Bayesian analysis of single server Markovian queueing model with balking under asymmetric loss functions

Abstract

The aim of this article is to obtain the Bayesian estimates of traffic intensity ($\rho$) in an M/M/1 queueing model with balking. Balking is a behavior of impatient customers in which upon arrival, customer decides not to enter the queue and leave the system without getting served. In this article, we considered balking probability as a function of the number of customers present in the system. We obtained the Bayesian estimates of $\rho$ for the model under study by using various asymmetric loss functions such as modified quadratic loss function (M/QLF), entropy loss function (ELF), De’groot loss function (DLF), and linex loss function (LLF). Also, we provide some simulation results for supporting our findings for different sample sizes and parametric values. Further, a numerical application, for the better understanding of the model, will also be analyzed.

Keywords:

• Balking
• Bayesian estimates
• Loss function
• M/M/1 queue
• Monte-Carlo simulation

Data availability

The data that supported the findings of this paper are provided in the manuscript.