Estimation of performance measures in a novel M/M/1 queueing model with reverse balking: A simulation-based approach

Abstract

This article introduces a novel M/M/1 queueing model that incorporates the concept of reverse balking, where customers are more likely to join the queue as the system size increases. Traditional queuing models often assume a constant balking rate or state-dependent balking rate where the balking rate decreases with increase in system size. In contrast, reverse balking reflects scenarios where customer behavior is influenced by more number of customers present in the system. We use a simulation-based approach to estimate key performance measures, including traffic intensity, average system size and average queue length of the proposed model using both classical and Bayesian approaches. In the classical approach, we used the Maximum Likelihood (ML) Estimation procedure to estimate the parameters using the Metropolis-Hastings (MH) algorithm. Moreover, the Bayesian approach employed the Sampling Importance Resampling (SIR) technique to estimate the parameters. The effectiveness of all the estimation techniques has been evaluated based on the root mean squared error (RMSE) of the estimates. The computational results demonstrate that estimates under both approaches converge to the true values as the sample size increases. Moreover, Bayesian estimates yield lower RMSE compared to ML estimates, highlighting their superior accuracy and robustness. Additionally, predictive probabilities for the number of customers in the system are obtained. A real-life application is presented to demonstrate the practical relevance of the proposed study. The findings offer valuable implications for managing and optimizing service systems where reverse balking is common.