The Chicago Skyway and Network Traffic
I have lived in Chicago my entire life. I often visit my grandma who lives around an hour away in Three Oaks, Michigan. Ever since I have been able to drive there myself I always find myself asking the same question: “Should I take the Skyway?”. The Chicago skyway is a 7.8 mile toll road that connects the Dan Ryan’s expressway to the Indiana toll roads. It is a shorter (distance wise) route option for those traveling to and from Indiana and Chicago, than just continuing on the I-94 all the way. But the skyway route comes with many tolls making drivers like myself ask, at what point is it worth it?
To answer this question I will examine the drive from downtown Chicago (The Willis Tower) to Hammond Indiana. The 2 routes that can be taken are shown in this google maps screenshot.
The grey route on the left (route 1) is the alternative to the Skyway, I-94. The colored route is Route 2:The Skyway Route
Now, here is a simple Network Traffic model of the two routes with formulas calculating the time each route takes with x being the amount of drivers on route 1 and y being the amount of drivers on route 2. In this scenario, there are 400 drivers.
Let’s unpack the two formulas. Route 1 is 28.9 miles and Route 2 is 23.9 miles. Assuming there is no traffic and cars are going an average 70 miles per hour Route 1 should have a base travel time of 24.77 minutes and Route 2 should have a base Travel time of 20.4 minutes. Both routes are mainly 3 lanes so the factor in which the number of cars increases travel time are relatively the same. For this model I have estimated a value of some number of cars divided by 15. Finally, the total toll cost for route 2 is $9.42. According to the US Bureau of Labor Statistics, the average hourly wage in the Chicagoland Area is $29.74. Therefore for this average chicagoan $9.42 is worth around .316 of an hour, or 19 minutes.
For this model, the nash equilibrium is at x=309.725 and y=90.275. These are the x and y values in which travel time is equal for the two routes. Here is the work:
In conclusion, which route you should take depends on what the other cars are deciding. This was a very simple model based on estimations. To make the model accurate I could calculate a more accurate number to divide the number of cars on each route by, by analyzing data about car numbers and travel times on each route. But for this simple model, it seems to be a pretty safe bet to take I-94, not the Chicago Skyway.
Sources-
https://tollguru.com/toll-calculator
https://www.bls.gov/regions/midwest/news-release/occupationalemploymentandwages_chicago.htm