Abstract
In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 156-174 |
| Number of pages | 19 |
| Journal | Transportation Research Part B |
| Volume | 46 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 2012 |
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Keywords
- Cell transmission
- Counting processes
- Fluid limit
- Random time headways
- Stochastic traffic flow
ASJC Scopus subject areas
- Management Science and Operations Research
- Transportation
Cite this
A stochastic model of traffic flow : Theoretical foundations. / Jabari, Saif Eddin; Liu, Henry X.
In: Transportation Research Part B, Vol. 46, No. 1, 01.2012, p. 156-174.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - A stochastic model of traffic flow
T2 - Theoretical foundations
AU - Jabari, Saif Eddin
AU - Liu, Henry X.
PY - 2012/1
Y1 - 2012/1
N2 - In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.
AB - In a variety of applications of traffic flow, including traffic simulation, real-time estimation and prediction, one requires a probabilistic model of traffic flow. The usual approach to constructing such models involves the addition of random noise terms to deterministic equations, which could lead to negative traffic densities and mean dynamics that are inconsistent with the original deterministic dynamics. This paper offers a new stochastic model of traffic flow that addresses these issues. The source of randomness in the proposed model is the uncertainty inherent in driver gap choice, which is represented by random state dependent vehicle time headways. A wide range of time headway distributions is allowed. From the random time headways, counting processes are defined, which represent cumulative flows across cell boundaries in a discrete space and continuous time conservation framework. We show that our construction implicitly ensures non-negativity of traffic densities and that the fluid limit of the stochastic model is consistent with cell transmission model (CTM) based deterministic dynamics.
KW - Cell transmission
KW - Counting processes
KW - Fluid limit
KW - Random time headways
KW - Stochastic traffic flow
UR - http://www.scopus.com/inward/record.url?scp=80755184698&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=80755184698&partnerID=8YFLogxK
U2 - 10.1016/j.trb.2011.09.006
DO - 10.1016/j.trb.2011.09.006
M3 - Article
AN - SCOPUS:80755184698
VL - 46
SP - 156
EP - 174
JO - Transportation Research, Series B: Methodological
JF - Transportation Research, Series B: Methodological
SN - 0191-2615
IS - 1
ER -