The parking problem
The following is from Deift (2007) :
A number of so-called “transportation” problems have now been analyzed in terms of Random Matrix Theory. These include: the “vicious” walker problem of M. Fisher, the bus problem in Cuernavaca, Mexico, the headway traffic problem on highways, and the airline boarding problem of Bachmat et al. Recently, researchers in London, Prague, and also Ann Arbor, have noticed an intriguing phenomenon. They found that the fluctuations in the spacings between cars parked on a long street exhibited Random Matrix Theory behavior. Furthermore, Šeba found that there was a difference whether the street is two-way or one-way (On a two-way street, the cars park only on the right, while on a one-way street one of course has the option of also parking on the left.) Quite remarkably, for two-way streets Šeba found Gaussian Unitary Ensemble statistics, but for left-side parking on one-way streets he found Gaussian Ortohogonal Ensemble statistics. It is a great challenge to develop a microscopic model for the parking problem, in analogy, perhaps, with the microscopic model introduced by Baik et al. to explain the RMT statistics for the bus problem in Cuernavaca. Šeba’s recent, intriguing calculations on the parking problem can be found posted on the web.
References & readings
- Percy Deift (2007) Some open problems in random matrix theory and the theory of integrable systems.(deift_2007).
- P. Šeba (2007) Parking in the City. Acta Physica Polonica A, Vol. 112(4), Proceedings of the 3rd Workshop on Quantum Chaos and Localisation Phenomena. Warsaw, Poland, May 25-27, 2007. (parking_in_the_city)
- Petr Šeba (2007) Parking in the city: an example of limited resource sharing (parking_in_the_city_an_example_of_limited_resource-sharing)
- Milan Krbálek1 & Petr Šeba (2007) Statistical variances in traffic data (statistical_variances_in_traffic_data)
- M.L. Mehta (2004) Random Matrices ed. Academic Press, New York.
- Makoto Katori, Hideki Tanemura & Taro Nagao (2004) Vicious walkers and random matrices. Nonequilibrium Statistical Physics of Complex Systems Satellite Meeting of STATPHYS 22 in Seoul, Korea, June 29 – July 2, 2004. (vicious_walkers_and_random_matrices)