I used the following two equations to implement a branch function:
\documentclass[conference]{IEEEtran}\usepackage{amsmath}\newcommand{\NC}{\mathrm{NC}}\begin{document} In Case A, \\ \begin{equation} \Pr\{\mathrm{NC}|\alpha\}= \left\{ \begin{array}{ll} (1-p)^{n-1}(1-p+p(\alpha + \beta)^{2})^{n-1} & 0\leq \alpha \leq \beta \\ (1-p)^{n-1}(1-p+4p\alpha\beta)^{n-1} & \beta\leq \alpha \leq \beta-1\\ (1-p)^{n-1} (1-p(\alpha - \beta)^{2})^{n-1} & 1-\beta\leq \alpha \leq 1 \\ \end{array} \right. \end{equation} \\ In Case B, \\ \begin{equation} \Pr\{\mathrm{NC}|\alpha\}= \left\{ \begin{array}{ll} (1-p)^{n-1}(1-p+p(\alpha + \beta)^{2})^{n-1} & 0\leq \alpha \leq \beta \\ (1-p)^{n-1}(1-p+4p\alpha\beta)^{n-1} & \beta\leq \alpha \leq \beta-1\\ (1-p)^{n-1} (1-p(\alpha - \beta)^{2})^{n-1} & 1-\beta\leq \alpha \leq 1 \\ \end{array} \right. \end{equation}\end{document}But the equations exceeded the line width (9&10) or in other words the column words as seen here:
