pairs are examined. $D_{s}$ is defined as $$\label{eq:succ_links}
{D_{s}} = \sum\limits_{k \ne l}^K {\Phi \left( {{Q_k}{Q_l}} \right)} \; ,$$ where $\Phi \left( {{Q_k}{Q_l}} \right)$ is equal to $$\begin{aligned}
\label{eq:succ_phi}
\Phi \left( {{Q_k}{Q_l}} \right) &= \prod\limits_{k = 1}^K {\Psi \left( {{Q_k}} \right)} \prod\limits_{l = 1}^K {\Psi \left( {{Q_l}} \right)}= \left\{ \begin{array}{l l}
1 &{\rm{ \hspace{1 mm} if \hspace{1 mm} }}0 < \Psi \left( {{Q_k}} \right) \le L \cap 0 \le \Psi \left( {{Q_l}} \right) < L \; ,\\
0 &{\rm{ \hspace{1 mm} elsewhere} \;.}
\end{array} \right.\end{aligned}$$ Moreover, an outage in the successive transitions will occur when $$\label{eq:succ_out}
{\bar p}^{\rm s}_{ij} \buildrel \Delta \over = 1 - \sum\limits_{k = 1}^{D_{\rm s}} p^{\rm s}_{ij} = \frac{{N_i - n_i}}{N_i}{{\left[ {\left( {1 - \exp \left( { - \frac{{{2^{2{r_0}}} - 1}}{{{P_{S}^*}}}} \right)} \right)\left( {1 - \exp \left( { - \frac{{{2^{2{r_0}}} - 1}}{P_{R_t}^*}} \right)} \right)} \right]}^{D_{\rm s}}}$$

Steady state distribution and outage probability {#steady_st}
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Since we have defined the entries of the transition matrix $\mathbf{A}$, the next step is to find the steady state distribution of the MC. In this way, the relationship among the different ways of leaving and reaching specific buffer states will be defined.

\[prop:3\] The state transition matrix $\mathbf{A}$ is Stochastic, Indecomposable[^5] 