Author: Dr. Jean-Paul Rodrigue

Transportation seeks to minimize the effort of moving passengers and freight between locations. A component of this effort involves route selection.

1. Route Selection

Human beings are natural effort minimizers, notably when it involves moving around. When given the opportunity, they will always try to choose the shortest path to go from one place to another. This behavior commonly characterizes pedestrians. When possible, a pedestrian will walk over a lawn, zigzag by cars in a parking lot, or cross a street sideways between intersections if the route selected enables them to reach a destination faster.

Transportation, as an economic activity, replicates this process of minimization, notably by trying to minimize the friction of distance between locations. Shorter times and lower costs are looked upon by all transport users, from individuals managing their own mobility to multinational corporations managing complex supply chains. For an individual, it is often only a matter of convenience, but for a corporation, it is strategically important as a direct monetary cost is involved. Under such circumstances, numerous methods have been developed to deal with the complex issue of route selection. One such classic application is the “traveling salesperson” problem, where the shortest route has to be selected from a set of possible paths.

Route selection has two major dimensions:

Construction. Involves activities related to the setting of transport networks, such as road and rail construction where a physical path has to be traced. Among the primary considerations are factors such as distance and topography.
Operation. Concerns the management of flows in a network. This is the most common route selection activity since it considers routes as fixed entities and seeks an optimal path considering existing constraints.

The Traveling Salesperson Problem | The Geography of Transport Systems — The Traveling Salesperson Problem

The Effects of Topography on Route Selection | The Geography of Transport Systems — The Traveling Salesperson Problem

2. Evaluating the Route Selection Process

The choice of linking a location to another, and more importantly, the path selected, is part of a route selection process that respects a set of constraints. Although route selection varies by mode, the underlying principles remain similar; in its most simple form, a route selection process (R) tries to respect these general constraints:

R = f(min C : max E)

Route selection tries to find or use a path minimizing costs (C) and maximizing efficiency (E). There are two major dimensions of this function:

Cost minimization. A good route selection should minimize the overall costs of the transport system. This implies construction as well as operating costs. The most direct route is not necessarily the least expensive, notably if rugged terrain is concerned, but a direct route is usually selected. It also implies that route selection must be the least damageable to the environment if environmental consequences are considered.
Efficiency maximization. A route must support economic activities by providing a level of accessibility, thus fulfilling the needs of regional development. Even if a route is longer and thus more expensive to build and operate, it might provide better services for an area. Its efficiency is thus increased at the expense of higher costs. In numerous instances, roads were constructed more for political reasons than for meeting economic considerations.

Route selection is consequently a compromise between the cost of a transport service and its efficiency. Sometimes, there are no compromises, as the most direct route is the most efficient. At other times, a compromise is very difficult to establish as cost and efficiency are inversely proportional.

Cost Minimization and Efficiency Maximization in Route Selection | The Geography of Transport Systems — Cost Minimization and Efficiency Maximization in Route Selection

3. Traffic Assignment

Contemporary transportation networks are intensively used and congested to various degrees, notably road transportation systems in urban areas. Less known is the spatial logic behind the generation, attraction, and distribution of traffic on a network. There are two important concepts related to understanding traffic in transport systems:

The transport demand between places must either be known or estimated. For instance, the gravity model offers a methodology to assess potential flows between locations if a set of attributes are known, such as respective distances and emission and attraction variables.
The transport supply between places must also either be known or estimated. This involves establishing a set of paths between places that are generating and attracting movements. This includes the geometric definition of transport networks with the graph theory.

However, a fundamental concept is absent: how traffic is distributed in a transport network when its structure, capacity, and spatial demand are known.

A traffic assignment problem is traffic distribution in a network considering a demand between a set of locations and the transport supply of the network. Assignment methods are looking to model the distribution of traffic in a network according to a set of constraints, notably related to transport capacity, time, and cost.

Traffic Assignment Problem | The Geography of Transport Systems — Traffic Assignment Problem

Purchasing an airplane ticket is a classic traffic assignment example. For instance, a potential traveler wishes to go from city A to city B at a specific date and time. A query to a reservation system will offer a set of choices (paths) along with a price quote for each path. The traveler will likely choose the least expensive path, which may not necessarily be a direct path and may involve a transfer at an intermediate airport C. When tens of thousands of travelers make these daily decisions, assigning passengers to paths (air service) becomes a very complex task for airlines and their reservation (traffic assignment) system. On the other hand, airline companies use these decisions to adjust their transport supply (mainly flights) to match the demand as closely as possible. This type of problem can be solved using optimization methods.

4. Traffic and its Properties

Traffic is the number of units passing on a link in a given period of time, and it is commonly represented by Q(a,b), that is, the amount of traffic passing on the a,b link (between a and b). Units can be vehicles, passengers, tons of freight, etc. Because of the characteristics of transportation networks, there are two major types of traffic flows:

Uninterrupted traffic. Traffic regulated by vehicle-vehicle interactions and interactions between vehicles and the transport infrastructure. The most common example of uninterrupted traffic is a highway.
Interrupted traffic. Traffic regulated by an external means, such as a traffic signal, often creates queuing. Under interrupted flow conditions, vehicle-vehicle interactions and vehicle-infrastructure interactions play a less important part. The most common example of interrupted traffic in urban circulation is regulated by traffic signals such as lights and stop signs.

Traffic is not a spatial interaction as an interaction represents movements between locations (origins and destinations), while traffic represents movements on network links. Traffic could be similar to an interaction when the transport network is equal to the set of Origin / Destination (O/D) pairs, but this is very unlikely.

Traffic is represented in a graph (network) by its value; the number of any units flowing (cars, people, tons, etc.). The intensity of the traffic is proportional to the load of the network.
Traffic is also represented in a graph by its assignment; how the traffic is distributed on a graph according to supply and demand.

Traffic is assigned on a network according to a sequence of links where every link has its value and direction where several conditions must be satisfied:

The graph must have nodes where traffic can be generated and attracted. These nodes are generally associated with centroids in an O-D matrix.
The minimal (l(a,b)) and maximal (k(a,b)) capacities of every link must be respected. k(a,b) is the transport supply on the link (a,b).
Transport demand must be respected. The O/D matrix has equal inputs and outputs (closed system).
There is a conservation of the traffic at every node that is not an origin or a destination.

There are also two general network traffic measures: maximum load and load.

Maximum Load (ML): Number of traffic units a network can support at any time. The maximal load is the summation of the capacity of all links.

$\large ML = \displaystyle\sum_{a} \sum_{b} k(a,b)$

Load (L): Number of traffic units that a network supports while fulfilling a transport demand. Load is the summation of the traffic of all links.

$\large L = \displaystyle\sum_{a} \sum_{b} Q(a,b)$

When the load of a network reaches the maximum load, congestion is reached.

5. Traffic Maximization and Costs Minimization

Traffic in a transportation network can be represented from two perspectives, traffic maximization and costs minimization. Traffic maximization involves the determination of the maximal transport demand that a network or a section of a network can support between its nodes.

$\large \displaystyle Max: Q(a,b), \forall (a,b) \\$
$subject \; to: \\$
$Q(a,b) \leqslant k(a,b)$

It involves maximizing traffic for all links, where the traffic on links must be equal to or lower than the link’s capacity. For simple networks, this procedure can be solved heuristically.

Cost minimization involves determining the minimal transport costs considering a known demand. Transport costs on a link are expressed by g(Q(a,b)) and the minimization function by:

$\large \displaystyle Min: \sum_a \sum_b g(Q(a,b)), \\$
$subject \; to: \\$
$Q(a,b) \leqslant k(a,b) \\$
$Q(a,b) \geq l(a,b) \\$

This equation aims to minimize the summation of transport costs (global cost) of each link subject to capacity constraints. Again, for simple networks, the procedure can be solved heuristically. Several types of costs are involved in the minimization procedure:

The global cost is the sum of transport costs for every link of a network, considering the demand.
The average cost expresses the transport cost per unit in a network considering the demand (global cost/load). It often varies with the demand.
The marginal cost expresses the costs incurred to transport a supplementary unit in a network considering an existing demand. The more a network is congested, the higher the marginal cost.

Two Perspectives for Considering Traffic | The Geography of Transport Systems — Two Perspectives for Considering Traffic

Heuristic Method for Traffic Maximization | The Geography of Transport Systems — Two Perspectives for Considering Traffic

Bibliography

Cambridge Systematics (2019) Quick Response Freight Methods, USDOT, Federal Highway Administration, Office of Planning and Environment Technical Support Services for Planning Research.