We consider the random multiple access of a slotted broadcast communication channel. Packet arrivals for such channels are often modeled as Poisson processes because the latter have attractive theoretical properties and are well understood, even though a number of tra c studies have shown that packet interarrival times are not always exponentially distributed. For example, recent studies argue convincingly that tra c from a variety of working packet networks (e.g., LANs, WANs, e.t.c), is much better modeled using statistically self similar processes to characterize the packet interarrival times of the aggregate tra c, which have much di erent properties than Poisson processes. Because of the great in uence the multiple access algorithms (used in the channel access subsystem) will have on the performance of third generation digital wireless mobile communication systems, we study in this paper the problem of random multiple access under a packet tra c generated by interactive data applications (e.g., reading/composing short email messages, responding to paging type messages, transferring les between the mobile and a xed computer, and querying of a database). We examine and demonstrate the performance robustness of the above RAAs when they are driven by a strongly bursty packet arrival process, commonly found in interactive data applications.