The waiting time problem

Domingo P. Prato and Pedro A. Pury

Physica A: Statistical Mechanics and its Applications, 1989, vol. 157, issue 3, 1261-1273

Abstract: 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.

Date: 1989
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:157:y:1989:i:3:p:1261-1273

DOI: 10.1016/0378-4371(89)90043-5

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