Asynchronous transfer mode (ATM) networks are expected to support a diverse mix of traffic sources with different quality-of-service (QOS) requirements. To providing satisfactory QOS to all network users, ATM networks are often required to prioritize users' traffic based on their service requirements. This paper initially examines several existing scheduling disciplines that offer delay guarantees for multiple service classes. Among them, the earliest-due-date (EDD) discipline has been regarded as one of the most promising scheduling disciplines. The EDD discipline schedules the departure of a cell belonging to a call based on the delay priority assigned for that call during the call set-up. Considering n delay-based service classes associated with n urgency numbers D0 to Dn-1 (D0 ≤ D1 ≤ ⋯ ≤ Dn-1) respectively, EDD allows a class-i cell to precede any class-j (j > i) cell arriving not prior to (Dj-D1)-slot time. The main goal of the paper is to determine the urgency numbers (D1's), based on a decent queueing analysis, in an attempt to offer satisfactory delay guarantees for higher priority calls while incurring only minimal delay degradation for lower priority calls. In the analysis, we derive the system-time distributions assuming two service classes, based on a discrete-time, single-server queueing model with heterogeneous arrivals including renewal and nonrenewal arrival processes. On the basis of the analysis, the urgency numbers (Di's) can be dynamically and effectively adjusted to provide a ninety-nine percentile delay guarantee for high priority calls under various traffic loads. Finally, we demonstrate the accuracy of the analysis via simulation results.