Differentiated service (DiffServ) has been proposed as an alternative for Integrated service. It aims to provide the same service to a group of flows that have similar quality of service requirements. Assured forwarding (AF) and expedited forwarding (EF) are two proposals for DiffServ provision. We present a performance analysis of an N drop-precedences threshold dropping (TD) queue, which is one of the proposed mechanisms for AF. In this analysis, traffic flows are assumed Poisson with exponentially distributed service time. We present simulation results that verify the analysis. This paper is an extension of the work attempted by Bolot et al. (see Proceedings of IEEE INFOCOM, 1999) and Sahu (see Umass CMPCSI Technical Report 99-09, University of Massachusetts) since it considers the general case with multiple classes of flow. We also show that the Poisson based analysis can be shown to hold for aggregation of bursty Markov sources in some cases and not to hold in others.