Transport technologies such as Optical Transport Network and Synchronous Digital Hierarchy are widely used in access and core networks to carry different types of traffic. These technologies define a hierarchy for multiplexing lower rate traffic containers onto higher rate traffic containers. Provisioning refers to the process of allocation of resources to meet a given traffic demand. Due to the continued expansion of transport networks, the power consumption increases, becoming a bottleneck for further expansion. Power-aware allocation of resources to traffic demands will enable power-efficient operation and help in minimizing the capital and operational costs of the network. In this paper, the power consumed by a switch matrix having the capability to switch different traffic containers at different amounts is considered. The objective is to minimize the number of network elements deployed in the network by allocating resources to traffic demands in power-efficient ways. A formulation based on Integer Linear Programming is first presented; later, four different heuristic approaches, based on how higher order trails are used and the use of grooming, are proposed. It is found that the grooming-based heuristics perform better in terms of the total power consumption relative to the weighted number of requests accepted. In the grooming heuristics, threshold on link utilization is set to determine when grooming is to be done, and for the same performance evaluation, it is found that the threshold of 80% gives better results. © 2019, Indian Academy of Sciences.