Relevance-based partial reliability in wireless sensor networks

Costa, Daniel G; Guedes, Luiz Affonso; Vasques, Francisco; Portugal, Paulo

doi:10.1186/1687-1499-2014-142

EURASIP Journal on Wireless Communications and Networking

Table 2 Semi-reliable transmission of complementary data packets

From: Relevance-based partial reliability in wireless sensor networks

Approach	Values for D_{( p, h)} and A_{( p, h)}
	B = 0, E < (H_(p) + 1)
Semi-reliable I-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . R d_{(p, h)}, h \leq E \\ W_{(p)} . k . \prod_{j = E}^{h - 1} (1 - P d_{(p, h)}), h > E \end{cases} \\ A_{(p, h)} = \{\begin{cases} W_{(p)} . a . R a_{(p, h)}, h \leq E \\ 0, h > E \end{cases} \end{array}$ (12)
Semi‒reliable O-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . \prod_{j = 0}^{h} (1 - P d_{(p, h)}), h \leq E \\ W_{(p)} . k . \prod_{j = 0}^{E} (1 - P d_{(p, h)}) . R d_{(p, h)}, h > E \end{cases} \\ A_{(p, h)} = \{\begin{cases} 0, h \leq E \\ W_{(p)} . a . \prod_{j = 0}^{E} (1 - P d_{(p, h)}) . R a_{(p, h)}, h > E \end{cases} \end{array}$ (13)
	B > 0, E < (H_(p) + 1)
Semi-reliable I-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . \prod_{j = 0}^{h} (1 - P d_{(p, h)}), h \leq B \\ W_{(p)} . k . \prod_{j = 0}^{B} (1 - P d_{(p, h)}) . R d_{(p, h)}, B < h \leq E \\ W_{(p)} . k . \prod_{j = 0}^{B} (1 - P d_{(p, h)}) . \prod_{j = E}^{h - 1} (1 - P d_{(p, h)}), h > E \end{cases} \\ A_{(p, h)} = \{\begin{cases} \begin{array}{l} 0, h \leq B \\ W_{(p)} . a . R a_{(p, h)}, B < h \leq E \end{array} \\ 0, h > E \end{cases} \end{array}$ (14)
Semi-reliable O-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . R d_{(p, h)}, h \leq B \\ W_{(p)} . k . \prod_{j = B}^{h - 1} (1 - P d_{(p, h)}), B < h \leq E \\ W_{(p)} . k . \prod_{j = B}^{E} (1 - P d_{(p, h)}) . R d_{(p, h)}, h > E \end{cases} \\ A_{(p, h)} = \{\begin{cases} \begin{array}{l} W_{(p)} . a . R a_{(p, h)}, h \leq B \\ 0, B < h \leq E \end{array} \\ W_{(p)} . a . \prod_{j = B}^{E} (1 - P d_{(p, h)}) . R a_{(p, h)}, h > E \end{cases} \end{array}$ (15)
	B > 0, E = (H_(p) + 1)
Semi-reliable I-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . \prod_{j = 0}^{h} (1 - P d_{(p, h)}), h \leq B \\ W_{(p)} . k . \prod_{j = 0}^{B} (1 - P d_{(p, h)}) . R d_{(p, h)}, h > B \end{cases} \\ A_{(p, h)} = \{\begin{cases} 0, h \leq B \\ W_{(p)} . a . \prod_{j = 0}^{B} (1 - P d_{(p, h)}) . R a_{(p, h)}, h > B \end{cases} \end{array}$ (16)
Semi-reliable O-Z retransmission	$\begin{array}{l} D_{(p, h)} = \{\begin{cases} W_{(p)} . k . R d_{(p, h)}, h \leq B \\ W_{(p)} . k . \prod_{j = B}^{h - 1} (1 - P d_{(p, h)}), h > B \end{cases} \\ A_{(p, h)} = \{\begin{cases} W_{(p)} . a . R a_{(p, h)}, h \leq B \\ 0, h > B \end{cases} \end{array}$ (17)

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