WIN-WIN DYNAMIC CONGESTION PRICING FOR CONGESTED URBAN AREAS

Transcription

1 1 WIN-WIN DYNAMIC CONGESTION PRICING FOR CONGESTED URBAN AREAS Aya Aboudina, Ph.D. Student University of Toronto Baher Abdulhai, Ph.D., P.Eng. University of Toronto June 12 th, 2012 ITS Canada - ACGM 2012

2 Outline 2 Motivation Do we need congestion pricing? Static pricing normal congestion vs. hyper-congestion Do we need dynamic congestion pricing? Dynamic pricing - the basic bottleneck model Setting optimum real-time dynamic tolls practical approach Proposed near-optimal real-time dynamic congestion pricing Control policies classifications overview Proposed dynamic congestion pricing system components Research vision

3 Motivation 3 Users/consumers should pay the full cost of whatever they consume Otherwise, they are subsidized Therefore, they unnecessarily consume more to the detriment of all i.e. Tragedy of the Commons Garrett Hardin, journal Science in 1968

4 Tragedy of the Commons 4 A dilemma arising when multiple individuals, acting independently and rationally consulting their own self-interest, will ultimately deplete a shared limited resource Examples: Overgrazing Congestion Criticized for promoting privatization Used here to encourage control

5 Motivation (Cont d) 5 Capacity expansions and extensions to public transit are eliminated as policies to combat traffic congestion On the other hand, vkt (vehicle kilometres travelled) is quite responsive to price Together these findings strengthen the case for congestion pricing as a policy response to traffic congestion

6 Do We Need Congestion Pricing? 6 Engineers Vs. Economists Definition of Congestion: Economists: performance of the system (e.g. travel time) rises with the intensity of use (e.g. flow levels) Traffic engineers: traffic density exceeds the critical density, resulting in traffic breakdown Flow (veh/hr) Capacity Economists Traffic Engineers Breakdown Cost (1/speed) AC Traffic Engineers p Economists Critical density Density (veh/km) Capacity (max flow) Flow (veh/hr)

7 Engineers vs. Economists Definition of Congestion 7 Congestion for traffic engineers is termed hypercongestion for economists Hyper-congestion causes a significant drop in capacity (at critical density) Flow (veh/hr) Uncongested capacity Congested capacity Normal- Congestion Hyper- Congestion Breakdown Eliminating hyper-congestion allows the sustenance of the original capacity Critical density Density (veh/km)

8 Static Congestion Pricing Normal Congestion 8 The un-priced equilibrium occurs at the intersection of demand and AC curves; it involves traffic flow V 0 and cost c 0 The optimal flow V 1 occurs at the intersection of demand and MC; it can be achieved by imposing a toll τ (marginal-cost pricing) The gain in the social surplus is depicted by the shaded triangle $ MC Toll Revenue Social Subsidy AC MC 1 AC 1 τ = mecc Demand V 1 V 0 Flow (V)

9 Static Congestion Pricing Hyper Congestion 9 The optimal congestion toll τ is the one that eliminates hypercongestion and maintains flow at maximum capacity Capacity-boosting congestion-reducing win-win congestion pricing d 2 $ Un-priced dynamically unstable equilibrium in hyper-congestion d 1 τ MC AVC τ Un-priced equilibrium in normal-congestion q max Flow Lower flow and higher price after tolling Higher flow and lower price after tolling

10 Do We Need Dynamic Congestion Pricing? 10 Static models limitations: Assumes static demand and cost curves for each congested link and time period Appropriate when traffic conditions do not change too quickly or when it is sufficient to focus attention on average traffic levels over extended periods We need dynamic models! The basic bottleneck model

11 The Basic Bottleneck Model 11 Assumptions: No delay if inflow is below capacity Queue exit rate equals capacity (when a queue exists) Single desired queue exit time t* (for all users) Number of vehicles Total demand for passages Q is inelastic Two costs in un-priced equilibrium: Travel delay cost c T (t) Schedule delay cost c s (t) (early and late arrival costs) Average cost Queue forms c s (t) Cumulative queue entries t q t* t q c T (t) c s (t) c(t) Cumulative queue exits (slope: V k ) Queue disperses c s (t) Time t q t* t q Exit time (t)

12 The Basic Bottleneck Model (Cont d) 12 The optimum toll τ(t): Replicates travel delay costs (triangular shape) Affects the patterns of entries (queue entry rate will equal capacity) (flattening the peak) Results in the same pattern of schedule-delay cost Produces zero travel delay costs Average cost Number of vehicles c s (t) τ(t) c s (t) c(t) c s (t) t q t* t q Exit time (t) Cumulative queue entries Queue forms Queue disperses Cumulative queue exits (slope: V k ) t q t* t q The main source of efficiency gains from optimal dynamic pricing is the rescheduling of departure times from the trip origin Time

13 The Basic Bottleneck Model (Cont d) 13 The optimum toll τ(t): Replicates travel delay costs (triangular shape) Affects the patterns of entries (queue entry rate will equal capacity) (flattening the peak) Results in the same pattern of schedule-delay cost Produces zero travel delay costs Average cost Number of vehicles c s (t) τ(t) c s (t) c(t) c s (t) t q t* t q Exit time (t) Cumulative queue entries Queue forms Queue disperses Cumulative queue exits (slope: V k ) t q t* t q The main source of efficiency gains from optimal dynamic pricing is the rescheduling of departure times from the trip origin Time

14 14 Setting Optimum Real-Time Dynamic Tolls Practical Approach In reality, departure and arrival curves are not linear; therefore, optimization algorithms are required to find the optimal tolling structure that minimizes the total travel delays (i.e., minimizes the area between both curves and flattens the peak) Problem gets more complex Number of vehicles Cumulative queue entries Total travel delay with stochastic human factors (responses to pricing) Queue forms Cumulative queue exits Queue disperses t q t q Time

15 Proposed Near-Optimal Real-Time Dynamic Congestion Pricing 15 Optimum Tolling Structure Optimizer Historical Demand Profiles (departures and arrivals) Optimum Traffic Conditions Open-Loop (Offline) Optimizer Regulator - Real-Time Dynamic Tolling Structure Process (Real World) Measured Traffic Conditions Closed-Loop Regulator Predictable Disturbances Non-Predictable Disturbances

16 Control Policies Classifications - 16Overview Optimal control vs. regulation: Optimal Control Regulation An objective function is optimized (max or min) Examples: min total travel time and max throughput Maintains output at a certain level Example: ramp metering (keep downstream flow below capacity) Open-loop vs. closed loop: Open-Loop No real-time measurements Closed-loop optimal control is the most accurate, yet too complex. Therefore, consider suboptimal control Closed- Loop Real-time measurements (feedback) Unexpected disturbances can be recovered

17 Proposed Dynamic Congestion Pricing 17System Components Demand Profiles (MTO Data) Emission Pricing Predicted Traffic Conditions Dynamic Congestion Pricing Optimizer (GA Platform at UofT) Mode and Departure-Time Choice Online Regulator Mesoscopic Simulator (DynusT)

18 Research Vision 18 To develop a real-time dynamic congestion pricing model for the GTHA Gentle pricing: the objective is congestion alleviation rather than revenue maximization (i.e. not monopoly pricing) Tolls set dynamically and adaptively according to location, time-of-day, distance driven (and if possible, the level of pollution emitted from the vehicle) To take possible user responses to pricing (mode choice, departure-time choice and route choice) into account.

19 Research Vision (Cont d) 19 The tolling system will target eliminating hypercongestion and maintaining flow at the maximum capacity in super-critical traffic conditions (win-win solution) Additionally, attempt an extra step of basing the toll on predicted (anticipated), rather than prevailing, traffic conditions (to prevent traffic breakdown before it occurs)

20 Thank You Questions, suggestions and comments are always welcome!