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Multihop Wireless Networks: Opportunistic Routing by Ming Li, Wenjing Lou, Kai Zeng

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2.2 Principles of Local Behavior of GOR

2.2.1 EPA Strictly Increasing Property

Intuitively, increasing the number of forwarding candidates would result in a larger EPA. We present Lemma 2.1 to confirm this intuition.

 

Definition 2.1 Define EM(images/c02_I0032.gif) be the maximum EPA (defined in Equation (2.1)) achieved by selecting r forwarding candidates from images/c02_I0033.gif.

 

Lemma 2.1 (Strictly increasing property) EMimages/c02_I0034.gif is a strictly increasing function of r.

 

Proof. Assume 1 ≤ m < nM, and without loss of generality, let images/c02_I0035.gif be the ordered node set achieving EMimages/c02_I0036.gif with forwarding priority i1 >…> im. We then select a subset with nm nodes from the remaining node set {im+1, im+2, …, iM}, say images/c02_I0037.gif. Assume we retain the relay priority of the m nodes in images/c02_I0038.gif unchanged and give the nodes in lower priorities than those in . Then in , we ...

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