Roadway capacity

A simple model can provide estimates for roadway capacity

Why develop a simple model? Three reasons (goals):

While constructing the model, we can make our assumptions perfectly clear, and understand more clearly what determines roadway capacity;
Once the model is formulated, we can calculate (roughly) the value of a road's capacity as a function of traffic's average speed; and
We can use the model to help compare one road configuration to another and to see potential performance problems.

Caveat: In applying the model, its simplicity and the elements of realism that it ignores must be kept in mind.

If you don't care about assumptions of the model, skip the first table below. Or, if you really want only the non-technical summary that represents my conclusions based on the simple model plus comparisons with the Study and "Reality", you may jump to here.

Model assumptions and rationale

Assumption 1. We assume an average car length of l = 14 ft. Keep it simple-- consider only those complications that are essential.

Assumption 2. We assume all cars travel with the same speed and the same bumper-to-bumper separation.

Assumption 3. We assume that there are no interactions between cars in adjacent lanes.

Assumption 4. We assume, if there are multiple thru-traffic lanes, that drivers use them equally. This is probably a reasonable assumption for moderately- to heavily-loaded urban streets. (Informal survey of traffic on Trinity suggests that a 50-50 split of traffic between the two lanes is reasonable, especially at peak times, which are of greatest concern in roadway design.)

Assumption 5. We assume that vehicles are separated, on average, by a follow-up headway of "hw" seconds. We specify the headway in terms of the time interval between vehicles at whatever speed they are traveling. Headway (in seconds) is equal to the separation distance (in feet) divided by the speed (in feet/sec). Here are a few examples at various speeds.

Headway is a real physical quantity that can be measured and studied under various conditions. There are some general characteristics of headway that are model-independent. Traffic conditions with lower headway are perceived by drivers as higher in congestion and are generally less safe.

As an ingredient in a capacity model, follow-up headway (hw) can be considered a parameter that idealizes the very complicated reality of vehicle capabilities, roadway conditions, and driver behaviors.

Examples of some important vehicle characteristics include

dimensions
weight
max acceleration and deceleration
turning agility
control interface with driver
current state (maintenance, operating conditions, breakdowns)

Roadway characteristics that impact safe and achievable headways include

surface
geometry
curvature and inclination
lines of sight
current state (maintenance, accidents, weather, traffic)

Driver behaviors that affect safe and achievable headways include

mental and physical capabilities
training and experience
current state (alertness, attentiveness, fatigue, emotions, intoxication)

In a sense, vehicles and roadways are designed to give a usable set of transportation tools, and "users" (mainly automobile drivers, in the current world of NM502) are the agents who use the tools to transport people and goods according to their best real-time judgments.

So, in the context of our simple model for roadway capacity, a single value of hw can be viewed as an average over a set of drivers and vehicles under a particular kind of driving conditions. We could use a range of hw values to consider different kinds of drivers, roadways, or driving conditions.

There are several ways one could motivate a particular follow-up headway value or range of values.

(1) One could use a guideline specified in the NM Driver's Manual called the "3-second rule" (described here, p.32; note that this guidance, while useful, is not conservative enough to avoid multi-car collisions in the case of an instantaneous stop).

(2) One could use a US-wide average from a standards document, such as the 2010 Highway Capacity Manual and/or a value from the roadway modeling literature, for example Akcelik (International Roundabout Conference, Transportation Research Board, Carmel, IN, May 18-20, 2011). The average headway recommended here is 3.2 sec.

(3) One could use a local measurement. Los Alamos County traffic data collected at two points along NM502 on August 12, 2010 yielded average headway at peak times of 2.8 sec (with a standard deviation of 0.14 sec).

Since these are fairly consistent, we will choose a "nominal" value of hw = 3 sec. To consider a variety of vehicle, roadway, and driver characteristics, we'll look at a range of headway values between 2 sec (straight roads, aggressive drivers, optimum weather and roadway conditions) and 4 sec (sharp curves, defensive drivers, adverse weather conditions).