Tricky Traffic
Traffic is something that can truly rule our everyday lives. Whether we admit it or not, the idea of sitting in a car and commuting can be a daunting and very time wasting task that is a necessity for survival. In my hometown, traffic has been growing exponentially over the past few years and it is truly a time for change. As discussed (in the article above), the idea of expanding the 241 freeway is a measure that will hopefully alleviate traffic in my hometown area. But, will finishing this freeway make the large difference that is expected?
If we really boil down the fat and take a look at the proposal for finishing this freeway it is very evident that its construction will be a HUGE benefit to the people of the southern California area. Funnily enough, we can use the tools of networks and game theory help rationalize the completion of this toll road.
*Notes About Facts Below
There are 21 million people who live in the san diego/orange county area(denoted by article). Lets take a number, such as 100,000 people, who use this freeway every day. We know that currently there are two ways of going from LA to San Diego. One route is 1 hour + x/100k. The other route is y/100k + .5 hours + x/100k. By this logic, we know that any route that we have to take, we use the x/100k route. Therefore, everyone uses the x/100k meaning: 100k/100k = 1 hour. We then Can see if we go straight from LA-OC-SanDiego (1+X/100k(really just 1)) =2 hours travel time. We can also see that by alternate route y/100k + .5+ x/100k (which is really 1) will also equal 2 hours. Why? Because We know that people will not choose a route that will take longest. That being said, if 50k (half of the people) choose the Alt route method… there travel time would be .5 + .5 +1 = 2 hours. Also Y/100k +.5+1= 2. Therefore Y=50K and X=100K
Now, let’s see what happens if the new route from ALT OC replaces the current 0.5 route. We can deduce that using the Alt Route yields y/100k + 1 and the Normal OC route yields 1+ x/100k. If we set those two equations equal to each other we can see that both X=Y=50K. That Being Said the travel time for either route is .5+1 = 1.5 hours!
As we can see, if we were to implement this new extension on the 241 toll road it would help reduce traffic for everyone. The pain of living in a traffic centered society is what cripples southern California and really takes a hit to the quality of life index in the area. I know that from my personal experiences sitting on that freeway during rush hour can be almost intolerable. I sometimes even worked late, an extra two hours, this summer just to avoid that freeway during the 5pm-7pm time period. If the politicians know what’s best, it would a very wise to fund this freeway project- to relieve that area of traffic once and for all. Either way, it is interesting to see that the tools needed to justify this solution is just a simple application of game & graph theory.
*The example numbers used in this article are not entirely accurate. The 21 milion people is a direct quote from the article, and the 100k is a general number used to justify the formula.(the model holds for any # of people using the freeways).The set travel times (.5, 1 etc…) are from my own personal experiences as well as google maps timing info.
It really ticks me off when I am stuck in a traffic jam, especially when I am in a hurry. Aging infrastructure across the country has cities scrambling for cash to pay for badly needed renovations. The economic impact is huge so it’s obvious that the government should make infrastructure a priority.