TIME DEPENDENT ANALYSIS OF A QUEUEING SYSTEM INCORPORATING THE EFFECT OF ENVIRONMENT, CATASTROPHE AND RESTORATION

  • Gulab Singh Bura Dept. of Mathematics & Statistics, Banasthali University, India
  • Ram Niwas Bura Dept. of Statistics & Operational Research, Kurukshetra University, India
Keywords: Markovian Queueing System, Catastrophes, Environmental Effects, Restoration, Laplace Transforms

Abstract

In the present paper, we consider an M/M/1/N queueing system with environmental, catastrophic and restorative effects. It is found that the change in the environment affects the state of the queueing system. The system as a whole suffers occasionally a disastrous breakdown in both the enviormentle conditions, upon which all present customers are cleared from the system and lost. A repair process then starts immidiately. Here the repair time is called the restoration time. During the repair time the customers may arrive in the system. Time dependent solution is obtained by using probability generating function technique and further the steady state probabilities of system size are also derived. Some measure of effectiveness and particular cases of the model have also been derived and discussed.

 

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Published
2015-10-01
Section
Articles