We consider the applicability of the data from operators of cellular systems to modelling demand for transportation. While individual-level data may contain precise paths of movement, stringent privacy rules prohibit their use without consent. Presence data aggregate the individual-level data to information on the numbers of transactions at each base transceiver station (BTS) per each time period. Our work is aimed at demonstrating value of such aggregate data for mobility management while maintaining privacy of users. In particular, given mobile subscriber activity aggregated to short time intervals for a zone, a convex optimisation problem estimates most likely transitions between zones. We demonstrate the method on presence data from Warsaw, Poland, and compare with official demand estimates obtained with classical econometric methods.