The waiting time problem
The traditional waiting time problem of a passenger arriving at a bus stop is considered. Giving a pausing time density (statistics of the buses arriving at the bus stop) the passenger waiting time density is calculated. A monoparametric family of pausing time densities is used which gives for a value of the parameter the Poissonian case, obtaining the well known waiting time paradox. Periodic sequence of events is obtained for a limit value of the parameter; in this case the averaged mean value of the waiting time is one half the time between successive events, as one should expect. From the expression of the waiting time density Feller's theorem for ongoing renewal processes is derived. Pathological pausing time densities are mentioned.
Year of publication: |
1989
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Authors: | Prato, Domingo P. ; Pury, Pedro A. |
Published in: |
Physica A: Statistical Mechanics and its Applications. - Elsevier, ISSN 0378-4371. - Vol. 157.1989, 3, p. 1261-1273
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Publisher: |
Elsevier |
Saved in:
Online Resource
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