Why Delhi’s odd-even plan might work

While it is too early to look at data and come to an objective decision, there is enough reason to believe that Delhi’s “odd-even” plan (that restricts access to streets on certain days to cars of a certain parity) might work.

The program was announced sometime in December and the pilot started in January, and you have the usual (and some unusual) set of outragers outraging about it, and about how it can cause chaos, makes the city unsafe and so forth. An old picture of a Delhi metro was recirculated on Monday and received thousands of retweets, by people who hadn’t bothered to check facts and were biased against the odd-even formula. There has been some anecdotal evidence, however, that the plan might be working.

It can be argued that the large number of exceptions (some of which are bizarre) might blunt the effect of the new policy, and that people might come up with innovative car-swap schemes (not all cars get out of their lots every morning, so a simple car-swap scheme can help people circumvent this ban), because of which only a small proportion of cars in Delhi might go off the roads thanks to the scheme.

While it might be true that the number of cars on Delhi roads might fall by far less than half (thanks to exemptions and swap schemes) due to this measure, that alone can have a significant impact on the city’s traffic, and pollution. This is primarily due to non-linearities in traffic around the capacity.

Consider a hypothetical example of a road with a capacity for carrying 100 cars per hour. As long as the number of cars that want to travel on it in an hour is less than 100, there is absolutely no problem and the cars go on. The 101st car, however, creates the problem, since the resource now needs to be allocated. The simplest way to allocate a resource such as a road is first come-first served, and so the 101st car waits for its turn at the beginning of the road, causing a block in the road it is coming from.

While this might be a hypothetical and hard-to-visualise example, it illustrates the discontinuity in the problem – up to 100, no problem, but 101st causes problem and every additional car adds to the problem. More importantly, these problems also cascade, since a car waiting to get on to a road clogs the road it is coming from.

Data is not available about the utilisation of Delhi roads before this new measure was implemented, but as long as the demand-supply ratio was not too much higher than 1, the new measure will be a success. In fact, if a fraction f of earlier traffic remains on the road, the scheme will be a success as long as the earlier utilisation of the road was no more than \frac{1}{f} (of course we are simplifying heavily here. Traffic varies by region, time of day, etc.).

In other words, the reduction in number of cars due to the new measure should mean significantly lower bottlenecks and traffic jams, and ensure that the remaining cars move much faster than they did earlier. And with lesser bottlenecks and jams, cars will end up burning less fuel than they used to, and that adds a multiplier to the drop in pollution.

Given that roads are hard to price (in theory it’s simple but not so in practice), what we need is a mechanism so that the number of cars using it is less than or equal to capacity. The discontinuity around this capacity means that we need some kind of a coordination mechanism to keep demand below the capacity. The tool that has currently been used (limiting road use based on number plate parity) is crude, but it will tell us whether such measures are indeed successful in cutting traffic.

More importantly, I hope that the Delhi government, traffic police, etc. have been collecting sufficient data through this trial period to determine whether the move has the intended effects. Once the trial period is over, we will know the true effect this has had (measuring pollution as some commentators have tried is crude, given lag effects, etc.).

If this measure is successful, other cities can plan to either replicate this measure (not ideal, since this is rather crude) or introduce congestion pricing in order to regulate traffic on roads.