Table 1 Terms and symbols

x _i

{x _ij } Rate allocation vector of node i

e _i

Available link bandwidth between node i and base station (BS) tower

w

Available capacity of WLAN

x _ii

Flow rate of node i directly connected to BS tower

x _ij

Flow rate of node i via the link of node j to the BS tower

The set of the nodes in CS

x _i,max

Max requirement of the traffic flow of node i

r

A requester

h

A helper

f

A forwarder

The set of the helpers in CS

The set of the requesters in CS

θ

A path $\theta \triangleq 〈f_0,f_1,\dots ,f_m〉$, which is defined as a sequence of forwarders, each of which, e.g., f _i , receives packets from its uplink node f_i−1 and sends to its downlink node f_i+1

$\mathcal{P}(h,r)$

The set of all possible paths between h and r

c _h , c _r

Constant coefficients for helper cost and relay cost per unit data, respectively

$\mathcal{ℒ}\left(\theta \right)$

The set of links that compose the path θ

δ _l

The link cost ${\delta }_l\triangleq \delta (i,j)\triangleq 1/p(i,j)$, which is defined as the reciprocal of the successful transmission probability between i and j