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Example 4-2 The travel time on a stretch of a highway lane connecting two activity centers has been observed to follow the equation representing the service function: t = 15 + 0.020 where t and v are measured in minutes and vehicles per hour, respectively. The demand function for travel connecting the two activity centers is v = 4000 - 120t (a) Sketch these two equations and determine the equilibrium time and speed of travel. (b) If the length of the highway lane is 20 mi, what is the average speed of vehicles traversing this length? Solution Solving the two equations: t = 15 + 0.02v U = 4000 - 120t results in the following values for v and t at equilibrium (as shown in Figure E4.2): U = 647 veh/hr t = 27.94 minSpeed = 20 X 60 = 42.95 mph 27.94 Time, t (min) t = 15 + 0.02v 40 (647, 27.94) 20 V = 4000 - 120t 2000 4000 v (vehicles/hr) Figure E4-2 Static equilibrium of demand and supply