Transient Analysis of Single Server Queueing system with Loss and Feedback

Authors

  • Sivanandam SS Department of Mathematics, Kanchi Mamunivar Centre for Post Graduate Studies, Pondicherry, India
  • Subramanian MG Department of Mathematics, Kanchi Mamunivar Centre for Post Graduate Studies, Pondicherry, India
  • Sekar G Department of Mathematics, Kanchi Mamunivar Centre for Post Graduate Studies, Pondicherry, India

Keywords:

Loss and Feedback, Single Server, Steady State Probabilities, System performance measures, Transient Probability Distributions

Abstract

Consider a single server queueing system with Loss and Feedback in which customers arrive in a Poisson process with arrival rate λ and service time follows an exponential distribution with parameter μ. If the server is free at the time of an arrival of a customer, the arriving customer begins to be served immediately by the server and satisfied customer leaves the system with probability (1-q) after the service completion and dissatisfied customers will join the queue with probability q to get service once again. This is called Feedback in queueing terminology. If the server is busy, then the arriving customer will join the queue with probability p in front of service station. This is called Loss in queueing terminology. In this paper, we have derived the closed form solutions of time dependent probabilities of the single server queueing systems with Loss and Feedback. The corresponding Transient distributions have been obtained. We also obtain the time dependent performance measures of the systems.

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Published

2025-11-25

How to Cite

[1]
S. S. Sivanandam, A. M. G. Subramanian, and G. Sekar, “Transient Analysis of Single Server Queueing system with Loss and Feedback”, Int. J. Comp. Sci. Eng., vol. 7, no. 5, pp. 270–276, Nov. 2025.

Issue

Vol. 7 No. 5 (2019): IJCSE Special Issue Mar Edition

Section

Research Article

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