Bayesian Inference of Traffic Intensity for an M/M/1 Queueing Model with State-Dependent Service Under Asymmetric Loss Functions

The paper explores parameter estimation in a Markovian queuing model with Poisson arrival rates and state-dependent service, where the server’s efficiency varies based on queue length. The focus is on estimating traffic intensity ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline" overflow="scroll"> <mml:mi>ρ</mml:mi> </mml:math> ) using a Bayesian approach with various asymmetric loss functions. This estimation process involves the exploration of different prior distributions, including beta, truncated gamma, and uniform, to assess traffic intensity. The study utilizes Markov Chain Monte Carlo (MCMC) simulations for robust traffic intensity estimation. Credible intervals are introduced alongside point estimates to account for uncertainties, providing a more comprehensive understanding. The analysis extends to incorporate posterior risk, considering both estimates and associated uncertainties in the assessment process. In the end, the analysis includes an evaluation of real-life data.