Mathematics and Computer Science, Volume 2

11Modelling and Analysis of a Congestion Dependent Queue with Bernoulli Scheduled Vacation Interruption and Client Impatience

K. Jyothsna^1⋆ and P. Vijaya Kumar²

¹Department of Mathematics, Anil Neerukonda Institute of Technology and Sciences, Visakhapatnam, Andhra Pradesh, India

²Department of Mathematics, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh, India

Abstract

This paper’s purpose is to model and analyze an impatient client renewal input Bernoulli scheduled vacation interruption queue. Two types of congestion dependent client impatience, namely balking and reneging, have been incorporated. The server shifts to working vacation mode whenever the system is completely depleted. The server follows Bernoulli’s vacation interruption schedule after executing a service during working vacation, i.e., the server either continues working during the vacation with certain probability or interrupts the working vacation with the complementary probability. Regular service durations, working vacation service durations, and vacation durations are expected to be congestion dependent and exponentially distributed. The stationary probability distributions at different epochs were estimated utilizing supplementary variable and iterative approaches. A few performance metrics and the model parameters’ influence on the performance metrics have been provided through numerical outcomes.

Keywords: Balking, reneging, congestion dependent, multiple working vacations, vacation interruption, ...