Road Pricing

Roadpricing is a controversial policy measure (e.g., Button and Verhoef, 1998). Its implementation in MATSim is conceptually straightforward (Rieser et al., 2007a, 2008; Grether et al., 2008): Essentially, for each vehicle entering a link at a given time, the appropriate toll is computed and charged to the vehicle’s driver. The scoring function will pick this up by the term (see Equation (3.4)) Strav,car,q = ...+βm · τ + ... ,


Introduction
Roadpricing is a controversial policy measure (e.g., Button and Verhoef, 1998).Its implementation in MATSim is conceptually straightforward (Rieser et al., 2007a(Rieser et al., , 2008;;Grether et al., 2008): Essentially, for each vehicle entering a link at a given time, the appropriate toll is computed and charged to the vehicle's driver.The scoring function will pick this up by the term (see Equation (3.4)) S trav, car, q = ... + β m • τ + ... , where τ is change in the monetary budget invoked by all toll payments (usually negative) and β m is the marginal utility of money (also see Chapter 3 and Chapter 51).The driver then takes this into account making decisions, e.g., for route choice, departure time choice, mode choice, destination choice, etc., and then trades o toll payments with other elements of his or her scoring function.
It should be clear that this automatically picks up all kinds of heterogeneities, for example: • Traveling at a di erent time may lead to a di erent toll, but possibly also to di erent schedule delay costs (Section 3.2.5).• Di erent vehicle types may be charged di erent tolls (Kickhöfer and Nagel, 2013).
• Di erent travelers may have di erent time values (Nagel et al., 2014), which may even vary according to the time of day.
However, one challenge is that the innovative modules (Section 4.5) must be consistent with the scoring now modi ed by road pricing.The approach just described will not work if, for example, the router consistently generates toll-avoiding routes for a synthetic person with a high time value, who would normally wish to pay for a faster option.In a case like this, if a suitable route is never generated, the scoring cannot identify it, giving the choice process no chance to select it in subsequent iterations.
However, processing every detail for each individual, i.e., not only the marginal utility of money, but also speci c time pressure at the route search time, is quite complex.
An alternative approach is to make the router randomizing, i.e., to run it with a randomly generated time value every time necessary for a given person.Computational experiments with this approach produce solutions for synthetic travelers approximately as good, or even better, than an "engineered" router (Nagel et al., 2014).At the same time, the so ware consistency burden is signi cantly reduced, noticeable in the smaller amount of information to be extracted from the agent during each router call.

E ect of an A ernoon Toll on Morning Tra c
In a rst demonstration of capabilities, an a ernoon toll for the Zürich area was simulated.While this is an unlikely policy scheme, it still clearly demonstrated the advantage of the integrated approach over other approaches.Not only did the synthetic travelers switch to public transit, but they also did so for the morning rush hour, where no toll was charged (Figure 15.1).Thus, the MATSim approach proved its ability to a ect the whole daily plan, not just the trip.For more information, see Rieser et al. (2008).

Integrated Passenger and Freight Toll Simulation for the Gauteng Province in South Africa
A large scale application was undertaken for the Gauteng province in South Africa (Chapter 69).
It is based on the so-called e-toll, which was switched on in December 2013.The e-toll should, logically, charge di erent rates for di erent vehicle types, with higher rates for heavy trucks.Again, logically, this should go along with higher time values of the driver-vehicle-units. Somewhat surprisingly, this turned out to be di cult to do with the MATSim so ware structure in place when the project was started in 2008.While it was easy to charge the freight vehicles a higher toll, it was di cult to give di erent replanning methods and di erent scoring function to the freight population; it was essentially impossible to feed the router with di erent time values for the freight population.This was an important driver for much development in recent years, including making the scoring function more accessible (Section 45.2.10), allowing di erent replanning strategies for di erent sub-populations (Section 4.5), and reducing consistency requirements between the router, the vehicle-based toll and the driver-based scoring function (Nagel et al., 2014).The simulation, as expected, predicts reduced tra c volumes on the tolled roads and increased volumes elsewhere (Figure 15.2).

Toll Schemes
Link toll The example refers to the "link" toll scheme, indicated by type="link".It charges the amount speci ed on the link.Distance toll Another useful scheme is "distance", indicated by type="distance".Here, the amount is interpreted as amount per length unit (see Section 2.2.1).This is most useful, with only a list of tolled links and a uniform distance cost for all these links noted at the end of the le.

Area toll
The simulation of an area toll-i.e., a toll where one has to pay a at fee for a given time period, o en a day, once one drives anywhere inside the area-su ers from a combinatorial challenge: driving through the tolled area early in the day may only pay o if one can re-use the permit later in the day.The code, in principle, addresses that by routing the agent twice: once under the assumption of a zero toll and once under the assumption of a very large toll.A erward, the toll is added to the generalized cost of the rst option, then both options are compared.In the end, the approach su ered from the same consistency burden as the general approach (see end of Section 15.2): the router made the decision about the better variant, rather than leaving the decision to the agent.It should be re-implemented using the same principles as Nagel et al. (2014).

Cordon toll
The cordon toll scheme was derived from the area scheme; one could use the same le, listing all area links, for the cordon toll as well.The code ensured that toll was only charged when a vehicle moved from an untolled link to a tolled link-thereby e ectively crossing the cordon.One di culty with this approach: confusion ensues if there is no connected area and several links in sequence are tolled instead.Then, if these links are connected, the toll is only charged on the rst of them; if there is a small section missing, perhaps overlooked, the toll is charged again.

Figure 15 . 1 :
Figure 15.1:An a ernoon city toll (between 3 pm and 7 pm) a ects mode choice not just during the toll time, but also in the morning.Source: Rieser et al. (2008)

Figure 15 . 2 :
Figure 15.2:Predicted di erences in link volumes a er introduction of the toll (red: higher volumes, green: lower volumes).