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This paper proposes a novel method for transporting various types of user traffic effectively over the next generation network called integrated services digital network 3 (ISDN3) (or quantum network) using quantum packets. Basically, a quantum packet comprises one or more 53-byte quanta as generated by a “quantumization” process. While connection-oriented traffic is supported by fixed-size quantum packets each with one quantum to emulate circuit switching, connectionless traffic (e.g., IP packets and active packets) is carried by variable-size quantum packets with multiple quanta to support store-and-forward switching/routing. Our aim is to provide frame-like or datagram-like services while enabling cell-based multiplexing. The quantum packet method also establishes a flexible and extensible framework that caters for future packetization needs while maintaining backward compatibility with ATM. In this paper, we discuss the design of the quantum packet method, including its format, the “quantumization” process, and support for different types of user traffic. We also present an analytical model to evaluate the consumption of network resources (or network costs) when quantum packets are employed to transfer loss-sensitive data using three different approaches: cut-through, store-and-forward and ideal. Close form mathematical expressions are obtained for some situations. In particular, in terms of network cost, we discover two interesting equivalence phenomena for the cut-through and store-and-forward approaches under certain conditions and assumptions. Furthermore, analytical and simulation results are presented to study the system behavior. Our analysis provides valuable insights into the design of the ISDN3/quantum network.