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.

Car-free days, traffic jams and social capital

While most news nowadays is fairly hilarious, one piece was more hilarious than the others. This was about traffic jams in Gurgaon yesterday, a day that had been declared as a “Car Free Day”.

You might wonder why there might be traffic jams on days that are supposedly “Car Free”. I don’t know the precise effect this can be classified under, but it’s somewhere in a linear combination of Prisoner’s Dilemma and Tragedy of the Commons and correlation, all led by a lack of social capital.

There are no rules that declare the day to be car free. It’s just a “request” by the local government (traffic police in this case). While there were some nominal efforts to improve public transport for the day, etc, there was nothing else that was different yesterday from other days. So why did it lead to a traffic jam?

If you know it’s a car free day and you have a car, you’ll assume that other people are going to leave their cars at home, and that you are going to have a free ride in free-flowing non-traffic if you take out your car. And so you take out your car. Unfortunately, the number of people who think such is enough to cause a traffic jam.

The problem stems with a lack of social capital in Indian cities (based on anecdotal experience (my own data point from 2008-09), I would posit it is lower in Gurgaon than in other Indian cities). As a consequence, when people are trying to make the “great optimisation”, they allocate a greater weight than necessary to their own interests, and consequently a lesser than necessary weight to others’ interests. And thus you end up with outcomes like yesterday’s. More generally, “requests” to people to give up a private benefit for others’ benefits can at best turn out to be counterproductive.

While designing policies, it’s important to be realistic and keep in mind ease of implementation. So if the reality is low social capital, any policy that requires voluntary giving up by people is only going to have a marginal impact.

Coming back to traffic, I’m increasingly convinced (I’ve held this conviction since 2006, and it has only grown stronger over time) that the only way to make people switch to public transport is to lead with supply – flood the streets with buses, which among other things actually increase the cost of private transport. Once there is sufficient density of buses, these buses can be given their own lanes which further pushes up the cost of driving. Then we can look at further measures such as prohibitive parking costs and congestion pricing.

We can have these notional “no car days” and “bus days” and “no honking days” but it is unlikely that any of them will have anything more than a token effect.

Where Uncertainty is the killer: Jakarta Traffic Edition

So I’m currently in Jakarta. I got here on Friday evening, though we decamped to Yogyakarta for the weekend, and saw Prambanan and Borobudur. The wife is doing her mid-MBA internship at a company here, and since it had been a while since I’d met her, I came to visit her.

And since it had been 73 whole days since the last time we’d met, she decided to surprise me by receiving me at the airport. Except that she waited three and a half hours at the airport for me. An hour and quarter of that can be blamed on my flight from Kuala Lumpur to Jakarta being late. The rest of the time she spent waiting can be attributed to Jakarta’s traffic. No, really.

Yesterday evening, as soon as we got back from Yogyakarta, we went to visit a friend. Since this is Jakarta, notorious for its traffic, we landed up at his house straight from the airport. To everyone’s surprise, we took just forty minutes to get there, landing up much earlier than expected in the process.

So I’ve described two situations above which involved getting to one’s destination much ahead of schedule, and attributed both of them to Jakarta’s notorious traffic. And I’m serious about that. I might be extrapolating based on two data points (taking into the prior that Jakarta’s traffic is notorious), but I think I have the diagnosis.

The problem with Jakarta’s traffic is its volatility. Slow-moving and “bad” traffic can be okay if it can be predictable. For example, if it takes between an hour and half to hour and three-quarters most of the time to get to a place, one can easily plan for the uncertainty without the risk of having to wait it out for too long. Jakarta’s problem is that its traffic is extremely volatile, and the amount of time taken to go from one place to the other has a massive variance.

Which leads to massive planning problems. So on Friday evening, the wife’s colleague told her to leave for the airport at 7 pm to receive me (I was scheduled to land at 10:45 pm). The driver said they were being too conservative, and suggested they leave for the airport at 8, expecting to reach by 10:30. As it happened, she reached the airport at 8:45, even before my flight was scheduled to take off from KL! And she had to endure a long wait anyways. And then my flight got further delayed.

That the variance of traffic can be so high means that people stop planning for the worst case (or 95% confidence case), since that results in a lot of time being wasted at the destination (like for my wife on Friday). And so they plan for a more optimistic case (say average case), and they end up being late. And blame the traffic. And the traffic becomes notorious!

So the culprit is not the absolute amount of time it takes (which is anyway high, since Jakarta is a massive sprawling city), but the uncertainty, which plays havoc with people’s planning and messes with their minds. Yet another case of randomness being the culprit!

And with Jakarta being such a massive city and personal automobile (two or four wheeled) being the transport of choice, the traffic network here is rather “complex” (complex as in complex systems), and that automatically leads to wild variability. Not sure what (apart from massive rapid public transport investment) can be done to ease this.

Correlations: In Traffic, Mortgages and Everything Else

Getting caught in rather heavy early morning traffic while on my way to a meeting today made me think of the concept of correlation. This was driven by the fact that I noticed a higher proportion of cars than usual this morning. It had rained early this morning, and more people were taking out their cars as a precautionary measure, I reasoned.

Assume you are the facilities manager at a company which is going to move to a new campus. You need to decide how many parking slots to purchase at the new location. You know that all your employees possess both a two wheeler and a car, and use either to travel to work. Car parking space is much more expensive than two wheeler parking space, so you want to optimize on costs. How will you decide how many parking spaces to purchase?

You will correctly reason that not everyone brings their car every day. For a variety of reasons, people might choose to travel to work by scooter. You decide to use data to make your decision on parking space. For three months, you go down to the basement (of the old campus) and count the number of cars, and you diligently tabulate them. At the end of the three months, you calculate that on an average (median), thirty people bring their cars to work every day. You calculate that on ninety five percent of the days there were forty or fewer cars in the basement, and on no occasion did the total number of cars in the basement cross forty five.

So you decide to purchase forty car parking spaces in the new facility. It is not the same set of people who bring their cars to work every day. In fact, each employee has brought his/her car to the workplace at least once in the last three months. What you are betting on here, however, is correlation, You assume that the reason Alice brings her car to office is not related to the reason Bob brings his car to office. To put it statistically, you assume that Alice bringing her car and Bob bringing his car are independent events. Whether Alice brings her car or not has no bearing on Bob’s decision to bring his car, and vice versa. And you know that even on the odd day when more than forty people bring their cars, there are not more than forty five cars, and you can somehow “adjust” with your neighbours to borrow the additional slots for that day. You get a certificate from the CEO for optimizing on the cost of parking space.

And then one rainy morning things go horribly wrong. Your phone doesn’t stop ringing. Angry staffers are calling you complaining that they have no place to park. Given the heavy rains that morning, none of the staffers have wanted to risk getting wet in the rain, and have all decided to bring their cars. Never before have they faced a problem parking so they are all confident that there will be no problem parking once they get to work, only to realize there is not enough parking space. Over a hundred employees have driven to work, and there are only forty slots to park.

The problem here, as you might discover, is that of correlation. You had assumed that Alice’s reason to get her car was uncorrelated to Bob’s decision. What you had not accounted for was the possibility that there could be an exogenous event that could suddenly drive the correlation from zero to one, thus upsetting all your calculations!

This is analogous to what happened during the Financial Crisis of 2008. Normally, Alice defaulting on her home loan is not correlated with Bob defaulting on his. So you take a thousand such loans, all seemingly uncorrelated with each other and put them in a bundle, assuming that 99% of the time not more than five loans will default. You then slice this bundle into tranches, get some of them rated AAA, and sell them on to investors (and keep some for yourself). All this while, you have assumed that the loans are uncorrelated. In fact, the independence was a key assumption in your expectation of the number of loans that will default and in your highest tranche getting a AAA rating.

Now, for reasons beyond your control and understanding, house prices drop. Soon it becomes possible for home owners to willfully default on their loans – the value of the debt now exceeds the value of their home. With one such exogenous event, correlations suddenly rise. Fifty loans in your pool of thousand default (a 1 in gazillion event according to your calculations that assumed zero correlation). Your AAA tranche is forced to pay out less than full value. The lower tranches get wiped out. This and a thousand similar bundles of loans set off what ultimately became the Financial Crisis of 2008.

The point of this post is that you need to be careful about assuming correlations. It is to illustrate that sometimes an exogenous event can upset your calculations of correlations. And when you go wrong with your correlations – especially those among a large number of variables, you can get hurt real bad.

I’ll leave you with a thought: assuming you live in a primarily two wheeler city (like Bangalore, where I live), what will happen to the traffic on a day when 10% more people than usual get out their cars?

Sadananda Gowda’s Set-up in South Bangalore

Ever since D V Sadananda Gowda became chief minister of Karnataka not so long ago, we residents of KR Road have been subjected to the holdup of the KR Road-SouthEnd Road signal several times a day. The convoy for which traffic is held up is huge, leading us to believe that it can’t belong to anyone but the chief minister. However, the chief minister’s house is in Milk Colony near Malleswaram, so what is he doing in South Bangalore? We wonder if a chinna veetu exists!

The Silence

It was amazing, the silence that greeted us when we returned to Leh from Nubra Valley. We had heard from drivers passing the other way that there had been some sort of disaster in Leh the previous night and that a hundred people had died. There was absolutely no traffic coming from the other side, and the heavy rain didn’t help; not least those of our group who were on the bike (I had finished my turn on the bike a while earlier; more on that in another post).

The only sign of activity on the way was the Rimpoche’s procession. Stanzin Nawang Jigmed Wangchuk is 5 years old and is believed to be the reincarnation of former Ladakh MP Bakula Rimpoche  He was at Sumur monastery (in Nubra Valley) and on that day he was on his way to Leh.

The previous day, our driver had informed us to get up early so that we could go to Sumur in time to see the festivities there, in honour of the departing Rimpoche. Unfortunately, late night drinkage meant by the time we reached Sumur the procession had long passed. There was little sign of their having been any celebration by the time we got there.

Coming back, as we descended into Leh valley from Khardung La (supposed to be the highest motorable pass in the world) it looked the same. From on top of the hills, it looked pretty much the same as it did when we left for Nubra the previous day. Except for the lack of traffic in the opposite direction, nothing was different. And the crowd we saw at the Rimpoche’s procession (it was some distance off the main road) only reinforced the sense of normalcy.

Of course, we knew in our heads that things were far from normal. Having gotten back into the Airtel network we had called our families and figured what had happened. Our driver Jugnes had got a call from a relative saying the authorities had requested his village to be evacuated as it was supposed to be in a dangerous low-lying area. We had ourselves been caught in the rain and seen very few army men at Khardung La. All I’m saying is that by the look of things nothing at all looked amiss.

And then when we entered town (and got past another crowd of people waiting for the Rimpoche) it hit us. Not a soul on the streets. Not a single shop open. No one picking up as we called the travel agent’s office. Us not sure if we had a reservation at the hotel where we’d stayed two nights prior before embarking for Nubra (it turned out we did have a reservation; and the kindly hotel staff conjured up some sort of a sandwich for our lunch from whatever supplies they had). It was surreal. And scary. We thought after a couple of hours of rest we should go check out the affected areas to see what has happened. But before that could happen, we realized we ourselves weren’t out of danger.

The National College Flyover

What will happen to the controversial National College Flyover when the Metro gets built? If I remember right, the proposed Metro goes from Lalbagh West Gate up Vani Vilas road, and is supposed to take a right turn on to K R Road at the National College circle. Surely there is no space on VV Road to for the metro and the flyover to exist side by side. They can’t take the metro underground there since the ground there has to bear the additional weight of the flyover.

So what will become of the flyover? Yet another example of the BBMP’s shortsightedness.

I don’t remember the forum (it might have been this blog, or its predecessor) but I had once mentioned as to how the National College Flyover was useless. And I had gotten shouted down by a bunch of people saying “go in the evening and see the number of vehicles on the flyover, and you’ll know it’s not useless”. I’ve gone there a few evenings after that (over the last 2-3 years) and watched the traffic in the evening, and still believe that it wasn’t necessary.

It wasn’t necessary because the traffic at the intersection isn’t enough of a reduction in petrol and time cost of going over the flyover to pay for the flyover in a reasonable number of years (if I remember my minor subjects right, this is the standard reasoning by transportation engineers). People on K R Road, and the traffic going towards Jain college from “north road” (the western part of VV Road) still have to spend an insane amount of time at the signal. People on VV Road have it easy but then they get stuck at the new signal that has been installed at the junction of VV Road and Shankar Mutt Road.

And to consider the amount of controversy that the flyover created when it was built. And the fact that it’s most likely going to get pulled down for the metro construction.