In this paper, we present a stochastic model with optimization and risk analyses in Communication Networks (CNs). The model is proposed for offline traffic engineering optimization with bandwidth allocation and performance analysis. First, we present an analysis of the bandwidth allocation problem to derive the optimal bandwidth capacity with a loss rate constraint. And, we also use a mean-variance approach to analyze the risk aversion in CNs. Second, we present an analysis of the bandwidth allocation problem with a penalty cost and derive the optimal bandwidth capacity. Finally, numerical results are shown to reveal the impacts of relationship between the revenue and the cost, loss rate constraint and risk aversion on the CNs' performance. The results presented in this paper reveal insights for CNs' design and planning.