Flow Behavior

An essential element of basic infrastructure of a country is the road network that links all parts of the country to promote and facilitate the movement of people and goods. US has one, so does Malaysia. The one glaring difference between the two is perhaps the much higher proportion of tolled road in the latter, i.e., roads built with private funds and the expenses are recouped through toll levies via concession agreements between the builders/operators and the government, usually for a fixed period but with provisions for fee hikes if the projected revenues fall short of the projection.

In Malaysia, this is an iron-clad agreement for the concessionaires where profits are guaranteed since by dint of the agreement, which oftentimes is classified under the Official Secrets Act, i.e., not open to public scrutiny, any shortfall in the agreed revenue collection, read profits, will be made up by government funds if a toll hike proves to be politically inexpedient.

What are government funds? Tax revenues. And where do they come from? Tax payers. And who are the tax payers? You and I. Since government funds are finite, that means government expenditure in some other areas will have to be cut and reallocated through virement. So going one big round, and to borrow from a popular Chinese saying, the wool has to come from the sheep no matter what.

Then I read just today the March 9, 2007 issue of Observing China on page B1 (Observing Immigration), an article loosely translated as Living in US: I finally realized that US is one big rural village by an anonymous author. Written in a tongue-in-cheek fashion, the authors observed that [words in parentheses and blue are my running comments]:

"Americans are by comparison simple folks, incapable of displaying the sophistication associated with a developed nation. Take for example, the Inter-state and state road network, criss-crossing the entire country. But no even a single toll booth [I guess the author has not been to the State of Florida where we do have our fair share of tolled road systems], hence letting such a golden commercial opportunity go to waste. I can’t wait to start building all these toll booths, and I’m sure in no time I would be able to afford a beachfront villa with gardens along the west coast or in Miami.”

As I said, this is a tongue-in-cheek comment. And I think the author is actually singing praise on the side of US that delivers a public good, the road network, rather than seeing it fit to enrich a few cronies, a system of largesse endemic in some developing countries.

However, putting that aside as there are other more appropriate forums for dissecting the ills of highway concession agreements as implemented in Malaysia, here I would like to look at something more physical, from the standpoint of a road user, and then of an engineer.

Most of the times the highways, or inter-states as they are often referred to in US, are free-flowing, each individual car moving at its own speed. Then there are times especially during festive seasons when the roads are flooded with cars eager to get from point A to point B. And gridlock ensues. If you are unlucky to be stuck in one, you do have a choice to make: go with the flow, regardless how sluggish it is, or turn into a rest place to catch a nap or whatever.

Then there is something in between. The weather is good, it’s a weekend, and you are seemingly cruising along, thinking ahead of your destination or what you plan to do once you get there. Unconsciously you kind of step harder on the pedal a bit until you realize that you are zooming by everybody, and then you have the good sense to relent your foot pressure just in time to see a blue strobe light dancing not far ahead by the road side. As you drive by the poor soul, whose driver's license is being checked by the Highway Patrolman and who is probably cursing his/her own indiscretion, you feel relieved.

Then you notice that the cars in front are all slowing down, and slowly grinding to a halt. You do the same, wishing that this is temporary. Maybe there has been an accident not to far ahead, and the emergency personnel is closing one lane.

The front car creeps forward for perhaps tens of yards, and stops. You do the same, at a pace that is entirely out of your control, much like a pawn that’s being pulled along by an imaginary tether. The worst part is being kept in the dark, wondering whether to bid one’s time or take the nearest exit.

That stop-creep-stop scenario plays on for another 30 minutes. Then suddenly you begin to see the light of day, cars picking up speed. And you are left to survey left and right, looking for possible clue for the backup. But nothing palpable is in sight. No tire marks on the grass verge. No tell-tale debris/oil slick on the road, and you never overtake a tow truck with a damaged good in tow or on a flatbed. The following day you scan the local papers to look for possible explanation for the “aberration”, finding none.

But something must have precipitated the “bottle-neck” or constriction that leads to cars backing up. Probably the “culprit” has been removed by the time you reach it, leaving behind no vestiges and probably the news has been reported in an inconspicuous corner of the local daily, and you don’t deem it important enough to check with the sheriff/Highway Patrol office. And the event begins to fade from your consciousness, until you bump into it again, even though you are not a frequent Inter-state user.

I had my first such encounter during last Thanksgiving, on Inter-state 75 while driving back from Gainesville. But then it was just a matter of too many cars on the road at the same time since it got better once I turned toward Tampa at the junction of I-75 and the Florida Turnpike (to Orlando and southward).

Then it happened again, also on I-75, but this time toward Gainesville not far after the I-275 junction. The date was March 18, and the time, about 12.30pm, and it started at milestone 285 (I think). I’ve earlier promised my S that I would get him to UF before the scheduled NCAA basketball game between the Gators and the Purdue Boilermakers at 2.15pm. I had everything worked out, with some to spare, until this, this snail’s crawl.

Then I got thinking, traffic flow, constriction, backup. They sound just like those terms I am already familiar with as a hydraulic engineer: fluid flow, flow constriction, backwater curve. So, on a hunch, I googled traffic flow, and sure enough, look what I found here [again, those in parentheses and blue are mine]:

“Because traffic involves flows, concentrations, and speeds, there is a natural tendency to attempt to describe traffic in terms of fluid behavior. Car-following models recognize that traffic is made up of discrete particles [as are fluids such as water comprising fluid particles. Even blood flow in our body is a kind of fluid flow] and determine the interactions between these particles. Continuum models are concerned more with the overall statistical behavior of the traffic stream [i.e., bulk characteristics] rather than with the interactions between the two particles.

In the fluid-flow analogy, the traffic stream is treated as a one-dimensional compressible fluid [but water flow is incompressible for all intents and purposes, except in the great depths of oceans]. This leads to two basic assumptions: (1) Traffic flow is conserved, and this leads to the conservation or continuity equation [i.e., no decay]. (2) A one-to-one relationship exits between speed and density or between flow and density.

The simple continuum model consists of the conservation equation and the equation of state (speed-density or flow-density relationship) [the equation of state is not necessary for hydraulic engineers to solve for the flow dynamics of water flow due to the aforesaid incompressibility condition, which together with the equivalent traffic flow equation, the momentum conservation equation, becomes a statement of the conservation of mechanical energy]. If these equations are solved together with the basic traffic-flow equation (flow equals density times speed), we can obtain the speed, flow, and density at any time and at any point in the roadway. By knowing these basic traffic-flow variables, we know the state of the traffic system and can derive measures of effectiveness, such as delays, stops, travel time, total travel, and other measures that allow the analysts to evaluate how well the traffic system is performing [the same way hydraulic engineers predicts river flow condition during a flood event].”

With one important distinction perhaps. The cars are driven by thinking human beings who seldom think alike let alone rationally. So I guess I will be better off as a hydraulic engineer analyzing fluid flow rather than a traffic engineer simulating traffic flow where human behavior is the least controllable and predictable element in the whole shebang.

As a footnote, I did manage to deliver my S to his dorm, on time for the Gators’ game. Also, did anybody experience the same traffic backup on March 18 and if so, do you have anything to share?