Algorithm 2 Predicting the probability of $u_i$ indirectly contacting a Wi-Fi AP within a time constraint

Input: the starting region $r_s$, the starting time interval t, the stop time interval $t_e$. Output: $p_i^I$ Initialize: $p_i^I=0,p_s\left(t\right)=1$ 1: for every historical records of $u_i$ do 2:  if ($(t<t_j<t_e)$&$(n_j>x)$) then 3:   Calculating $p_j^j\left(t_j\right)$ using (4); 4:   Calling Algorithm 1($r_j,t_j,t_e$) to get $p_j^D$; 5:   $p_i^I+=p_j^j\left(t_j\right)·p_j^D$; 6:  end if 7: end for 8: return $p_i^I$;