Traffic Theory

Moving Bottlenecks: A Numerical Method that Converges in Flows

Daganzo, Carlos F.
Laval, Jorge A.
2005

This paper presents a numerical method to model kinematic wave (KW) traffic streams containing slow vehicles. The slow vehicles are modeled discretely as moving boundaries that can affect the traffic stream. The proposed scheme converges in flows, densities and speeds without oscillations, and therefore can be readily used in situations where one wishes to model the effect of the traffic stream on the bottlenecks too.

A Variational Formulation of Kinematic Waves: Solution Methods

Daganzo, Carlos F.
2005

This paper presents improved solution methods for kinematic wave traffic problems with concave flow-density relations. As explained in part I of this work, the solution of a kinematic wave problem is a set of continuum least-cost paths in space-time. The least cost to reach a point is the vehicle number. The idea here consists in overlaying a dense but discrete network with appropriate costs in the solution region and then using a shortest-path algorithm to estimate vehicle numbers. With properly designed networks, this procedure is more accurate than existing methods and can be applied to...

Lane-Changing in Traffic Streams

Laval, Jorge A.
Daganzo, Carlos F.
2006

It is postulated that lane-changing vehicles create voids in traffic streams, and that these voids reduce flow. This mechanism is described with a model that tracks lane changers precisely, as particles endowed with realistic mechanical properties. The model has four easy-to-measure parameters and reproduces without re-calibration two bottleneck phenomena previously thought to be unrelated: (i) the drop in the discharge rate of freeway bottlenecks when congestion begins, and (ii) the relation between the speed of a moving bottleneck and its capacity.

A Note on Asymptotic Formulae for One-Dimensional Network Flow Problems

Daganzo, Carlos F.
Smilowitz, Karen R.
2006

This note develops asymptotic formulae for single-commodity network flow problems with random inputs. The transportation linear programming problem (TLP) where N points lie in a region of R1 is one example. It is found that the average distance traveled by an item in the TLP increases with N1/2; i.e., the unit cost is unbounded when N and the length of the region are increased in a fixed ratio. Further, the optimum distance does not converge in probability to the average value. These one-dimensional results are a useful stepping stone toward a network theory for two and higher dimensions...

In Traffic Flow, Cellular Automata = Kinematic Waves

Daganzo, Carlos F.
2006

This paper proves that the vehicle trajectories predicted by (i) a simple linear car-following model, CF(L), (ii) the kinematic wave model with a triangular fundamental diagram, KW(T), and (iii) two cellular automata models CA(L) and CA(M) match everywhere to within a tolerance comparable with a single “jam spacing”. Thus, CF(L)=KW(T)=CA(L,M).

On the Variational Theory of Traffic Flow: Well-Posedness, Duality and Applications

Daganzo, Carlos F.
2006

This paper describes some simplifications allowed by the variational theory of traffic flow (VT). It presents general conditions guaranteeing that the solution of a VT problem with bottlenecks exists, is unique and makes physical sense.

Bus Lanes with Intermittent Priority: Strategy Formulae and an Evaluation

Eichler, Michael
Daganzo, Carlos F.
2006

This paper evaluates strategies for operating buses on signal-controlled arterials using special lanes that are made intermittently available to general traffic. The advantage of special bus lanes, intermittent or dedicated, is that they free buses from traffic interference; the disadvantage is that they disrupt traffic. We find that bus lanes with intermittent priority (BLIPs), unlike dedicated ones, do not significantly reduce street capacity. Intermittence, however, increases the average traffic density at which the demand is served, and as a result increases traffic delay. These delays...

Macroscopic Modeling of Traffic in Cities

Geroliminis, Nikolas
Daganzo, Carlos F.
2007

Most of the existing models for large scale arterial networks are not realistic and appropriate to deal with crowded conditions. As an alternative, we propose observation-based models that circumvent the fragility problems of traditional models. Monitoring replaces prediction, and the system is repeatedly modified based on observations. To succeed this goal a city is modeled in an aggregated manner and relations between state variables are developed. Macroscopic control strategies are introduced which rely on real-time observation of relevant spatially aggregated measures of traffic...

Counteracting the Bullwhip Effect with Decentralized Negotiations

Ouyang, Yanfeng
Daganzo, Carlos F.
2007

This paper shows how to reduce the bullwhip effect by introducing advance demand information (ADI) into the ordering schemes of supply chains. It quantifies the potential costs and benefits of ADI, and demonstrates that they are not evenly distributed across the chain. Therefore, market-based strategies to re-distribute wealth without penalizing any supplier are presented. The paper shows that if a centralized operation can eliminate the bullwhip effect and reduce total cost, then some of this reduction can also be achieved with decentralized negotiation schemes. Their performance is...

The Bullwhip Effect in Supply Chains with Stochastic Dynamics

Ouyang, Yanfeng
Daganzo, Carlos F.
2007

This paper analyzes the bullwhip effect in single-echelon supply chains operated nondeterministically. The supply chain is modeled as a Markovian jump linear system driven by arbitrary customer demands. The paper presents robust analytical conditions to diagnose the bullwhip effect, and bound its magnitude. The tests are independent of the customer demand. Examples are given. Policies that pass these tests, and thus avoid the bullwhip effect in random environments for arbitrary customer demands, are shown to exist. The paper also presents extended tests for multi-echelon chains.