Each message (m in mathcal M ) can only be assigned to one of them, but not to both.
where the value of δ m is chosen in such a way that the discovery latency in each sector (m in mathcal {M}) is minimized.
C2: (k in mathcal {H}_{l}) and (m in mathcal {H}_{j} Rightarrow ) the packet combination k⊕m is instantly decodable for both devices j and l.
Fig. 3 Effect of parameter I on average power consumption of the BS and relays; N=7, (|mathcal {K}_{0}|=6, |mathcal {K}_{m}|=1, m in mathcal {M}) Fig. 4 Effect of parameter I on virtual power queue size of the BS over time; N=7, (|mathcal {K}_{0}|=6, |mathcal {K}_{m}|=1, m in mathcal {M}).
(g_{t}^{m,n}) is the cost associated with assigning task (m in mathcal {M}) to sensor node (n in mathcal {N}), at time slot (t in mathcal {T}).
Initially, each sensor node (s in mathcal {S}) starts to explore neighbors in all of its sectors (m in mathcal {M}) by switching its direction clockwise after a certain interval of T seconds.
It is important to note that, for any (v = (mathbf {z},f_{1},...,f_{m})in mathcal {H}), the computation of P_{C_{j}} v =argmin_{v'in C_{j}}parallel v-v'parallel (20). is restricted to the locally accessible training examples by node j.
For example, blue links will not exist if ((n,m) in mathcal {A}_{2}), red links will not exist if ((n,m) in mathcal {A}_{3}), and neither blue nor red link will exist if ((n,m) in mathcal {A}_{1}).
The state probabilities, (left {hat {P}_{n,m} (hat {C}_{text {v}},hat {C}_{text {d}}), n(n,m) in mathcal {S}(hat {C}_{text {v}},hat {C}_{text {d}}) right }), which obviously also depend on the pair ((hat {C}_{text {v}},hat {C}_{text {d}}) ), need to be calculated numerically by adopting the theory of stationary continuous Markov chains.
begin{array}{*{20}l} &(11),{mathbf{W}_{nk}}succeq mathbf{0},~{mathbf{Sigma}_{n}}succeq mathbf{0}, &forall k in mathcal K ,~forall lin mathcal L,~forall s in mathcal S,~forall n,m in mathcal N_{mathrm{c}}.
begin{array}rcl@ X^{m,n}_{t} in {0,1}~~~ forall n in mathcal{N},~~forall m in mathcal{M},~~forall t in mathcal{T}.
