It is expected that, in near future, the multi-class traffic previously in Public Switched Telephone network (PSTN), cable television network and IP network will be multiplexed at backbone and carried by the converged Next-Generation Network (NGN). A pragmatic challenge in facilitating NGN is how to schedule traffic and allocate bandwidth among the triple-play services, namely voice (VoIP), video (IPTV) and data. Different from traditional strict-priority based scheduling intensively used in industry, in this paper, we try to discuss this issue from the objective of Network Utility Maximization (NUM). We first investigate the characteristics of most existing traffic classes and explicitly formulate their utilities to be the function of occupied bandwidth. After that, a novel scheduling scheme to achieve NUM is derived using Lagrange method with KKT conditions. Numerical results under two network scenarios are calculated. Both of them reveal the unique nature of this scheduling, compared with strict-priority scheduling, still highest priority is provided for VoIP traffic, however, no strict priority should be given to IPTV traffic since it will conflict with NUM objective. We hope our results will shed lights on the evolvement towards the converged network.