In this paper, we propose an ATM-LAN IWU(interworking unit) with threshold based dynamic bandwidth allocation scheme. We analyze a discrete-time based finite queueing model with deterministic service times in order to investigate the performance of the proposed scheme. It is known that the arrival process of IP packets is bursty. So we use an MMPP(Markov Modulated Poisson Process) to model the bursty input traffic. As performance measures, we obtain the packet loss probability and the mean packet delay. We present some numerical results to show the effects of the thresholds on the performance of the DBAS(dynamic bandwidth allocation scheme).