Analysis of state-dependent discrete-time queue with system disaster

¹ Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus Anna University, 620024 Tiruchirappalli, India
² Department of Mathematics, IFET College of Engineering, 605108 Villupuram India

^* Corresponding author: sudhesh@aucev.edu.in; sudheshanna@gmail.com

Received: 26 March 2017
Accepted: 8 September 2018

Abstract

An explicit expression for time-dependent system size probabilities is obtained for the general state-dependent discrete-time queue with system disaster. Using generating function for the nth state transient probabilities, the underlying difference equation of system size probabilities are transformed into three-term recurrence relation which is then expressed as a continued fraction. The continued fractions are converted into formal power series which yield the time-dependent system size probabilities in closed form. Further, the busy period distribution is obtained for the considered model. As a special case, the system size probabilities and busy period distribution of Geo/Geo/1 queue are deduced. Finally, numerical illustrations are presented to visualize the system effect for various values of the parameters.