In
my attempts at understanding the flow of traffic on Indian roads to find more
efficient and faster ways of commuting, I have had limited success due to the randomness
of the entire situation. Note that these faster ‘ways’ are not limited to
alternate roads, but more like the windows of opportunity from Cars 3—routes
between cars and other larger vehicles. And to answer your probable next
question: No, nothing illegal or immoral like driving on the walkway or ignoring
red lights. You might wonder, “Hey, E.Go, how is going between cars—absolutely ignoring
safe distances—moral or ethical?” To that, I say that a safe distance depends
heavily on the circumstance. Since it is essentially a function of the speed and
the road conditions, it varies. City roads here rarely allow one to speed even
modestly, and the roads are rugged enough—with plenty of potholes and
surprising speed breakers—to break any will of attaining said modest speeds. On
top of all this, its monsoon! Rainwater covers all these potholes and you can
enjoy a free, real-life annual (and a relatively safer) experience of how it
must feel to drive in a minefield.
The
Multi-Phase Model
As a
chemical engineering student, the flows of vehicles immediately directed me
towards fluid flow. There are a few similarities but a lot of differences. In multiphase
flow, you could differentiate between solids, liquids (yes, plural) and gases.
Each phase would have its own properties and characteristics. I thought of
classifying vehicles into categories based primarily on their size: I clubbed
buses, trucks and other bulky vehicles (BVs); all cars were grouped into one class
(CRs); the three-wheeled rickshaws (RKs) were granted a class of their own due to their
unpredictable and sharp changes of direction; and finally, all two-wheelers (2Ws)—bicycles,
motorbikes and scooters—were placed together. Note that I have used classes,
categories etc. interchangeably. BVs usually accelerate and decelerate slower
and maintain lower speeds in general. BVs, especially buses, also tend to stop
at the side of the road—you know, because bus stops. CRs are mostly faster than
BVs in most respects. They are also the most likely to be on the left side of
the road wanting to turn right, or the other way around. RKs have variable
speeds. Some rickshaws can overtake you at more-than-modest speeds while others
look as if their tormented engines are about to sign off permanently. 2Ws are arguably
the speediest mode of travel because of their ability to ‘trickle’ through
traffic. I’m fortunate to be in this group. You may be thinking I’ve missed
something—I haven’t. Cattle and people on the road are accounted as stationary
particles.
2Ws anywhere
on the road rarely hesitate to throttle through a gap which is about 50% greater
than their own width. Exceptions include gaps near BVs (because BVs have
limited visibility and too much bulk) and higher order of seating, i.e.
triple-seating (which is illegal) and further. Between the leftmost car and the
sidewalk is a place where you’ll typically find 2Ws. In actual fluid flow, we
assume a no-slip condition at the boundaries between solids (e.g. the pipe
wall) and the fluids, i.e. the fluid in contact with the solid moves (or doesn’t)
with the solid. Unless the gap is smaller or there are obstructions, viz.
people, parked cars, weird sewer plates and storm drains, dogs etc., the 2Ws
are faster than the cars, even besides the sidewalk—the opposite occurs most of
the times. This is also true for the CRs when other classes are absent, and the
BVs—not for the RKs though. It was difficult to go on thinking about various
such conditions that each phase must fulfil to represent traffic well enough.
Another problem I ran into was the nature of the ‘driving force’ (geddit?). How are
these phases affected by the available routes and their destinations? Knowing
that they have to turn left at the next signal, why do some CRs end up in the
rightmost lane? What can account for the apparent non-recognition of lanes by
the RKs? Flaws just kept popping up.
Until
today, that is. I thought of another possible model.
Discrete
Particle Model
The
categories still exist. Instead of looking at them as phases, let us look at
every individual vehicle as a single particle. BVs will be big and long. CRs
will be relatively rounder. 2Ws will be mostly needle-shaped. These particles
will have certain parameters ascribed to them: maximum acceleration, maximum
velocity and so on. The 50% excess width criteria can be attributed to the 2Ws.
Since the particle size is now taken into account, we can expect the model to
represent phenomena like a CR not perfectly following a lane and blocking an
otherwise straight path for the vehicles behind it. Assigning probabilities to
BVs for stopping at the roadside for a fixed period of time will represent
perturbations in traffic flow due to bus stops. Cattle and people can still be
represented as stationary obstructions. The particles will be assigned some randomness
as well. For instance, BVs will be the least random in terms of horizontal
(with reference to the road) changes while 2Ws and RKs will be the height of
randomness. Today, driving in the rain moving at lesser-than-pedestrian speeds
with another 2W about 4 inches ahead of me and another behind (probably closer),
with a CR dangerously close to the side, with bright and rude oncoming headlights,
the main point hit me in a mild ‘Eureka!’ moment—the safe driving distance
will be a parameter too. It will act as a kind of spring between adjacent
particles, mimicking the slowing down and speeding up in response to the
vehicle in front doing the same. But wait, if the maximum acceleration condition
doesn’t allow a particle to completely avoid another, what do we have? An
accident! Though I shouldn’t be this excited, this model serendipitously accounts
for accidents as well! That means, given the chance and resources, one could compare
the model to actual moving traffic, input measured (or estimated) values, and
really figure out optimised strategies for vehicular traffic to get to places
faster!
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