Background Network lifetime is an essential performance metric for medical body area networks (MBAN) since nodes meant to monitor medical parameters continuously for a longer amount of time. This paper focuses on various schemes for enhancing the network lifetime through an analytical approach. Methods An analytical model for enhanced lifetime of sensor nodes is proposed. The proposed model consists of both relay nodes (RN) and sensor nodes (SN) towards enhancing the longevity of network lifetime. The routing protocol is designed to collect the sensed information from SN by adapting optimal path towards gateway. The optimal distance between SN and RN is chosen based on best quality link which ensures the packet delivery. The total installation cost of RN, the total energy consumption of both RN and SN, the traffic serviced from all sensors and data routing to nodes are the constraints considered in the proposed framework for achieving the optimal path though efficient relaying. Results The proposed multi-tier telemedicine system is extensively simulated for describing the optimal network path for MBAN-based e-health services. The proposed work is modelled using integer linear programming that optimizes the location and number of relays. Relays are deployed for minimizing the cost of network installation of RN. The energy which is consumed by both sensors and relays is minimized while ensuring full coverage with effective routing of e-health services. The network longevity is analyzed during both normal and emergency scenarios. © Springer Nature Singapore Pte Ltd. 2019.