An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems

Larsson, Torbjörn; Patriksson, Michael

doi:10.1016/0191-2615(95)00016-7

Cited by 166 publications

(122 citation statements)

References 35 publications

(63 reference statements)

Supporting

Mentioning

114

Contrasting

Unclassified

Order By: Relevance

“…2 Branston (1976) and Larsson and Patriksson (1995) argue that functions of that kind are unrealistic in the sense that the resulting travel times are finite whenever the arc flows are finite, so that the arcs are actually assumed to be able to carry arbitrarily large volumes of traffic flows; in practice, however, road links have some finite limits on traffic flows. Moreover, they point out that travel times predicted in the overloaded range do not have a real meaning.…”

Section: Network With Capacitiesmentioning

confidence: 99%

“…Boyce, Janson, and Eash (1981) have empirically found that asymptotic travel time functions yield unrealistically high travel times and devious rerouting of trips. In addition, Larsson and Patriksson (1995) criticize the inherent numerical ill conditioning of this approach. They go on to exalt the extension of the basic model by including explicit arc capacities as an interesting alternative to the use of asymmetric traffic assignment models, where such extensions are made through the development of complex travel cost functions, which, in practical applications, are difficult to calibrate.…”

Section: Network With Capacitiesmentioning

confidence: 99%

“…It also is worth mentioning that some traffic control policies give rise to link flow capacity constraints (Yang and Yagar 1994), that some of the first mathematical models of traffic assignment problems used link flow capacity constraints to model congestion effects (Charnes and Cooper 1961), and that several authors discussed the consequences of including capacities on existing algorithms for the uncapacitated case (Daganzo 1977a;Daganzo 1977b;Hearn 1980;Hearn and Ribera 1980;Hearn and Ribera 1981;Larsson and Patriksson 1994;Larsson and Patriksson 1995;Larsson and Patriksson 1999).…”

Section: Network With Capacitiesmentioning

confidence: 99%

“…It is interesting to note that the model (3.2) -(3.6) has been used before without the formal introduction of the concept of a capacitated user equilibrium; see Daganzo 1977a;Daganzo 1977b;Hearn 1980;Hearn and Ribera 1980;Hearn and Ribera 1981;Larsson and Patriksson 1995;Patriksson 1999, among others. However, Hearn (1980) noted that a Beckmann user equilibrium is an uncapacitated user equilibrium with respect to latencies a (·) + γ a , where γ a ≥ 0 is the shadow price (Karush-Kuhn-Tucker multiplier) of the capacity constraint x a ≤ c a for arc a ∈ A in an optimal solution to (3.2) -(3.6).…”

Section: Network With Capacitiesmentioning

confidence: 99%

See 3 more Smart Citations

Selfish Routing in Capacitated Networks

Correa¹,

Schulz²,

Moses³

2003

SSRN Journal

149

View full text Add to dashboard Cite

Abstract. According to Wardrop's first principle, agents in a congested network choose their routes selfishly, a behavior that is captured by the Nash equilibrium of the underlying noncooperative game. A Nash equilibrium does not optimize any global criterion per se, and so there is no apparent reason why it should be close to a solution of minimal total travel time, i.e. the system optimum. In this paper, we offer extensions of recent positive results on the efficiency of Nash equilibria in traffic networks. In contrast to prior work, we present results for networks with capacities and for latency functions that are nonconvex, nondifferentiable and even discontinuous.The inclusion of upper bounds on arc flows has early been recognized as an important means to provide a more accurate description of traffic flows. In this more general model, multiple Nash equilibria may exist and an arbitrary equilibrium does not need to be nearly efficient. Nonetheless, our main result shows that the best equilibrium is as efficient as in the model without capacities. Moreover, this holds true for broader classes of travel cost functions than considered hitherto.

show abstract

Section: Network With Capacitiesmentioning

confidence: 99%

Section: Network With Capacitiesmentioning

confidence: 99%

Section: Network With Capacitiesmentioning

confidence: 99%

Section: Network With Capacitiesmentioning

confidence: 99%

See 2 more Smart Citations

Selfish Routing in Capacitated Networks

Correa¹,

Schulz²,

Moses³

2003

SSRN Journal

149

View full text Add to dashboard Cite

show abstract

“…A VI model was proposed by Chen et al (2011) to formulate the DUE problem with side constraints. Taking as a simple case of the side constraints, the link capacity constraints problem in the context of DUE has also been widely investigated, see, e.g., Larsson and Patriksson (1995), Nie et al (2004).…”

Section: Literature Reviewmentioning

confidence: 99%

Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

Liu

Meng

Wang

2013

Transportmetrica A: Transport Science

View full text Add to dashboard Cite

A major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behaviour is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown that such an optimal toll charge pattern can be attained by solving a SUE problem with side constraints.A variational inequality (VI) model is first proposed for the optimal toll pattern, where the monotone property of this model is rigorously proved. Then, a convergent self-adaptive prediction and correction method can be adopted for solving the VI model. It is shown that when used in practice, the solution method only needs traffic counts on entry links of each cordon. ABSTRACTA major objective of the practical implemented cordon-based congestion pricing schemes is to maintain the traffic conditions within the cordon area, which is rarely considered in most of the existing studies. Thus, this paper addresses the optimal toll charge pattern that can restrict the total inbound flow of each cordon to a predetermined threshold. The toll charges on all the entry links of one cordon are required to be identical, for the ease of implementation and users' recognition. The users' route choice behavior is assumed to follow stochastic user equilibrium (SUE) with asymmetric link travel time functions. It is shown that such an optimal toll charge pattern can be attained by solving a SUE problem with side constraints. A variational inequality (VI) model is first proposed for the optimal toll pattern, where the monotone property of this model is rigorously proven. Then, a convergent self-adaptive prediction and correction method can be adopted for solving the VI model. It is shown that when used in practice, the solution method only needs traffic counts on entry links of each cordon.

show abstract

An intersection turning movement estimation procedure based on path flow estimator

Chen

Chootinan²,

Ryu

et al. 2010

J of Advced Transportation

View full text Add to dashboard Cite

Estimation of intersection turning movements is one of the key inputs required for a variety of transportation analysis, including intersection geometric design, signal timing design, traffic impact assessment, and transportation planning. Conventional approaches that use manual techniques for estimation of turning movements are insensitive to congestion. The drawbacks of the manual techniques can be amended by integrating a network traffic model with a computation procedure capable of estimating turning movements from a set of link traffic counts and intersection turning movement counts. This study proposes using the path flow estimator, originally used to estimate path flows (hence origin-destination flows), to derive not only complete link flows, but also turning movements for the whole road network given some counts at selected roads and intersections. Two case studies using actual traffic counts are used to demonstrate the proposed intersection turning movement estimation procedure. Figure 5. Estimated (Observed) turning movements for arterial network (RMSE turn ¼ 209.048). A. CHEN ET AL.especially when the turn penalties at intersection are likely to be mis-specified. The observed (in parenthesis) and estimated turning movement flows are shown in Figure 5 for comparison. St. Helena networkThe City of St. Helena is located in the famous wine-producing region of Napa Valley in California, approximately 65 miles north of San Francisco. St. Helena is a full service City with a population of 6,019 (as of January 1, 2002) within an area of 4 square miles. The City's development pattern is relatively compact, with commercial development and wineries concentrated along Highway 29 (Main Street) corridor, and residential development radiating out from Main Street (see Figure 6).Link volumes collected during the evening peak hour, the time of day when traffic congestion on Highway 29 presents a serious issue, were assembled and a network with 28 TAZs was coded with the observed link volumes. The network contains 113 links and 54 of the links do not have traffic count data. Turn penalties, based on the actual traffic conditions, were also coded with the network such that the shortest paths among TAZ centroids replicate actual travel patterns in the area. PFE was applied to the network for estimation of the O-D table as well as turning movements.For this set of experiments, link counts were aggregated from turning movement counts. As a result, there are link counts on all approaches (both in-bounds and out-bounds) of each intersection. In addition, turning movement counts at two intersections (Fulton/Main and Mitchell Dr./Oak Avenue) were also considered to assist the estimation (used as constraints in addition to link observation constraints). The following three sets of traffic counts were used for the estimations.1. Link counts only (Base case). 2. Base case plus turning counts at Fulton/Main (Option A). 3. Option A plus turning counts at Mitchell Dr./Oak Avenue (Option B). Figure 6. Topology of St. Helena network an...

show abstract

An augmented lagrangean dual algorithm for link capacity side constrained traffic assignment problems

Cited by 166 publications

References 35 publications

Selfish Routing in Capacitated Networks

Selfish Routing in Capacitated Networks

Variational inequality model for cordon-based congestion pricing under side constrained stochastic user equilibrium conditions

An intersection turning movement estimation procedure based on path flow estimator

Contact Info

Product

Resources

About