Asynchronous Transfer Mode (ATM) network is being deployed in carrier backbone. ATM can transmit a wide variety of traffic, such as video, voice, and data. Available Bit Rate (ABR) service is one of six ATM services, which is now under intensive research for its closed loop feedback control feature. ABR service supports two types of connections: unicast and multicast. There are also three types of multicast connections: point-to-multipoint, multipoint-to-point, and multipoint-to-multipoint. Multipoint communication is the exchange of information among multiple senders and multiple receivers, forming a multicast group. Examples of multicast applications include audio and video conferencing, video on demand, tele-metering, distributed games, and data distribution applications. In this dissertation, we focus on queuing and packet scheduling management for multipoint-to-point ABR connections. Although there are so many proposed fairness definitions for all ABR sources in a multipoint-to-point connection, there are still problems about queue lengths, queuing delays, and throughputs, when ABR sources are with variable-length packets. From the nature of VC-merge scheme on merged points in a multipoint-to-point connection, merged switches cannot transmit cell-stream of a packet out until the packet is completely and totally queued. If there is no complete packets queued, the switch can then choose an incomplete packet for cut-through forwarding for efficiency. Therefore, if the switch chooses a long packet from a branch that has smaller cell input rate, for cut-through forwarding, the throughput of output ports will experience severe oscillations. At the same time, ABR queue lengths will be also occupied with severe growth, and ABR cells will be experienced long queuing delays. We proposed a scheme, named MWTF (Minimum Waiting Time First), which is architecture-independent of any rate allocation schemes and fairness definitions, to resolve the problems by providing length of each packet to merged switches. Thereby the scheduler can choose an appropriate incomplete packet for cut-through forwarding, by selecting the packet that has the smallest packet waiting time. Simulation results show that merged switch has good performances. Throughput will be no severe oscillations and will be getting smoother. Also cells have smaller and smoother queuing delays in average, and the switches have much smaller queue lengths and smoother variations.