Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue

Abstract

In this article, maximum likelihood estimator (MLE) as well as Bayes estimator of traffic intensity (ρ) in an M/M/1/∞ queueing model in equilibrium based on number of customers present in the queue at successive departure epochs have been worked out. Estimates of some functions of ρ which provide measures of effectiveness of the queue have also been derived. A comprehensive simulation study starting with the transition probability matrix has been carried out in the last section.

Keywords:

• Bayes estimator
• Effectiveness measures
• Hypergeometric function
• M/M/1/∞ queue
• Queue length
• Root mean square error
• Transition Matrix

Mathematics Subject Classification:

• Primary 60K25
• Secondary 90B22