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Two-law approximation for voice delay in packet networks

Traditionally, voice has been transported using circuit switched networks, the Public Switched Telephone Network (PSTN) for example. However, driven by the ubiquity of the Internet and the development of low bit-rate digital voice codecs there has been increasing focus on using packet-switched networks for voice traffic. We focus on one such application. Our model comprises of a relatively slow packet link (between 1.5 and 5.0 Mbps) being utilized for voice traffic. Large number (of the order of 100) voice sources are multiplexed on this link. For such a link we obtain delay distributions seen by a voice source. Specifically, we exploit key characteristics of the model, such as the large number of sources to obtain a heavy traffic approximation for the system. The key result is that the delays can be well approximated by concatenation of two exponential distributions. We also provide valuable insight into how the delay distribution is connected with the statistical properties of the voice sources, in particular their correlation behavior. Our analytical results are validated with simulation results.