1. bookVolume 16 (2015): Edizione 3 (September 2015)
Dettagli della rivista
License
Formato
Rivista
eISSN
1407-6179
Prima pubblicazione
20 Mar 2000
Frequenza di pubblicazione
4 volte all'anno
Lingue
Inglese
access type Accesso libero

Mixed Vehicle Flow At Signalized Intersection: Markov Chain Analysis

Pubblicato online: 22 Jun 2015
Volume & Edizione: Volume 16 (2015) - Edizione 3 (September 2015)
Pagine: 190 - 196
Dettagli della rivista
License
Formato
Rivista
eISSN
1407-6179
Prima pubblicazione
20 Mar 2000
Frequenza di pubblicazione
4 volte all'anno
Lingue
Inglese
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.

Keywords

1. Darroch, J.N. (1963) On the Traffic-Light Queue, Ann. Math. Statist., 15, 380-388.Search in Google Scholar

2. Feller, W. (1963) An Introduction to Probability Theory and Its Applications, Vol.1, 2nd edition, John Wiley& Sons, Inc.Search in Google Scholar

3. Gertsbakh, I. (2008) Equilibrium waiting time and queue length on an intersection: group arrival of cars. Proceedings of International. Conference ”Modeling of Business, Industrial and Transport Systems”, May 7-10, Riga, Latvia.Search in Google Scholar

4. Haight, Frank, A. (1963) Mathematical Theories of Traffic Flow, Academic Press New York London.Search in Google Scholar

5. McNeil, D.R. (1968) A solution to the fixed cycle traffic light with compound Poisson arrivals. Journal of Applied Probability, 5(3),624-635.10.2307/3211926Search in Google Scholar

6. Miller, A.J. (1963) Settings for Fixed-Cycle Traffic Signals. Operational Research Quarterly, 14, 373-386. 1963.Search in Google Scholar

7. Newell, G.F. (1960) Queues for a fixed-cycle traffic light, Annals of Mathematical Statistics, 31, 589-597.10.1214/aoms/1177705787Search in Google Scholar

8. Newell, G. (1965) Approximation Methods for Queues with Application to to Fixed Traffic Light. SIAM Review, 7.10.1137/1007038Search in Google Scholar

9. Slinn, M., Guest, P, and P. Matthews. (2005) Traffic Engineering Design, Principles and Practice, 2nd edition, Elsevier.Search in Google Scholar

10. Viti, F. T. (2006) The Dynamics and the Uncertainty of Delays at Signals. Ph.D. thesis, Delft University of Technology, TRAIL Press, The Netherlands.Search in Google Scholar

11. Webster, F.V. (1958) Traffic signal settings. Paper No 39, Her Majesty Stationery Office, London.Search in Google Scholar

Articoli consigliati da Trend MD

Pianifica la tua conferenza remota con Sciendo