ADDING A NEW ROAD MAY NOT EASE TRAFFIC

We always think that adding a new road will ease traffic congestion. On the contrary, it may create a traffic jam. Let us see this paradox in detail.

    Look at the above diagram carefully.  There are two roads to go from start to end.  One via A and another via B.   First road has a narrow bridge between ‘start’ and A.  The second road has narrow bridge between B and 'End'.
     The time taken to cross the narrow bridge depends on number of vehicles.  More cars mean more time.  The time taken to cross the bridge is given by N/100, where N is the number of vehicles crossing the bridge.  Hence, the time taken to go from "start to A or B to end" is N/100 because of bridges.
    The time taken to go from A to End or start to B (hilly roads) is always 45 minutes irrespective of the traffic.

On a fine morning, 4000 vehicles try to go from start to end. Naturally, (Probability theory) half of them will go via A and another half (2000) of them will go via B.
The time taken for the drivers going via A
= 2000/100 +45 here N=2000
= 20+45 =65 minutes.
The time for the drivers going via B = 2000/100 +45 = 65 minutes. refer figure
Hence both the roads require 65 minutes time. So far, so good.

    Now the national highways department construct a new road from A to B to reduce congestion and time.  The time taken to go from A to B through the new road is practically zero.
    The highways department thinks in these lines: "suppose 1000 cars start from 'start'.  They will reach A in 1000/100 =10 minutes.
Then they will reach B in no time. From B to end, it will again take 1000/100 =10 minutes.  Totally, it will take only 20 minutes for the drivers to go from start to end", a good reduction.

But now, there is a new short route, everybody wants to use this route. Suppose 4000 drivers take the same route. What will happen? The time of travel will be 4000/100+4000/100=40 +40 =80 minutes. The time has increased from 65 to 80 minutes. Hence the new road from A to B, only increased the congestion. So, it is better to remove the new road. This is called Brass's paradox.

In Seoul, south Korea, the congestion eased, the traffic speeded up. When a motorway was removed as part of the restoration project.
In 2009, Newyork, experimented with closures of Broadway at times square and Herald Square which resulted in improved traffic flow and permanent pedestrian plazas.

Comments

Your heart -you do not know

Size and Location: The human heart is roughly the size of a clenched fist and is located slightly to the left of the center of the chest. Despite its relatively small size, the heart plays a crucial role in pumping blood throughout the entire body. Heartbeat Variability: The heart does not beat at a constant rate. The interval between heartbeats can vary, and this variability is considered a sign of a healthy heart. Factors such as breathing, emotions, and physical activity influence the heartbeat. Electrical Conduction: The heart's contractions are controlled by electrical impulses. The sinoatrial (SA) node, often called the "natural pacemaker," generates electrical signals that regulate the heartbeat and coordinate the pumping of blood. Blood Pumping Capacity: On average, the human heart pumps about 2,000 gallons (or 7,570 liters) of blood each day. Over a lifetime, this amounts to pumping enough blood to fill several Olympic-sized swimming pools. Heart Chambers and V...

THE WORK HORSE "="

One cannot think of a mathematical step without 'is equal to ' . It balances right hand side and left hand side. It aids simplification and manipulation of a mathematical expression. example: 2(A+B) = C 2A+2B = C 2A = C-2B A = C-2B/ 2 In an electronic calculator, the pressing of ' = " sign executes an asthmatic expression or simply calculates. In computer languages, it plays very important role. A = B When a computer looks at this expression, the value stored in the location named B is just transferred to the storage named A . After execution both A and B will have the same value an...

How does your smart phone detect motion, steps, rotation, and location?

How it works-1 An accelerometer in a smartphone is a microelectromechanical system (MEMS) device that measures acceleration and tilt. It works by detecting changes in motion by measuring the vibration or acceleration of the device. The accelerometer consists of a small mass suspended on a spring inside a sealed chamber. When the device is subjected to acceleration, the mass moves relative to the device, causing a change in capacitance that can be measured and processed by the smartphone's hardware. The accelerometer measures acceleration in three dimensions (x, y, and z) and provides data that the smartphone's software can use to determine the device's orientation, detect motion, and track changes in velocity and acceleration. The accelerometer is used for a variety of purposes in a smartphone, including screen rotation, motion tracking for games and fitness apps, and detecting the position of the device for navigation and location services. Additionally, it can be used t...

sciencecapsules

Search This Blog