Networks are collections of connected linear objects such as roads, railroads, or rivers that branch from place to place. They come in different sizes, numbers of branchings, and angular configurations.
You can measure connectivity in a network by comparing the number of actual node-to-node links that exist in a given network to the maximum number of nodes that are possible. This measure of connectivity is called the gamma index. Usually, the index ranges from a value of 0 (which indicates no connected links at all) to 1 (where all possible links are connected). Both general and transportations specific GIS software packages contain algorithms that allow you to calculate the gamma index, which the software records as decimal values. Most applications of the gamma index relate to human transportation on systems.
MEASURING AND USING CONNECTIVITY
A GIS calculates the gamma index by counting all possible connections (links) among all the nodes in the database and then dividing this total (the number of actual links) by the maximum number of possible links. You use the gamma index connectivity figure indirectly when you perform shortest-path analysis.
WORKING WITH IMPEDANCE VALUES
When you treat networks as corridors, the movement of fluids, objects, animals, and/or vehicles is your primary concern. For any movement, the nature of the network as a corridor has an impact on how fast things move and in some cases, even whether they move at all. The resistance to movement is called impedance and can be a function of the size of pipeline in a water delivery system, the roughness of dirt or gravel roads, or the number of lanes in highways. The most common use of network impedance is to model street patterns for transportation routing.
REAL WORLD GIS – Street patterns provide an excellent example of how factors can affect speed in a network. Speed may increase or decrease for several reasons. Here’s a quick list:
- Posted speed limits help determine the maximum travel speeds for streets and highways (sometimes even the minimum speeds).
- Fluctuations in traffic density often determine how fast the traffic will move at different times of the day.
- Accidents and other unplanned disruptions are bound to slow traffic, especially if lanes are closed off.
- Street repairs and changes in road condition often result in changes in traffic flow.
- The existence of border checks, sobriety checkpoints, weigh stations, and other regulatory facilities result in slower traffic flow.
- Changes in weather, especially the existence of dust storms, rain and hailstorms, blizzards, and sleet storms will often have huge impacts on traffic flow.
MODELING IMPEDANCE FOR TRAFFIC FLOW
Given the many factors that affect the movement of flow, especially traffic flow on streets, modeling these changes really improves your ability to know when your grocery deliveries will arrive, how fast a fire engine can get to a fire, the fastest way to get to a particular restaurant for dinner, or the route that you might need to take to pick up your children from their many activities.
When you model impedance, you do have to deal with one complexity – most software gives you many options. And you simply won’t use some of those options because they require that you know much more about your traffic network than you probably do. Ever see those little black traffic counters (they look like rather large power cords) running your streets from time to time? Traffic engineers and transportation geographers use these counters to determine how much traffic flows past a particular point at any given time. You could easily include this important information in your GIS as impedance data. Other common traffic-flow impedance data include speed limits, stoplights, and stop signs.
Here’s a short list of some of the attributes, or options, that you can put into a GIS impedance layer that you might use for traffic modeling:
- Impedance attribute: How long it normally takes to travel a certain distance.
- Default cutoff value: The value at which the computer stops searching for a location. You can override or change this value.
- Accumulation information: A list of possible attributes that accumulate while distance increases, including costs, students riding a bus, and many more.
- Restrictions: Restrictions that you place on the use of links (for example, the permitted types of traffic on portions of your road network). For example, you can choose to force hazardous cargo to use certain streets.
- Hierarchy: A set of rules of travel, regardless of how your software determines the impedance values.
These factors (and others that depend on the software you use) are sometimes referred to as the Origin-Destination (OD) matrix. The data for these factors form a separate table. When you use the GIS for transportation modeling, the software compares the network by examining the OD matrix so that it knows the rules to apply and where to apply them. The OD matrix contains several components, including origin, destination, and barrier information. By reading the OD matrix, the software knows the ID codes you have placed at strategic locations, how to read the impedances you have linked to those ID codes, and other necessary factors that give you the power to simulate how real traffic flows operate.
WORKING WITH ONE WAY PATHS
Impedance, like surface friction values, can be low or high, can have short distances or long, and even prevent movement entirely. Dead ends, checkpoints, and bridge collapses prevent the movement of travel. You model these impedances by placing no=movement commands at these points. However, you can restrict movement only to one direction by creating unidirectional (or one-way) paths.
UNDERSTANDING UNIDIRECTIONAL PATHS
In certain situations, travel along a network normally takes place only in a given direction. A fast-moving stream moves rafts in only one direction. Some gate entries allow traffic to move in only one way and out another for control – some gates even place those nasty spikes to rip up your tires if you try to back up. The most common example of a unidirectional path is the one-way street. I focus on that example in the following section because it’s easy to understand and modeled frequently in transportation GIS applications.
MODELING UNIDIRECTIONAL PATH
GIS software is pretty adept at handling the factors that influence travel through a network. One of the most common (and aggravating) situations that street maps don’t often show is the location and direction of one-way streets.
One-way streets are coded in a GIS by including a travel direction restriction in your OD matrix. When the computer tries to model vehicle access to a north-directed one-way street from the south, or even to make turns into it in the opposite direction, the GIS stops the movement and redirects the search to look elsewhere for a path. In essence, the effect is the same as when you put up a barricade across the street that prevents travel in that direction.
Figure: The GIS software prevents movement in directions opposite to the direction of one-way streets.
A network’s complexity is partly measured by the number of links it has compared to the maximum number it could have (the gamma index). One other factor both characterizes complexity of a network and adds to the robustness of traffic modeling capabilities. That characteristic, called circuitry, is based on the idea of closed loops. Closed loops allow moving objects, fluids, and so forth to travel alternate routes when moving along a network.
KNOWING WHEN LINES CREATE CIRCUITS
When you perform traffic analysis for routing, allocating customers or bus riders, or finding the nearest facility, having circuits greatly increases your route options. In some cases, the routes may be longer but could save travel time because of reduced traffic and less traffic-related impedances.
MEASURING AND MODELING CIRCUITS
The algorithm for modeling circuitry is very similar to the one you use for network connectivity (which I discuss in the earlier section “Measuring and using connectivity”). Rather than a gamma index, you use another ratio called the alpha index. In transportation geography, the alpha index, like the gamma index, is a ratio. In the alpha index, the ratio compares the actual number of circuits (loops in a network composed of nodes and links) divided by the maximum circuits possible. Like with the gamma index, both general and transportation-specific GIS software has the alpha index built in for you.
DIRECTING TRAFFIC AND EXPLOITING NETWORKS
Networks provide a selection of really useful techniques that you can employ in businesses, government, organizations, emergency services, and many other applications. After you add to your GIS a complete network that has appropriate road designations and ID codes for your impedance values, the impedance values themselves, plus turn information, you have one of the most powerful networking tools available anywhere. Here’s a quick list of the operations you can use in most GIS software:
- Finding the best route (shortest, fastest, or even the most scenic)
- Finding the closest geographic feature to you
- Finding service areas, such as what parts of town are served by a single fire station.
FINDING THE SHORTEST PATH, OR ROUTE
Many people use street maps to figure out the shortest route from their current location to some specified location. If you search for the shortest path, you use the length of the network links to decide the best route. Because you’re not concerned with time, you don’t need to include impedance values in your search. Although the GIS ignores most impedance values when you specify that they aren’t needed, the software always includes some indication of one-way streets and dead ends so that it doesn’t send you a wild goose chase.
Even if you don’t own a complete professional GIS, you may have already seen this ability to find the shortest path in action. Yahoo! Maps and Google Maps find the shortest path from one town to another or one address to another. These packages are rudimentary GIS software and do a reasonable job for general routing tasks. For detailed, time-critical routing, especially for business and emergency services, these packages typically don’t include the detail that you need to efficiently navigate through road networks, especially during critical times of the day like rush hour.
The shortest path means shortest in terms of distance traveled. If you want to get there fast, use the fastest-route feature of your GIS.
Finding the shortest route to one destination is pretty handy, but you can also use the GIS to find the closed of a group of possible destinations, as well. You’ve probably used this kind of feature when you wanted to find the closest Sears or Walmart store by using the store’s web site. The software finds the addresses of all the possible locations and performs a shortest-path analysis on all of them from your current location. Business have found that providing interactive maps directing traffic to their front door (so to speak) is a really powerful marketing tool.
- FINDING THE FASTEST PATH
The shortest way from one place to another isn’t always the fastest. The fastest-path search allows your GIS to start from one location and accumulate impedance values while it searches through the network to find your destination. Instead of keeping track of just distance, it combines distance and impedance to calculate the route that has the least amount of total impedance. Typically, GIS software measures impedance in time, so a street that has a 25 mile-per-hour speed limit has a higher impedance value (longer time) than one that has a 75-mile-per-hour speed limit.
Figure: The shortest path versus the fastest path
One aspect of the fastest-path approach is a bit unique because your impedance values are based not just on speed limits, impedances, and typical traffic volumes, but also on the time of day. Some construction zones operate at different times of day, traffic congestion is worse during rush hours, and even the season might impact which roads are open. Encode in the OD matrix the times of day when traffic is congested on which streets to make sure that the software can determine how drivers can avoid those streets at those times. In some hilly cities and towns, selected streets are blocked off at times in winter because the snow and ice makes those streets dangerous to drive. You can code all sorts of impedances as windows of time along selected portions of the network and store them in an attribute table.
- FINDING THE NICEST PATH
You may be concerned about factors other than speed or distance. Many highways have scenic routes that are a bit slower or perhaps even longer than a more direct route, but you may want to view the scenery. GIS software can help you find the scenic routes, as well as the fastest and most direct routes, because you can create scenic impedance, values. When you run your search, you simply ask the GIS to search for links that have the nicest scenery. You just need to remember to include the values that you want to search for in your network database attributes.
- FINDING THE SERVICE AREAS
The network database allows you to create all sorts of values to put into your tables. You can include distance, impedance, turning and even scenic information. One really powerful tool for service providers and business alike is the ability to find services areas.
A service area identifies places that are within a reasonable distance for use and relies on knowing how many people or houses are located along individual links in a network, much like impedance values, except that the database has to know how many people are along each link. The software stats at some point location and searches either along a chosen path or outward in all directions. While it searches, it counts all the houses or people it passes until it reaches the end of the database, some specified search radius, or some maximum quantity of people or houses.
REAL WORLD GIS – You may find the service area tool useful in a number of different settings. Here’s a list of some common uses:
- Creating bus routes for school children, limiting the search by the number of passenger seats on the bus.
- Determining how many fire stations a town needs, based on a search of the number of homes one fire station can safely service (based on historical numbers of fires and other factors) in a worst-case scenario.
- Marketing to potential newspaper subscribers based on an accumulated search of households that don’t currently subscribe to your paper.
- Creating service areas in which a pizza delivery store can deliver pizza within an assigned time period.
Service-area analysis allows you to use all the impedance and turning tools that you use for any other analysis. His process of finding service areas, often called allocation by geographers, is a very popular tool among business analysts because they cannot only allocate for their own facility, but also compare themselves to their competition. Allocation is one of the more popular economic placement tools available in GIS today.