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In a Bluetooth piconet, the Master essentially controls the channel. Due to an absence of coordination between independent Masters while accessing the wireless medium, devices will encounter high packet interference if several piconets are simultaneously operating in the same area. Since even a headset and a mobile phone can be connected with a Bluetooth link forming a piconet, it may not be unusual to find tens of independent piconets in crowded places like airports, international conferences, shopping malls, and so on. Study of packet interference is important because interference affects the throughput of a piconet. Motivated by the fact that applications will benefit, in terms of higher available data rate in one direction, by using multiple-slot packets in an asymmetric manner, in this paper, we present an analytical model of packet interference in a cluster of piconets using multiple-slot packets. Also, considering that all the portable devices can have a Bluetooth interface and people are highly mobile these days, it will not be uncommon to find a cluster of piconets of both the 79-hop and the 23-hop types in the same area. We then present an analytical model of interference of multiple-slot packets in a heterogeneous cluster of Bluetooth piconets. By a heterogeneous cluster we mean some piconets are of the 23-hop type and the rest are of 79-hop type. We show how the aggregate throughput in a cluster of piconets degrade under various traffic scenarios, such as 1-slot, 3-slot, and 5-slot packets in symmetric and asymmetric modes in synchronous and asynchronous conditions of Master clocks. Our analytic model is based on the idea of probabilistic graphs, where a node denotes a piconet and an edge denotes the probability of interference between two nodes. Though the 23-hop system has been phased out, our work gives a general approach to model packet interference in multiple, frequency-hopping systems that need not be Bluetooth systems.