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Modeling Spacing Distribution of Queuing Vehicles in Front of a Signalized Junction Using Random-Matrix Theory
Modeling of headway/spacing between two consecutive vehicles has many
applications in traffic flow theory and transport practice. Most known
approaches only study the vehicles running on freeways. In this paper, we
propose a model to explain the spacing distribution of queuing vehicles in
front of a signalized junction based on random-matrix theory. We show that the
recently measured spacing distribution data well fit the spacing distribution
of a Gaussian symplectic ensemble (GSE). These results are also compared with
the spacing distribution observed for car parking problem. Why
vehicle-stationary-queuing and vehicle-parking have different spacing
distributions (GSE vs GUE) seems to lie in the difference of driving patterns
A note on eigenvalues of random block Toeplitz matrices with slowly growing bandwidth
This paper can be thought of as a remark of \cite{llw}, where the authors
studied the eigenvalue distribution of random block Toeplitz band
matrices with given block order . In this note we will give explicit density
functions of when the bandwidth grows
slowly. In fact, these densities are exactly the normalized one-point
correlation functions of Gaussian unitary ensemble (GUE for short).
The series can be seen
as a transition from the standard normal distribution to semicircle
distribution. We also show a similar relationship between GOE and block
Toeplitz band matrices with symmetric blocks.Comment: 6 page
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