Note on the article: Maximum entropy analysis of the M [ x] /M/1 queueing system with multiple vacations and server breakdowns

• Published in: Computers & industrial engineering Vol. 54; no. 4; pp. 1078 - 1086
• Main Authors: Omey, Edward, Van Gulck, Stefan
• Format: Journal Article
• Language: English
• Published: New York Elsevier Ltd 01.05.2008; Pergamon Press Inc
• Subjects: Batch arrival; Estimating techniques; Maximum entropy; Maximum entropy method; Multiple vacation; Queueing model; Queuing; Server breakdowns; Simulation; Studies; Vacations; Queueing model; Multiple vacation; Simulation; Batch arrival; Maximum entropy; Server breakdowns
• ISSN: 0360-8352; 1879-0550
• DOI: 10.1016/j.cie.2007.10.019

Wang et al. [Wang, K. H., Chan, M. C., & Ke, J. C. (2007). Maximum entropy analysis of the M [ x] /M/1 queueing system with multiple vacations and server breakdowns. Computers & Industrial Engineering, 52, 192–202] elaborate on an interesting approach to estimate the equilibrium distribution for the number of customers in the M [ x] /M/1 queueing model with multiple vacations and server breakdowns. Their approach consists of maximizing an entropy function subject to constraints, where the constraints are formed by some known exact results. By a comparison between the exact expression for the expected delay time and an approximate expected delay time based on the maximum entropy estimate, they argue that their maximum entropy estimate is sufficiently accurate for practical purposes. In this note, we show that their maximum entropy estimate is easily rejected by simulation. We propose a minor modification of their maximum entropy method that significantly improves the quality of the estimate.