Some Comments On Highly Dynamic Network Routing

Cover Some Comments On Highly Dynamic Network Routing
Some Comments On Highly Dynamic Network Routing
Herbert J Bernstein
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ForO< a, . < 1, 2«, = 1 Define di = a, /, - and compute the partial derivatives which will be needed in finding minima of W . for J = 1, ... , « — 1 and aa, (M-, - - oCiXf dd„ \^nL da, (l^n - "nM' by taking a„ = 1 - aj — ... — a„_i, so that the critical points of W as a function of ttj, ... , a„ _ 1 occur when = i. E. When dW M-, -/, - M-n In aaj ~ (tJL, - a, -\)2 {^„ - a„X)2 \^ili 2 (jjL. - - a. X)2 -8- for some t independent of i, i = 1, ... , n . We will solve these equations for a, -, but first note that iLi - a, \ = e, (ii'ili) with €, • = ±1. The negative value of e, - is "unphysical", since that would require an overload of the first queue on path / by the distributed traffic. Thus we accept only the positive roots and obtain 1 "'= X M-, (y^iii) 1 2^ We can solve for t by i = S«/ = x2m-. - - -^^ii^ih) T = so that a. - = — \^i - (Sm-; - M (M-//, ) 2(M-, /, ) While all the resulting values of a, - are certainly critical points of W, they may not be valid minima.

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