Skip to main content


Table 1 Terminology for MIP formulation

From: Optimal number of routing paths in multi-path routing to minimize energy consumption in wireless sensor networks

Variable Description
N Number of nodes
f ij kl Number of data packets generated at node-k forwarded on
  the lth path flowing from node-i to node-j
s i Number of data packets generated at node-i
E rx (L P ) Energy consumption for receiving L P bits of data
Et x,i j(L P ) Energy consumption for transmitting L P bits of data from
  node-i to node-j
d ij Distance between node-i and node-j
ρ Energy dissipated in the electronic circuitry
ε Transmitter efficiency
α Path loss exponent
E Battery energy of each sensor node
G= (V,A) Directed graph that represents network topology
V Set of nodes, including the base station as node-0
W Set of nodes, except the base station (node-0)
A Set of edges (links)
l Set of paths
a ij kl Binary variable to determine if arc (i,j) A is used in the
  l th routing configuration originated at sensor kW.
b k l Total amount of data sensed by sensor kW and
  transmitted on the l th configuration to the base station
R Radius of deployment area
R max Maximum transmission range
N p Number of paths
L P Packet length in bits
M rnd Number of rounds
T rnd Round duration
ξ Channel data rate (bits/s)
γ Interference range multiplier
φ BER (bit error rate)
χ Packet error rate
λ Average packet retransmission rate