This paper investigates bandwidth allocation for services on multiple connections/paths in networks, and presents the mapping models from services to paths via connections based on Network utility maximization (NUM). Elastic services with concave utilities are firstly considered and the optimum of model can be obtained. Inelastic services with nonconcave (e.g., sigmoidal or discontinuous) utilities are also analyzed and the Models with certain QoS guarantee for these services are presented. These models are significant to QoS guarantee for inelastic services transferred over multiple paths. Numerical examples verify optimization of the models with QoS guarantee for inelastic services.