Fragmentation of Variable Length Packets
Fragmentation of Variable Length Packets
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. , k.
Let p. S and a s be the mean and variance of this distribution, respectively. We further assume that for the indices i\ 0, p, 2 > 0, ... , p„ > 0, and all other p^'s are zero. Also, let m = GCD(t'i, i 2, . . . , i().
Thus there are integer coefficients a, \, a?, . ■ . , a/, such that va — a\ • i\ + a-i • t'2 + • • • + a/ • t;.
Let Un denote the probability that a sequence of sticks chosen under the above distribution has a total length equal to JV, where N > k. Then, we have Un = Pi • U...n-i + P2 • Un-2 + \- Pk ■ ^N-fc- The characteristic equation for the above condition is then given by x k -p 1 x k - l -p 2 x k - 2 p fc = 0. (1) Lemma 4. 1 Let X be a (complex) root of the characteristic equation (1). Then 1. |A| m is an m th root of unity.
PROOF.
1. Since A is a root of the characteristic equation, we have A* =p 1 A fc - 1 +p 2 A*- 2 + ... + p t, and |A| fc = \p l X k - 1 - r p 2 X k -* + ...
What to read after Fragmentation of Variable Length Packets?
You can find similar books in the "Read Also" column, or choose other free books by Dayton Clark to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
. , k.
Let p. S and a s be the mean and variance of this distribution, respectively. We further assume that for the indices i\ 0, p, 2 > 0, ... , p„ > 0, and all other p^'s are zero. Also, let m = GCD(t'i, i 2, . . . , i().
Thus there are integer coefficients a, \, a?, . ■ . , a/, such that va — a\ • i\ + a-i • t'2 + • • • + a/ • t;.
Let Un denote the probability that a sequence of sticks chosen under the above distribution has a total length equal to JV, where N > k. Then, we have Un = Pi • U...n-i + P2 • Un-2 + \- Pk ■ ^N-fc- The characteristic equation for the above condition is then given by x k -p 1 x k - l -p 2 x k - 2 p fc = 0. (1) Lemma 4. 1 Let X be a (complex) root of the characteristic equation (1). Then 1. |A| m is an m th root of unity.
PROOF.
1. Since A is a root of the characteristic equation, we have A* =p 1 A fc - 1 +p 2 A*- 2 + ... + p t, and |A| fc = \p l X k - 1 - r p 2 X k -* + ...
What to read after Fragmentation of Variable Length Packets?
You can find similar books in the "Read Also" column, or choose other free books by Dayton Clark to read onlineMoreLess
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