Modeling User Responses to Pricing

2008 ◽  
Vol 2085 (1) ◽  
pp. 124-135 ◽  
Author(s):  
Chung-Cheng Lu ◽  
Hani S. Mahmassani
Keyword(s):  
Dynamic Pricing ◽  
User Equilibrium ◽  
Infinite Dimensional ◽  
Network Applications ◽  
Multiple User ◽  
Schedule Delay ◽  
Departure Time ◽  
Class B ◽  
Joint Consideration ◽  
User Heterogeneity

In a previous contribution, the authors showed how to incorporate user heterogeneity in determining equilibrium route choices in a network in response to pricing. Presented here is a generalization of that framework to incorporate joint consideration of route and departure time as well as heterogeneity in a wider range of behavioral characteristics. A multicriterion simultaneous route and departure time user equilibrium (MSRDUE) model is presented, along with a simulation-based algorithm intended for practical network applications. The model explicitly considers heterogeneous users with different values of time (VOTs) and values of (early or late) schedule delay (VOESDs or VOLSDs) in their joint choice of departure times and paths characterized by a set of trip attributes that include travel time, out-of-pocket cost, and schedule delay cost. The problem is formulated as an infinite-dimensional variational inequality problem and solved by a column generation-based algorithmic framework that embeds (a) an extreme nondominated alternative-finding algorithm to obtain the VOT, VOESD, and VOLSD breakpoints that define multiple user classes and the associated least trip cost (joint departure time and path) alternative for each user class; (b) a traffic simulator to capture traffic flow dynamics and determine travel costs experienced; and (c) a path-swapping multiclass alternative flow-updating scheme to solve the restricted multiclass SRDUE problem defined by a subset of feasible alternatives. Application to an actual network illustrates the properties of the algorithm and underscores the importance of capturing user heterogeneity and temporal shifts in the appraisal of dynamic pricing schemes.

Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic Capacity

2021 ◽  
Author(s):  
Jiancheng Long ◽  
Hai Yang ◽  
W. Y. Szeto
Keyword(s):  
User Equilibrium ◽  
Single Step ◽  
Numerical Results ◽  
General Distribution ◽  
Time Varying ◽  
Bottleneck Model ◽  
Schedule Delay ◽  
Departure Time ◽  
Stochastic Capacity ◽  
Departure Time Choice

This paper develops a bottleneck model in which the capacity of the bottleneck is assumed to be stochastic and follow a general distribution that has a positive upper bound. The user equilibrium principle in terms of mean trip cost is adopted to formulate commuters’ departure time choice in the stochastic bottleneck. We find that there exist five possible equilibrium departure patterns, which depend on both commuters’ unit costs of travel time, schedule delay early and late, and the uncertainty of the stochastic capacity of the bottleneck. All possible equilibrium departure patterns are analytically derived. Both the analytical and numerical results show that increasing the uncertainty of the capacity of the bottleneck leads to an increase of commuters’ individual mean trip cost. In addition, both a time-varying toll scheme and a single-step coarse toll scheme are designed within the proposed stochastic bottleneck model. We provide an analytical method to determine the detailed toll-charging schemes for both toll strategies. The numerical results show that the proposed toll schemes can indeed improve the efficiency of the stochastic bottleneck in terms of decreasing mean total social cost, and the time-varying toll scheme is more efficient than the single-step coarse toll scheme. However, as the uncertainty of the capacity of the bottleneck increases, the efficiency of the time-varying toll scheme decreases, whereas the efficiency of the single-step coarse toll scheme fluctuates slightly.

scholarly journals Congestion Behavior under Uncertainty on Morning Commute with Preferred Arrival Time Interval

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
LingLing Xiao ◽  
Ronghui Liu ◽  
HaiJun Huang
Keyword(s):  
Arrival Time ◽  
Numerical Solutions ◽  
Fixed Time ◽  
User Equilibrium ◽  
Time Interval ◽  
Work Schedule ◽  
Schedule Delay ◽  
Departure Time ◽  
Morning Commute ◽  
Bottleneck Capacity

This paper extends the bottleneck model to study congestion behavior of morning commute with flexible work schedule. The proposed model assumes a stochastic bottleneck capacity which follows a uniform distribution and homogeneous commuters who have the same preferred arrival time interval. The commuters are fully aware of the stochastic properties of travel time and schedule delay distributions at all departure times that emerge from day-to-day capacity variations. The commuters’ departure time choice follows user equilibrium (UE) principle in terms of the expected trip cost. Analytical and numerical solutions of this model are provided. The equilibrium departure time patterns are examined which show that the stochastic capacity increases the mean trip cost and lengthens the rush hour. The adoption of flexitime results in less congestion and more efficient use of bottleneck capacity than fixed-time work schedule. The longer the flexi-time interval is, the more uniformly distributed the departure times are.

scholarly journals On the Impact of HOT Lane Tolling Strategies on Total Traffic Level

2012 ◽  
Vol 48 (3) ◽  
Author(s):  
Soheil Sibdari ◽  
Mansoureh Jeihani
Keyword(s):  
Numerical Analysis ◽  
Dynamic Pricing ◽  
User Equilibrium ◽  
Pricing Strategies ◽  
Peak Period ◽  
Dynamic Strategy ◽  
Traffic Level ◽  
The Right ◽  
The Impact ◽  
High Occupancy Toll

This paper shows how tolling (or pricing) strategies can be used to control the congestion levels of both untolled and high occupancy toll (HOT) lanes. Using a user-equilibrium method, the paper calculates the number of travelers on each route during the peak period and provides a numerical analysis that determines the distribution of travelers for different tolling strategies. It shows that with the right tolling strategy some travelers who initially plan to use the untolled lane during the peak period will change both their routes (i.e., select the HOT lane) and departure times (i.e., depart earlier or later). Using this result, the paper compares static and dynamic pricing strategies and shows that with a dynamic strategy a larger profit can be earned and congestion reduced in the untolled lane.

A THEORY OF MULTIPLE VEHICLE TYPE DYNAMIC MARGINAL COST CONSIDERING DEPARTURE TIME CHOICES

Transport ◽  
2010 ◽  
Vol 25 (3) ◽  
pp. 307-313
Author(s):  
Shu-Guang Li ◽  
Qing-Hua Zhou
Keyword(s):  
Marginal Cost ◽  
User Equilibrium ◽  
System Optimum ◽  
Equilibrium Conditions ◽  
Traffic Demand ◽  
Vehicle Type ◽  
Departure Time ◽  
Single Vehicle ◽  
Link Model ◽  
Analytic Expression

The analysis of single vehicle type dynamic marginal cost is extended to multiple vehicle type dynamic one based on time‐dependent multiple vehicle type queue analysis at a bottleneck. First, a dynamic link model to rep‐ resent the interactions between cars and trucks is provided. Then, the analytic expression of a multiple vehicle type dynamic marginal cost function considering departure time choices is deduced under congested and un‐congested conditions and consequently, a dynamic toll function is given. A heuristic algorithm is introduced to solve multiple vehicle type dynamic queues and toll under system optimum and user equilibrium conditions taking into account traveler's departure time. A numerical example shows that a dynamic congestion toll can diminish queues and improve system conditions when traffic demand is not changed.

Comparison of Morning and Evening Commutes in the Vickrey Bottleneck Model

2002 ◽  
Vol 1807 (1) ◽  
pp. 26-33 ◽  
Author(s):  
André de Palma ◽  
Robin Lindsey
Keyword(s):  
Sufficient Conditions ◽  
User Equilibrium ◽  
Dynamic User Equilibrium ◽  
Peak Period ◽  
Time Pattern ◽  
Travel Costs ◽  
Bottleneck Model ◽  
Schedule Delay ◽  
Deterministic Dynamic ◽  
Traveler Heterogeneity

Dynamic user equilibrium has received considerable theoretical attention for morning peak-period travel but very little for the evening peak. In an attempt to redress this imbalance, morning and evening travel are characterized and compared by using Vickrey’s bottleneck model. To focus ideas, it is assumed that morning and evening travel differ in just one respect: scheduling preferences for the morning are defined in terms of arrival time at work, whereas preferences for the evening are defined in terms of departure time from work. Sufficient conditions are identified for the existence and uniqueness of a deterministic dynamic user equilibrium in terms of departure times for the morning and evening peaks. These conditions, which go well beyond previous work, involve relatively general assumptions about the schedule delay cost functions for morning and evening and essentially no restrictions on the degree of heterogeneity in trip-timing preferences of travelers. Plausibility of the conditions is examined in light of the limited empirical evidence. A numerical example is developed at length to illustrate the importance of traveler heterogeneity and the extent of differences between morning and evening in the time pattern of departures and aggregate travel costs.

scholarly journals Commute Equilibrium for Mixed Networks with Autonomous Vehicles and Traditional Vehicles

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Yangbeibei Ji ◽  
Mingwei Xu ◽  
Hua Wang ◽  
Chaowu Tan
Keyword(s):  
Autonomous Vehicles ◽  
Autonomous Vehicle ◽  
User Equilibrium ◽  
Analytical Models ◽  
Sensitivity Analyses ◽  
Queuing Delay ◽  
Travel Costs ◽  
Traffic Pattern ◽  
Schedule Delay ◽  
Mixed Networks

Recent development of autonomous vehicle (AV) provides new travel opportunities for citizens, and traditional vehicles (TVs) will still be used for a long time. Therefore, it is highly possible that both AVs and TVs will be used as travel modes in a city. In a transportation system with both AVs and TVs, the traffic pattern is worthy of studying. This paper investigates user equilibrium traffic pattern based on the traditional bottleneck model considering AVs and TVs. For both TVs and AVs, travel costs include queuing delay and schedule delay. However, they also have different components of travel costs; more specifically, for AVs, passengers have to pay a riding fare, and, for TVs, travelers encounter a walking time cost after parking their cars. For different combinations of travel demands and riding fare of AVs, analytical solutions of three different user equilibrium traffic patterns are obtained. Finally, numerical examples are provided to demonstrate the usefulness of the analytical models. Sensitivity analyses are examined to show the impacts of AV’s time-dependent fee and trip-based fixed fee on the traffic pattern and travel costs.

Optimal Toll Design Problem in Dynamic Traffic Networks with Joint Route and Departure Time Choice

2005 ◽  
Vol 1923 (1) ◽  
pp. 61-72 ◽  
Author(s):  
Dusica Joksimovic ◽  
Michiel C. J. Bliemer ◽  
Piet H. L. Bovy
Keyword(s):  
Travel Behavior ◽  
Dynamic Pricing ◽  
Design Problem ◽  
Road Pricing ◽  
Control Measures ◽  
Time Varying ◽  
Dynamic Traffic ◽  
The Road ◽  
Departure Time ◽  
Departure Time Choice

Road pricing is one of the market-based traffic control measures that can influence travel behavior to alleviate congestion on roads. This paper addresses the effects of uniform (constant, fixed) and time-varying (step) tolls on the travel behavior of users on the road network. The problem of determining optimal prices in a dynamic traffic network is considered by applying second-best tolling scenarios imposing tolls only to a subset of links on the network and considering elastic demand. The optimal toll design problem is formulated as a bilevel optimization problem with the road authority (on the upper level) setting the tolls and the travelers (on the lower level) who respond by changing their travel decisions (route and departure time choice). To formulate the optimal toll design problem, the so-called mathematical program with equilibrium constraints (MPEC) formulation was used, considering the dynamic nature of traffic flows on the one hand and dynamic pricing on the other. Until now, the MPEC formulation has been applied in static cases only. The model structure comprises three interrelated levels: (a) dynamic network loading, (b) route choice and departure time choice, and (c) road pricing level. For solving the optimal toll design problem in dynamic networks, a simple search algorithm is used to determine the optimal toll pattern leading to optimization of the objective function of the road authority subject to dynamic traffic assignment constraints. Nevertheless, uniform and time-varying pricing is analyzed, and a small hypothetical network is considered.

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