Recent studies of Local Area Network and Wide Area Network Traffic have provided much evidence of what has been called "self-similar'', "long-range dependent", "fractal'', "chaotic", "heavy-tail", or "power-tail" network traffic. These studies heave indicated that conventional traffic models (e.g. Poisson) generate overly optimistic performance measurements. In this paper we present an interarrival process which extends previous work in this area regarding a heavy-tailed ON/OFF source model described in [6]. Extending their work, we construct a heavy-tailed ON/OFF traffic model which attempts to characterize traffic generated from multiple sources which may be generating traffic concurrently. The primary application of this process is the characterization of traffic generated by, say, (World Wide Web) WWW servers and/or users on an Ethernet. With regards to network planning, rue derive are analytic formula to compute the "critical point" (e.g. system utilization beyond which performance rapidly degrades), and a means to compute buffer over flow probabilities for, say, WWW gateways and/or routers.