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Mobile Worldwide Interoperability for Microwave Access (WiMAX) includes a multimedia multicast/broadcast service (MBS), but delay-sensitive applications such as video and audio streaming require the combination of efficient handling of wireless-link bandwidth and reduced handover delays, which remains a challenge. To reduce the handover delay in the MBS, the IEEE 802.16e standard introduces an MBS zone, which is a group of base stations that are broadcasting the same multicast packets. However, this raises the MBS traffic load on Mobile WiMAX networks, particularly the wireless part. This paper presents an MBS architecture that is based on location-management areas (LMAs), which can increase the sizes of MBS zones to reduce the average handover delay without too much bandwidth waste. An analytical model is developed to quantify service-disruption time, bandwidth usage, and blocking probability for different sizes of MBS zones and LMAs while considering user mobility, user distribution, and MBS session popularity. Using this model, we also propose how to determine the best sizes of MBS zones and LMAs, along with performance guarantees. Analytical and simulation results demonstrate that our LMA-based MBS scheme can achieve a bandwidth-efficient multicast delivery while retaining an acceptable service-disruption time.