QoS routing via multiple paths using bandwidth reservation

We consider two generic routing problems via multiple paths in a computer network wherein bandwidth can be reserved, and guaranteed, once reserved, on the links. The first problem requires that a message of finite length be transmitted from s to d within τ units of time. The second problem requires that a sequential message of τ units be transmitted at a rate of η such that maximum time difference between two units received out of order is no more than q. We propose a polynomial-time algorithm to the first problem, and present simulation results to illustrate its applicability. We show the second problem to be NP-complete, and propose a polynomial-time approximate solution