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A Versatile Birth—Death Model Applicable to Four Distinct Problems

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Summary

This paper revisits a simple birth–death model which arises in slightly different forms in four distinct stochastic problems. These are the barbershop queue, coupon collecting, vocabulary usage and geological dating. Discrete and continuous time Markov chains are used to characterize these problems. Somewhat different questions are posed for each particular case, and practical results are derived for each process. The paper concludes with some comments on the versatility of this applied probability model.
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Keywords: coupon collecting; geological strata; queueing model; species replacement; type—token relationship

Document Type: Research Article

Affiliations: Mathematical Sciences Institute, The Australian National University, Canberra, Australia

Publication date: March 1, 2004

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