Journal of Communications Technology and Electronics

, Volume 58, Issue 6, pp 602–612

An Mθ/G/1 system with hysteretic switching of the service intensity

  • K. Yu. Zhernovyi
  • Yu. V. Zhernovyi
Mathematical Models, Computational Methods

DOI: 10.1134/S1064226913060193

Cite this article as:
Zhernovyi, K.Y. & Zhernovyi, Y.V. J. Commun. Technol. Electron. (2013) 58: 602. doi:10.1134/S1064226913060193

Abstract

For an Mθ/G/1 system, two—basic and post-threshold—service modes with distribution functions F(x) and \(\tilde F\)(x) of the service time are applied. The post-threshold mode starts functioning if, at instant t of the beginning of the current customer service, number ξ(t) of customers in the system satisfies the condition ξ(t) > h2. The basic mode is restored at the instant when the customer such that ξ(t) ≤ h1, where h1h2, begins to be served. The mean duration of the busy period is determined, formulas for the stationary distribution of the number of customers in the system and stationary characteristics are derived. The results are verified with the help of simulation models developed with the use of the GPSS World tools.

Keywords

queueing systembatch arrival of customersswitching of the service intensityhysteric strategythe stationary distribution of the number of customers

Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  • K. Yu. Zhernovyi
    • 1
  • Yu. V. Zhernovyi
    • 1
  1. 1.Ivan Franko National University of LvivLvivUkraine