1.6 System Model and Assumptions

We consider a multi hop wireless network with N nodes arbitrarily located on a plane. Each node ni (1 ≤ iN) can transmit a packet at J different rates R1, R2, …, RJ. We say there is a usable directed link lij from node ni to nj, when the packet reception ratio (PRR), denoted as pij, from ni to nj is larger than a non-negligible positive threshold ptd. The PRR we consider is an average value of the link quality in a long timescale (e.g. in tens of seconds). There exist several link-quality measurement mechanisms (Couto et al. 2003; Kim and Shin 2006) to obtain the PRR on each link. We assume that there is no power control scheme and the PRR on each link for each rate is given. We define the effective transmission range Lm at rate Rm (1 ≤ mJ) as the sender-receiver distance at which the PRR equals ptd.

The basic module of opportunistic routing is illustrated in Figure 1.1. Assume node ni is forwarding a packet to a remote sink/destination nd. We denote the set of nodes within the effective transmission range of node ni as the neighboring node set images/c01_I0001.gif (e.g., all the five nodes around ni in Figure 1.1). Note that, for different transmission rates, the corresponding effective transmission ranges are different, then we have different neighboring node sets of node ni, and the PRR on the same link lij may be different at different rates. We define the ...

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