Article1965

Problems of Statistical Inference for Birth and Death Queuing Models

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Advanced Queuing Theory Analysis Probability and Statistical Research Statistical Distribution Estimation and Applications

Abstract

A large sample theory for birth and death queuing processes which are ergodic and metrically transitive is applied to make inferences about arrival and service rates. Likelihood ratio tests and maximum likelihood estimators are derived for simple models. Composite hypotheses, for example that the arrival rate does not vary with the number in the system, are considered. A numerical example illustrating these results, based on data generated by simulating a known model, is presented, which includes the testing of both true and false composite hypotheses.

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1957Maximum Likelihood Estimates in a Simple Queue

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1988Large sample inference from single server queues 1969Sixty Years of Queueing Theory 2013Estimation of Traffic Intensity Based on Queue Length in a Single M/M/1 Queue 1997A Bayesian analysis of a queueing system with unlimited service 1994Bayesian inference in Markovian queues 1992Empirical Bayes estimation for queueing systems and networks 2007Estimation for queues from queue length data 2000Prediction in Markovian bulk arrival queues

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