Volume 53, Number 5, November-December 2019
|Page(s)||1915 - 1927|
|Published online||28 October 2019|
Analysis of state-dependent discrete-time queue with system disaster
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
Accepted: 8 September 2018
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.
Mathematics Subject Classification: 60k25
Key words: Generating function / continued fraction / power series / Geo/Geo/1 queue / busy period distribution / ballot numbers
© EDP Sciences, ROADEF, SMAI 2019
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