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Network performance with statistical multiplexing of heterogeneous, packetized, and bursty traffic in optical code-division multiple access (CDMA) networks needs to be characterized in order to understand the scalability of such networks. The analysis uses the Engset multi-rate loss model for a network that implements variable weight multi-length carrier-hopping prime codes. Such codes support packetized, bursty, and asynchronous transmission. Unlike traditional calculations that use total number of active interferers or total occupied bandwidth to determine the blocking probability, here, network error probability is used as a thresholding condition. To optimize the performance, the network allows subscribers from different classes to transmit at different power levels. Examples show differentiated qualities of service for two classes in terms of data rate, error probability, and blocking probability. By such analysis, the scalability of the heterogeneous optical CDMA network with bursty traffic is shown.