This paper addresses a group-based bandwidth-efficient mobile multimedia-on-demand (GMMOD) service over wireless networks, e.g. multimedia broadcast multicast system (MBMS) and digital video broadcasting network (DVB). In this service model, user requests are first aggregated or batched and then served over a shared multicast or broadcast channel to achieve the objective of high system satisfactory ratio. We first analyze the tradeoff between service blocking probability and user reneging probability for a basic timeout-based batching approach. A theoretical model is developed from which we propose an optimal timeout-based approach that is able to identify the optimal tradeoff point that maximizes the system satisfactory ratio at a particular cell status, traffic and user profile. The optimal timeout-based approach is then compared with previously studied approaches and the simulation results demonstrate that the proposed approach gives better performance in improving the satisfactory ratio and reducing the reneging probability while maintaining a small blocking probability.