Abstract
Abstract We assume that a Poisson flow of vehicles arrives at isolated signalized intersection, and each vehicle, independently of others, represents a random number X of passenger car units (PCU’s). We analyze numerically the stationary distribution of the queue process {Zn}, where Zn is the number of PCU’s in a queue at the beginning of the n-th red phase, n → ∞. We approximate the number Yn of PCU’s arriving during one red-green cycle by a two-parameter Negative Binomial Distribution (NBD). The well-known fact is that {Zn} follow an infinite-state Markov chain. We approximate its stationary distribution using a finite-state Markov chain. We show numerically that there is a strong dependence of the mean queue length E[Zn] in equilibrium on the input distribution of Yn and, in particular, on the ”over dispersion” parameter γ= Var[Yn ]/E[Yn ]. For Poisson input, γ = 1. γ > 1 indicates presence of heavy-tailed input. In reality it means that a relatively large ”portion” of PCU’s, considerably exceeding the average, may arrive with high probability during one red-green cycle. Empirical formulas are presented for an accurate estimation of mean queue length as a function of load and g of the input flow. Using the Markov chain technique, we analyze the mean ”virtual” delay time for a car which always arrives at the beginning of the red phase.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.