Capacity dimensioning in production systems is an important task within strategic and tactical production planning which impacts system cost and performance. Traditionally capacity demand at each worksystem is determined from standard operating processes and estimated production flow rates, accounting for a desired level of utilization or required throughput times. However, for distributed production control systems, the flows across multiple possible production paths are not known a priori. In this contribution, we use methods from algorithmic game-theory and traffic-modeling to predict the flows, and hence capacity demand across worksystems, based on the available production paths and desired output rates, assuming non-cooperative agents with global information. We propose an iterative algorithm that converges simultaneously to a feasible capacity distribution and a flow distribution over multiple paths that satisfies Wardrop's first principle. We demonstrate our method on models of real-world production networks.