Pervasive health care is regarded as a key driver in reducing expenditure and enabling improvements in disease management. Advances in wireless communication and sensor technologies permit the real time acquisition, transmission and processing of critical medical information. In this paper, we examine different approaches of streaming physiological data from body sensors over a wireless network. Modern mobile phones provide sufficient storage and computational abilities and provide a flexible programming environment, making them ideal to process and store sensed data from multiple sources. We compare the approach of using a central data server, against using a smart phone, to store and process the medical data. The competing requirements of minimization of energy consumption versus the timely delivery of anomalous conditions are investigated using a simulated body sensor network. The measurements show that when a patient is mobile, a smart phone is the device best suited to perform the initial processing of vital signs and sending of medical alerts.