An M/M/1 Queuing System with Three Types Input Sources


Abstract views: 22 / PDF downloads: 24

Authors

  • Prabhat Bansal Research Scholar, Department of Mathematic, Mangalayatan University, Beswan, Aligarh, Uttar Pradesh, India
  • Gajendra K. Saraswat Supervisor and Ex Assistant Professor, Department of Mathematics, Mangalayatan University, Aligarh, Uttar Pradesh, India

Keywords:

Queuing Theory, Markovian Process, Laplace Transform, Exponential Distribution, Poisson distribution, Probability Generating Function

Abstract

This paper considers an M/M/1 queuing system with three types input sources, where the rate of arrival and service capacity follow Poisson distribution. The arrival process consists of three stages said to be active state, sick state and passive state. The system remains in three state for a random time which is exponentially distributed. The queue discipline is first-come-first-serve (FCFS). Laplace transforms of the various probability generating functions are obtained and the steady state results are derived. The probability that the arrival process (input) will be in active state, sick state and passive state, is also analyzed.

Downloads

Published

15-12-2018

How to Cite

Prabhat Bansal, & Gajendra K. Saraswat. (2018). An M/M/1 Queuing System with Three Types Input Sources. International Journal of Mathematics And Its Applications, 6(4), 175–186. Retrieved from http://ijmaa.in/index.php/ijmaa/article/view/340

Issue

Section

Research Article