Travel planning and mathematics
Travel planning and mathematics intersect in the field of transportation planning, which encompasses everything from individual travel choices to larger regional transportation infrastructures. Professionals, including civil engineers and transportation planners, employ mathematical equations and computer models to analyze different transportation modes and routes, aiming to minimize journey costs. These planning efforts can be categorized into long-term and short-term strategies. Long-term planning focuses on substantial projects such as land use and freeway placements, balancing various objectives like cost reduction and environmental impact, while short-term planning involves more immediate actions like adjusting traffic light timings and modifying public transport schedules.
To evaluate alternatives effectively, planners often use simplified formulas that consolidate multiple factors—such as fare prices and travel times—into a single cost measure. This helps in determining the most efficient transport options. Additionally, metrics like traffic density and flow are employed to assess network performance, which varies based on specific urban conditions. The gravity model is another mathematical tool used to estimate traffic patterns between different zones, reflecting the relationship between origin and destination traffic and the distance between them. Overall, travel planning relies heavily on numerical data to inform decisions that impact transportation systems and urban mobility.
Travel planning and mathematics
Summary:Mathematical models are used to plan and evaluate short- and long-term transportation infrastructure decisions.
Travel planning is a broad field that covers everything from individual journey planning (for example, deciding which form of transportation to use when commuting) to regional transportation planning (for example, deciding on the layout for a new train line or arterial road). Professional transportation planners and civil engineers use equations and computer programs to directly compare different transportation modes and routes. These equations can be very simple with just a handful of terms, or incredibly complex models with hundreds of interacting variables. Regardless of the complexity of the analysis, the ultimate goal is to satisfy the objectives of the planning project and often the most important objective is to minimize journey costs.
Governments aim to maintain effective road networks and public transportation systems. Within certain cities, however, there can be a distinct bias toward either private or public transportation. This bias reflects the fact that governments prioritize certain planning decisions over others. These decisions fall into two broad categories: long-term and short-term planning.
Long-Term Planning
Long-term planning includes decisions such as the use of land and placement of new freeways or bypasses. The objectives for these projects are often manifold: reduce costs, reduce pollution, reduce noise, maintain traffic flow, and maintain priority for public transport and carpool vehicles. It is the challenge of the transport planner to balance these objectives and ensure that the final decision satisfies these criteria.
Long-term planning also incorporates projections of future effects. For example, a wider freeway leads to better accessibility in certain urban areas, which eventually leads to more construction in those areas. Construction, in turn, leads to more traffic on the freeway and a renewed need to widen the road, thus creating a cycle. Long-term projects typically take several years to implement and even longer to monitor their impact.
Short-Term Planning
Short-term planning includes the introduction of bus priority lanes, changing the timing of traffic light signals, using trains with a greater numbers of cars during peak travel times, changing the price of parking in a particular area, changing taxi regulations, introducing new public transport fare systems, and so on. These are changes that can be implemented and evaluated within weeks as opposed to years.
Comparing Alternatives
To make any long-term or short-term planning decisions, it is necessary to compare a range of alternatives, side by side, using as few indices as possible. As a simple example, a set of four time and money measurements can be reduced to a single measurement of cost (C) using the equation
C = a(P) + b(tT) + c(tw) + d(tJ)
where P is the fare price, tT is the transit time, tW is the wait time, tJ is the journey time, and the coefficients a, b, c, and d are used to weight the components relative to one another (for example, for a given individual, wait time may be perceived to be twice as costly as journey time). This equation is particularly useful for comparing different forms of public transport. The single cost values will paint a very clear picture of which mode and route has the optimum mix of short times and low costs. Cost is often expressed in minutes, as opposed to dollars, as this measure will remain stable even as prices increase.
Some other measures used by transport planners include traffic density (number of vehicles on a given stretch of road), traffic flow (number of vehicles passing through a given stretch of road every minute), and performance index (an aggregate measure of the delays experienced in a given transport network). Each of these measures must be interpreted in context because acceptable ranges for the values will vary depending on road type, city size, and network connectivity.
Another common method used to estimate the amount of traffic passing between two zones (for example, a neighborhood and a commercial center) is called the “gravity model.” It was given this name because the form of the equation is similar to Isaac Newton’s equation of gravity. The traffic passing between two zones, A and B, is proportional to the product of the traffic originating in zone A and the traffic arriving in zone B but inversely proportional to a function of the distance between the two zones.
Governmental transport planners use these measures to test for weaknesses in the transport network—places where demand exceeds supply—and to gauge the effects of previous planning decisions. The act of planning is therefore firmly rooted in the interpretation of numerical output from mathematical analyses.
Bibliography
Banister, David, ed. Transport Planning. 2nd ed. New York: Taylor & Francis, 2002.
Black, John. Urban Transport Planning. London: Croom Helm, 1981.
Button, Kenneth. Transport Economics. Cheltenham, England: Edward Elgar Publishing, 2010.
O’Flaherty, Coleman. Transport Planning and Traffic Engineering. Oxford, England: Elsevier, 1997.
Wells, Gordon Ronald. Comprehensive Transport Planning. London: Griffin, 1975.