Abstract—Over the past decade, the problem of fair bandwidth allocation among contending traffic flows on a link has been extensively researched. However, as these flows traverse a computer network, they share different kinds of resources (e.g., links, buffers, router CPU). The ultimate goal should hence be overall fairness in the allocation of multiple resources rather than a specific resource. Moreover, conventional resource scheduling algorithms depend strongly upon the assumption of prior knowledge of network parameters and cannot handle variations or lack of information about these parameters. In this paper, we present a novel scheduler called the Composite Bandwidth and CPU Scheduler (CBCS), which jointly allocates the fair share of the link bandwidth as well as processing resource to all competing flows. CBCS also uses a simple and adaptive online prediction scheme for reliably estimating the processing times of the incoming data packets. Analytically, we prove that CBCS is efficient, with a per-packet work complexity of O(1). Finally, we present simulation results and experimental outcomes from a real-world implementation of CBCS on an Intel IXP 2400 network processor. Our results highlight the improved performance achieved by CBCS and demonstrate the ease with which it can be implemented on off-the-shelf hardware.