Understanding the Traffic Nature of Mobile Instantaneous Messaging in Cellular Networks: A Revisiting to $\alpha $ -Stable Models

Mobile instantaneous messaging (MIM) services significantly facilitate personal and business communications, inevitably consume substantial network resources, and potentially affect the network stability. In this paper, we aim to understand the traffic nature of MIM in cellular networks. Specifically, in order to reach credible conclusions, our research takes account of practical measurement records of MIM services from China Mobile at two different levels. First, a data set of individual message level (IML) traffic is exploited and reveals power-law distributed message length and lognormal distributed interarrival time, the heavy-tailness of which completely diverts from the geometric model and the exponential model recommended by the 3rd generation partnership project (3GPP). Second, another data set considers the statistical pattern of aggregated traffic within one whole base station, and demonstrates the accuracy of α-stable models for the aggregated traffic. Furthermore, it verifies that the α-stable models are suitable for characterizing the traffic in both the conventional fixed core networks and the cellular access networks. At last, with the aid of the generalized central limit theorem, we build up a theoretical relation between the distributions of IML traffic and aggregated traffic.