Estimation of Measures in M/M/1 Queue

Abstract

Maximum likelihood and uniform minimum variance unbiased estimators of steady-state probability distribution of system size, probability of at least ℓ customers in the system in steady state, and certain steady-state measures of effectiveness in the M/M/1 queue are obtained/derived based on observations on X, the number of customer arrivals during a service time. The estimators are compared using Asympotic Expected Deficiency (AED) criterion leading to recommendation of uniform minimum variance unbiased estimators over maximum likelihood estimators for some measures.

Keywords:

• Asymptotic expected deficiency
• Maximum likelihood estimator
• Nonlinear program
• Queues
• Uniform minimum variance unbiased estimator

Acknowledgments

The first author is thankful to Dr. Ramesh C. Gupta, University of Maine, Orono, USA, for providing his articles, and to Council of Scientific and Industrial Research (CSIR), India. The authors are thankful to a reviewer for his suggestions which led to a revision.

Notes

Note: Range of ρ is approximate.