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The fair charge on a car ferry

Published online by Cambridge University Press:  14 July 2016

D. R. Grey
D. R. Grey*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, University of Sheffield, Sheffield S10 2TN, U.K.
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Abstract

Vehicles whose lengths are independent identically distributed random variables with known distribution function are loaded onto ferries of fixed known length, each ferry departing as soon as it can no longer accommodate the next vehicle in the queue. We work out how much a vehicle of any particular length ought to pay for use of the ferry, as well as the expected number of vehicles per ferry and expected revenue per ferry in equilibrium.

Keywords

MARKOV PROCESSEQUILIBRIUMABSORPTION PROBABILITYMARTINGALEOPTIONAL STOPPING THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 654 - 661
Copyright
Copyright © Applied Probability Trust 1980 

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References

Doob, J. L. (1953) Stochastic Processes. Wiley, New York.Google Scholar
Karlin, S. and Taylor, H. M. (1975) A First Course in Stochastic Processes , 2nd edn. Academic Press, New York.Google Scholar