A cost analysis of single-server discouraged arrivals with differentiated vacation queueing model

Authors

  • Srinivasan Keerthana Department of Mathematics, Karpagam Academy of Higher Education, Salem - Kochi Highway, Eachanari, Coimbatore, Tamil Nadu, Pincode - 641021, India.
  • Jaisingh Ebenesar Anna Bagyam Department of Mathematics, Karpagam Academy of Higher Education, Salem - Kochi Highway, Eachanari, Coimbatore, Tamil Nadu, Pincode - 641021, India
  • Ramachandran Remya Department of Mathematics, Karpagam Academy of Higher Education, Salem - Kochi Highway, Eachanari, Coimbatore, Tamil Nadu, Pincode - 641021, India

Abstract

This paper investigates an M/M/1 queueing system with differentiated vacations and discouraged arrivals, focusing on two types of vacations. The server switches to type I vacation with rate γ1 when the system is empty during an active state. If no customers are waiting when it returns from a type I vacation, it then switches to a type II vacation with a rate of γ2. Both vacation times and service duration follow exponential distributions. The study utilises the Probability Generating Function (PGF) technique to derive steady-state solutions for both vacation policies. Furthermore, the research explores relevant performance metrics and provides numerical examples to illustrate the system's behaviour under various conditions. The cost analysis of the M/M/1 differentiated vacation system with discouraged arrival queueing and various aspects of the system's behaviour under different arrival rates (λ, λ1, λ2) are discussed

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Published

2024-10-07

Issue

Vol. 15 No. 2 (2024): CRORR

Section

CRORR Journal Regular Issue

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