Thursday, August 2, 2012

Optimal Location of Speed Limit Signs

One of the nice things about the relatively more recent automobile GPS products is that they are able to inform us of the current speed limit. Sometimes, when we take our eyes of the road for a second to grab a soda, we may have driven past a speed limit sign and be unaware of the new speed limit. Of course, there are times when the GPS unit itself does not display the speed limit for certain areas, and at other times, it is off by 10 mph, perhaps due to recent road updates. Like any decision support system, the GPS unit cannot be a fail-safe backup for user negligence.

The problem of optimally locating speed limit signs on a network must have been studied and solved a long time ago especially since the analysis of traffic and transportation networks has long been popular research area among ORMS folks. Perhaps there exists a practical combinatorial optimization problem in terms of determining minimal/safest/least ambiguous ways of locating speed signs in the presence of scarce resources and budget limits. A partial list of assumptions and constraints include:
- Speed limits change in discrete quantities of 5mph or 10 mph
- Every driver will treat the last speed limit sign (or update) they saw on the network as the prevailing speed limit
- Every driver at every point in the road network must be in unanimous agreement on what the speed limit is. This is the ideal situation.
- In practice, perhaps the above requirement can be relaxed to stipulate that any non-trivial ambiguity must be resolved with a certain time or distance threshold whose value is location-specific
- Different types of speed limit signs are possible - they may be time-dependent (day/night) as well as location-dependent (school, bridge, tunnel) - Speed limit values can be fixed or variable ("smart roads"). This requirement can potentially inject a dynamic optimization aspect into the problem.

Perhaps a greedy method may be sufficient to generate a good answer to the (fixed value) speed-limit signpost location problem. There are of course, numerous other related location optimization problems on road networks:
locating advertisement hoardings, direction/information signs, emergency vehicles, detours, etc. All these models appear to be well studied in the literature. The proliferation of smart-phones can also have an impact on future 'smart road network' design in general. All in all, location, location, location science continues to be a very interesting sub-area of Operations Research.