How to generate the route for Ride sharing service? : Equity vs Society

There are two principles in explaining the route choice behavior of travelers in the transportation network field.

In the User Equilibrium (UE) principle, the travel times of all routes used should be the same, and the travel times must be less than or equal to those of unused routes. When this state is reached, all passengers are no longer motivated to change their route, their route choices are stabilized.

This is Wardop's first principle, and as it was later revealed, this state can be reached through the process of all passengers choosing their shortest route uncompromisingly. (Thx for S. Dafermos and other transportation researchers)

(Say sorry to readers who have read so far and have a headache. This article is mainly for transportation network optimization or transportation planning enthusiasts. But if you haven't had a headache yet, an interesting story will follow from now on.)

With this background, let's talk about the route generation problem of DRT. The route choice problem of passengers is essentially an individual's optimal choice problem. However, the route generation problem of ride sharing, such as DRT, is a problem of creating 'one path' by considering all the shortest paths of all riders.

Unless all riders have the same origin and destination, there is no optimal route for everyone. In other words, not all passengers are satisfied all the time. We must make a choice.

Let's start with Studio Galilei’s (Studio G) experience in Naju City, Korea. TAMOS-O, Studio G's DRT Operation Platform, has Maximum Detour Rate (MDR). Suppose you have 50% MDR set.

One day, three riders boarded the same fleet. Rider A experienced 49% of detours based on one’s shortest route. Rider B and C both experienced 0% of detours. Under the given constraint(MDR 50%), this route has no problem. Total travel time of three rides is also minimum.

However, passenger A raised a strong complaint. In Community DRT, all riders are aware of the local transportation network well. Therefore, rider A knows that only he/she took a detour, and rider B and C took the shortest route. B and C are also the same.

TAMOS-O created the shortest route for the three riders under the constraint accurately. This route is a kind of group compromise route. So, It is a social optimum route for ride sharing.

But we can understand rider A's complaint. Can we create a more equal path, a route that is closer to Nash equilibrium, that divides detours and burdens each other? The answer is yes. We can use various route calculation technologies.

What is the problem?

As all transportation planners know, the total travel time of all riders will be greater than that of the social optimum sharing route when traveling on this equivalent detour-share route. In the transportation network theory, the total travel time of the UE state is greater than or equal to that of the SO state

Now, the choice is up to the algorithm designer.

SO principal? UO principal? Or what in between?

Algorithm designers in Studio G are also suffering from this problem. And they will apply a few algorithms in this year.

The results can be presented at the TRB meeting in 2025, or if many of you can't wait until then, it can be released first through Studio G's report posting.

Fortunately (or unfortunately), there are still a lot of exciting, but challenging homework for transportation researchers in the mobility field.