A day-to-day dynamical model for the evolution of path flows under disequilibrium of traffic networks with fixed demand

Kumar, Amit; Peeta, Srinivas

doi:10.1016/j.trb.2015.07.014

Cited by 26 publications

(11 citation statements)

References 48 publications

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“…Table 1 lists the relationship between each OD pair and each section/path, and the values of relevant parameters. The cost function of each section is c a (f a ) = A a + B a ( f a (t) K a ) 4 . During the road network test, the path selections were made according to Hypothesis 2 and formula (4).…”

Section: Road Network Testmentioning

confidence: 99%

“…The cost function of each section is c a (f a ) = A a + B a ( f a (t) K a ) 4 . During the road network test, the path selections were made according to Hypothesis 2 and formula (4). If a path has five or more sections, its residual congestion was computed as the weighted sum of the three smallest section residual congestions, with the weight coefficients being 0.5, 0.3 and 0.2, respectively; if a path has four sections, its residual congestion was computed as the weighted sum of the two smallest section residual congestions, with the weight coefficients being 0.6 and 0.4, respectively; if a path has fewer than four sections, its residual congestion was computed as the smallest section residual congestion.…”

Section: Road Network Testmentioning

confidence: 99%

“…The early models on traffic flow evolution generally assume the travellers can grasp the traffic information well and minimize their travel costs. However, their results are impractical because real-world travellers have bounded rationality (BR) [4], [5]. To solve the problem, many scholars started to investigate traffic flow evolution under the BR.…”

Section: Introductionmentioning

confidence: 99%

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A Day-to-Day Stochastic Traffic Flow Assignment Model Based on Mixed Regulation

Li-xuan

Huang

et al. 2020

IEEE Access

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In many cases, the final path selection of travellers' is not the shortest path, due to the limited computing power and high cost of path search. To solve the problem, this paper proposes a day-today (DTD) stochastic traffic flow assignment model that regulates the traffic flow based on the travel time (travel cost) and residual congestion of optional paths. The regulation mechanism is called the mixed regulation. Then, the authored proved the existence, uniqueness and stability of the model solution. The proposed model was verified through simulation on a Nguyen-Dupuis road network. The results show that traffic flows and travel times of all paths reached the equilibrium state, thanks to the DTD mixed regulation for 20 ∼ 30 days. From the traffic flows and congestion degrees of different sections, it can be seen that our model with mixed regulation diverts the traffic flow to the sections with a low congestion degree, and encourages travellers to drive through the sections with a low traffic flow. In addition, the congestion degrees of the four most congested sections decreased by 5.8%, 4%, 7% and 1.2%, respectively, and the entire road network exhibited a slight downward trend in mean congestion degree. These results prove that our model can uniformize the traffic flow, improve the operation efficiency and alleviate the congestion of the road network. These findings shed new light on the control, guidance and planning of traffic flow in road networks.

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Section: Road Network Testmentioning

confidence: 99%

Section: Road Network Testmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Day-to-Day Stochastic Traffic Flow Assignment Model Based on Mixed Regulation

Li-xuan

Huang

et al. 2020

IEEE Access

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“…Stability is an important property of a dynamical model for its applicability in practice ([1,4,7,10,22,23,25,31,48–52]). A FP is (asymptotically) stable if from any (sufficiently close) starting state the system state tends to the fixed-point as t tends to infinity.…”

Section: Theoretical Analysis Of the Proposed Dtd Modelmentioning

confidence: 99%

Modeling Day-to-day Flow Dynamics on Degradable Transport Network

2016

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Stochastic link capacity degradations are common phenomena in transport network which can cause travel time variations and further can affect travelers’ daily route choice behaviors. This paper formulates a deterministic dynamic model, to capture the day-to-day (DTD) flow evolution process in the presence of degraded link capacity degradations. The aggregated network flow dynamics are driven by travelers’ study of uncertain travel time and their choice of risky routes. This paper applies the exponential-smoothing filter to describe travelers’ study of travel time variations, and meanwhile formulates risk attitude parameter updating equation to reflect travelers’ endogenous risk attitude evolution schema. In addition, this paper conducts theoretical analyses to investigate several significant mathematical characteristics implied in the proposed DTD model, including fixed point existence, uniqueness, stability and irreversibility. Numerical experiments are used to demonstrate the effectiveness of the DTD model and verify some important dynamic system properties.

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“…There is now extensive literature analysing and modelling the extent to which traffic flows systematically vary within a day, due to time-of-day variations in demand, time-of-day variations in capacity (e.g. due to traffic signals), and the temporal and spatial interactions of congestion (Ukkusuri et al, 2012, Du et al, 2015, Han et al, 2015, Long et al, 2016, Ngoduy et al, 2016, Wang and Du, 2016 A corresponding body of work has additionally sought to address the considerable variation observed in traffic flows between days, known as day-to-day variability (Watling and Cantarella, 2013a, Watling and Cantarella, 2013b, Guo et al, 2015, Hazelton and Parry, 2015, Kumar and Peeta, 2015, Xiao et al, 2016. This twin focus, on within-day and day-to-day variation, is the topic of the present paper.…”

Section: Introductionmentioning

confidence: 99%