Privacy Aware Incentivization for Participatory Sensing

. 2019 Sep 19;19(18):4049. doi: 10.3390/s19184049

Algorithm 3: Computing the Reward

Create Supply Curve for

{[N_{actual}], r}

from Historical Dataset //Create Supply Curve.

M_{predict}

= Linear Regression Model for Supply Curve

{[N_{actual}], r}

//Construct Linear Regression model.

[r] = 0 . . r_{m a x}

//Predict the responses for different reward levels.

[N_{predict}, r]

p r e d i c t (M_{predict}, [r]])

foreach

r

//Construct the each reward’s queuing state variables.

Z_{forfeit} (t) = N_{predict} (t) - N_{desired} (t)

{[r, N_{predict} (t), Z_{forfeit} (t))]} + [r, N_{predict} (t), Z_{forfeit} (t))]

end foreach

B_{constant} (t) = 0.5 * {(N_{received} (t - 1) - N_{desired} (t))}^{2}

//Compute Lyapunov Optimization constant.

V = [U, V]

//Map data utility weighting U to V
foreach [

r, N_{predict} (t), Z_{forfeit} (t))]

//Use Lyapunov Optimization to evaluate each reward.

B (t) = r * N_{predict} (t) /

/Compute the budget used by this reward.
if

B (t)

B_{{proportion}_{\max}}

then //Check that budget consumption does not exceed set maximum.
break
end if

L = ½ * Z_{forfeit} {(t)}^{2}

//Carry out the Lyapunov Optimization computation.

Δ (t)

L - L_{l a s t} (r)

//Compute one-slot conditional Lyapunov drift.

D P P_{LHS}

Δ (t)

(V * B)

//Evaluate drift plus penalty expression.

D P P_{RHS} = B_{constant} (t) + (V * B)

+ Z (t) (N_{received} (t - 1) - N_{desired} (t)))

D P P_{LHS} > = D P P_{RHS}

then
continue
end if

O P T_{current} = N_{predict} * ((V * r) + Z (t))

//Evaluate the current optimization computation.
if

O P T_{current} > O P T_{solution}

then

O P T_{solution} = O P T_{current}

r_{optimal} = r

end if
end foreach