# Agreement Technologies for Coordination in Smart Cities
## 3 Applications
### Coordination of Traffic Flows through Intelligent Intersections
#### 3.1.2 Mechanisms for Multiple Intersections  
In the previous section, we analysed the performance of an auction-based policy for the allocation of reservations in the _single_ intersection scenario. A driver is modelled as a simple agent that selects the preferred value for the bid that will be submitted to the auctioneer. The decision space of a driver in an urban road network with _multiple_ intersections is much broader: complex and mutually dependent decisions must be taken, such as route choice and departure time selection. Therefore, this scenario opens up new possibilities for intersection managers to affect the behaviour of drivers. For example, an intersection manager may be interested in influencing the collective route choice performed by the drivers, using variable message signs, information broadcast, or individual route guidance systems, so as to evenly distribute the traffic over the network. This problem is called _traffic assignment_. In the following, we first evaluate how market-inspired methods can be used within a traffic assignment strategy for networks of reservation-based intersections (_competitive traffic assignment_ (CTA) strategy). Then, we combine this traffic assignment strategy with the auction-based control policy into an integrated mechanism for traffic management of urban road networks (CTA-CA strategy). Finally, the performance of the different approaches is evaluated. The complexity of the problem puts limits to coordination approaches based on cooperative multiagent learning [28]. Therefore, our CTA models each intersection manager as a provider of the resources (in this case, the reservations of the intersection it manages). Each intersection manager is free to establish a price for the reservations it provides. On the other side of the market, each driver is modelled as a buyer of these resources. Provided with the current prices of the reservations, it chooses the route according to its personal preferences about travel times and monetary costs. Each intersection manager is modelled so as to compete with all others for the supply of the reservations that are traded. Therefore, our goal as market designers is making the intersection managers adapt their prices towards a price vector that accounts for an efficient allocation of the resources. In CTA, for each incoming link \(l\), an intersection manager defines the following variables:  
* Current price \(p^{t}(l)\): the price applied by the intersection manager to the reservations sold to the drivers that come from the incoming link \(l\). * Total demand \(d^{t}(l)\): the total demand of reservations from the incoming link \(l\) that the intersection manager observes at time \(t\), given the current price \(p^{t}(l)\), i.e., the number of vehicles that intend to cross the intersection coming from link \(l\) at time \(t\). * Supply \(s(l)\): the reservations supplied by the intersection manager for the incoming link \(l\). It is a constant and represents the number of vehicles that cross the intersection coming from link \(l\) that the intersection manager is willing to serve. * Excess demand \(z^{t}(l)\): the difference between total demand at time \(t\) and supply, i.e., \(d^{t}(l)-s(l)\). Figure 5: Average delay. We define the price vector \(p^{t}\) as a vector that comprises all prices at time \(t\) (i.e., the prices applied by all intersection manager to each of its controlled links). In particular, we say that a price vector \(p^{t}\) maps the supply with the demand if the excess demand \(z^{t}(l)\) is 0 for all links \(l\) of the network. This price vector, which corresponds to the market equilibrium price, can be computed through a Walrasian auction [29], where each buyer (i.e., driver) communicates to the suppliers (i.e., intersection managers) the route that it is willing to choose, given the current price vector \(p^{t}\). With this information, each intersection manager computes the demand \(d^{t}(l)\), as well as the excess demand \(z^{t}(l)\), for each of its controlled links.