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Wireless Networking Complete by Adrian Farrel, Bruce S. Davie, Larry L. Peterson, Pei Zheng

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• Flows f(k,i),j are all nonnegative and positive flows are not assigned to nonexistent links.

• Packets that have reached the destination are not injected back into the network.

We can show the following lemma.

Lemma 7.3

If λΛ1 then there exists a stationary randomized algorithm to choose μ(i,k),j(t) independent of the history of the arrivals and departures up to timeslot t, such that

E(kNout (i)μ(i,k),j(t)-kNin (i)μ(k,i),j(t))>λi,j (7.20)

image (7.20)

for all 1 ≤ iN, and 1 ≤ jJ.

The following is an informal proof. Recall that any link capacity vector in Co(S) can be achieved by a stationary randomized schedule that chooses the link ...

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