Traffic lights, clumping and QBDs
Abstract
In discrete time, $\ell$-blocks of red lights are separated by $\ell$-blocks of green lights. Cars arrive at random. \ We seek the distribution of maximum line length of idle cars, and justify conjectured probabilistic asymptotics algebraically for $2\leq\ell\leq3$ and numerically for $\ell\geq4$.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2019
- DOI:
- 10.48550/arXiv.1911.01134
- arXiv:
- arXiv:1911.01134
- Bibcode:
- 2019arXiv191101134F
- Keywords:
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- Mathematics - Probability
- E-Print:
- Final : Stochastic Models, 37:102--126, 2021