The concept of road use pricing is not new. Research on the topic started way back in 1920's; Pigou's work on the economics of welfare (1920) and Knight's work on fallacies in the interpretation of social cost (1924). Since then, a wide range of theoretical and practical models have been studied and proposed. Cities like London, Stockholm and Singapore have successfully implemented a form of congestion pricing.
In an ongoing research with my PhD students Ziyuan Gu and Sajjad Shafiei, we have developed and evaluated different pricing schemes for Melbourne road network using our state-of-the-art dynamic traffic assignment model of Melbourne (DynaMel) and an in-house developed simulation-based optimization (SBO) framework. Let me know if you are interested in the details of the methodology and I will send you the draft paper.
We first test a simple cordon-based pricing scheme with Melbourne CBD selected as the cordon (see the picture below: the inner rectangle is the cordon). A limitation of the cordon toll is that the distance traveled within the cordon is not taken as a determinant. Users are equally charged regardless of their actual usage of the urban road space. The resulting social inequity may create negative public acceptability towards the cordon charge.
The optimal toll to mitigate congestion in the CBD was found to be $2 per entry to the CBD. This is a not final number though. There are quite a few assumptions and limitations behind it that makes it not ready for real-world implementation yet.
We then propose a linear distance toll that keeps the congestion of the pricing zone (Melbourne CBD) below a critical value. Users, if entering the CBD, need to pay a toll that is linearly related to their travel distance within the cordon like a pay as you go system. Since users are charged according to their trip lengths within the pricing zone, the distance toll distinguishes, for example, between a user who reaches the destination immediately upon crossing the cordon and a user who traverses the whole pricing zone, thereby creating a more equitable and efficient pricing scheme.
The optimal distance-based pricing was found to be $1 per kilometer. Again, this is a not final number given the assumptions and limitations behind the methodology.
Joint distance- and time-based pricing
We then propose a joint distance and time toll. In a distance only based pricing, users tend to be driven into the shortest paths within the cordon. Although the travel time on these shortest paths increases as a result of a larger traffic volume, the majority of users may not change their routes because the utility from paying a lower distance toll may dominate the disutility from the increase in travel time. Hence the concentration of users into a few shortest paths within the cordon makes the congestion distribution in the city uneven and as a result reduce the network performance. Therefore, a novel solution is to charge users jointly based on the distance traveled and the time spent within the cordon. Under this scheme, users are more likely to distribute themselves into the second or third best shortest path.
The optimal joint distance- and time-based pricing was found to be $0.35 per kilometer and $9 per hour. Again, this is a not final number given the many assumptions and limitations behind the methodology.
Does congestion pricing work?
All three pricing schemes were successful in mitigating congestion in the CBD without actually pushing traffic to the periphery. The Melbourne CBD, here, is selected only as an example area for pricing. We can (and actually should) change the boundary of the pricing area to better capture the existing and future traffic patterns. Given the input demand to the model, the pricing activates a little after 8:30 am and will last until 9:15 am. This could change depending on the time-profile of demand. If congestion (above the critical threshold) starts earlier, let's say 8:00 am, the pricing will also activate earlier.
Overall, the results were promising. All three pricing schemes were successful in keeping the congestion level (measured by average network density) below the selected threshold as shown in the following figure (left). As expected, the total distance traveled within the CBD was also reduced. See the right figure.
Limitations and assumptions
There are quite a few limitations and assumption behind this work though. First, the area for pricing is arbitrarily selected and may not be the best cordon. Second, we assumed an average value of time of $15 per hour with no consideration of heterogeneity or any distribution. Third, the demand is assumed inelastic or fixed. It means that users do not change their departure time or shift to other modes because of pricing.
We are working to relax some of these limitations and assumptions. We are trying to make the demand elastic. So, users can shift to other modes like public transport if they find the congestion toll too high to drive, just like how parking cost in CBD works sometimes. Also, we would like to consider a distribution of value of time and travel time reliability in the model.
We welcome collaboration with government and industry partners to further progress this research. We hope our work contributes to the discussion on transport network pricing in Australia, especially in Victoria.