Question

The travel time on a stretch of a highway lane connecting two activity center has been obsery to follow the equation representing the service function 10+ 0.02y where and v are measured in minutes and vehicles/hour, respectively. The demand function for travel connecting the two centers is v= 4000 - 1001. Determine the equilibrium time of travel and number of vehicles per hour that will travel on the road section ct

Answer 1

Given Data

Travel Time Equation

$t=10+0.02\nu$

Vehicles Demand Function Equation

V = 4000 – 100t

Here Travel time b/w centers in minutes

$\nu =$ No of vehicles per hour

To determine : Equilibrium time of travel and number of vehicles/hour on road.

Solution:

Equilibrium is achieved in this case when Travel time () and Vehicles/hour ($\nu$) both satisfy the Travel time and Demand Function equation.

$t=10+0.02\nu$ .......................................... (1)

   ............................................(2)

V = 4000 – 100t

Put Value of from equation 1 in equation 2

$\nu =4000-100(10+0.02\nu )$

$\nu =4000-1000-2\nu$

$3\nu =3000$

$\nu =1000$

now put value of $\nu$ in equation 1.

$t=10+0.02*1000$

$t=10+20$

$t=30$

$t=30~min~~~;~~~\nu=1000~vehicle/hour$

Hence in equilibrium condition travel time b/w centers will be 30 min and no of vehicle on road will be 1000 vehicle/hour.