Modeling and Estimation of Traffic Intensity in M/M/1 Queueing System with Balking: Classical and Bayesian Approaches

This article focuses on both classical and Bayesian inference of traffic intensity in a single-server Markovian queueing model considering balking. To reflect real-world situations, the article introduces the concept of balking, where customers opt not to join the queue due to the perceived waiting time. The essence of this article involves a comprehensive analysis of different loss functions, namely, the squared error loss function (SELF) and the precautionary loss function (PLF), on the accuracy of the Bayesian estimation. To evaluate the performance of the Bayesian method with various priors such as inverted beta, gamma, and Jeffreys distributions, an assessment is performed using the Markov Chain Monte Carlo (MCMC) simulation technique. The efficacy of the Bayesian estimators is assessed by comparing the mean squared errors (MSEs).