Problems of Statistical Inference for Birth and Death Queuing Models

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.