153 utility versus latency trade o in a network we

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: for the problem instance with data σ = 1, 0.3 −0.1 −0.9 0.3 −0.3 . G = −0.6 −0.3 0.6 0.2 Give an optimal F , and the associated optimal objective value. 14.10 Fuel use as function of distance and speed. A vehicle uses fuel at a rate f (s), which is a function of the vehicle speed s. We assume that f : R → R is a positive increasing convex function, with dom f = R+ . The physical units of s are m/s (meters per second), and the physical units of f (s) are kg/s (kilograms per second). (a) Let g (d, t) be the total fuel used (in kg) when the vehicle moves a distance d ≥ 0 (in meters) in time t > 0 (in seconds) at a constant speed. Show that g is convex. 124 (b) Let h(d) be the minimum fuel used (in kg) to move a distance d (in m) at a constant speed s (in m/s). Show that h is convex. 14.11 Minimum time speed profile along a road. A vehicle of mass m > 0 moves along a road in R3 , which is piecewise linear with given knot points p1 , . . . , pN +1 ∈ R3 , starting at p1 and ending at...
View Full Document

Ask a homework question - tutors are online