Algorithm 1: Dynamic pre-backoff algorithm (DPBO)

Input: $L,\lambda ,N_{M2M},T,\alpha ,\beta ,\theta ,\gamma ,\tau ,{\delta }_1,{\delta }_2,\eta ,Q,W_{BO}$, QoS requirements of H2H traffic  Initialization:   Solve Equation (13) and return $I_{\max }$;   $X_i^{M2M}[1]=0,\forall i\in [1,I_{\max }]$;   $W_{PBO}=0$;  Step1: Solve Equations (34), (48) and (49) and return $L_{TP}$;     Solve Equation (10) and return $L_{SP}$;     Solve Equation (50) and return ${\lambda }_{th}^{M2M}$;  Step2: for each cycle $i=1:I_{\max }$ do      Solve Equation (12) and return $N_i^{M2M}$;      # Newly arrived M2M devices execute pre-backoff procedure       for $k=1:W_{PBO}+1$ do       $X_{i+k-1}^{M2M}[1]=X_{i+k-1}^{M2M}[1]+\frac{1}{W_{PBO}+1}{N}_i^{M2M}$;       end for      # Adjust the pre-backoff window size dynamically       if $X_i^{M2M}[1]\ge {\lambda }_{th}^{M2M}$        $W_{PBO}=W_{PBO}+1$;        else if $X_i^{M2M}[1]<{\lambda }_{th}^{M2M}$ continuously in time interval $[i-\eta ,i]$          $W_{PBO}=W_{PBO}-1$;       end if       $I_{\max }=\max \left[i+W_{PBO}+\left(Q-1\right)\left(W_{BO}+1\right),I_{\max }\right]$     end for