 56, 1570–1584 (2011). https://doi.org/10.1134/S1064226911120242

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  • DOI: https://doi.org/10.1134/S1064226911120242

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