Recently, an upsurge of interest has been observed in providing multimedia on-demand (MoD) services to mobile users over wireless networks. Nevertheless, due to the rapidly varying nature of mobile networks and the scarcity of radio resources, the commercial implementation is still limited. This paper presents an efficient group-based multimedia-on-demand (GMoD) service model over multicast-enabled wireless infrastructures, where users requesting the same content are grouped and served simultaneously with a single multicast stream. The grouping is fulfilled through a process named "batching". An analytical model is derived to analyse a timeout-based hatching scheme with respect to the tradeoff between user blocking probability and reneging probability. Based on the deduced analytical model, an optimal timeout-based hatching scheme is proposed to dynamically identify the optimal tradeoff point that maximizes the system satisfaction ratio given a particular system status. The proposed scheme is evaluated by means of simulation and compared with two basic hatching schemes (timeout-based, size-based), and two hybrid ones (combined-for-profit, combined-for-loss). The simulation results demonstrate the proposed approach can ensure significant gains in terms of user satisfaction ratio, with low reneging and blocking probabilities.