Transient analysis of traffic generated by bursty sources, and its application to measurement-based admission control

The first part of the paper is devoted to a transient analysis of traffic generated by bursty sources. These sources are governed by a modulating process, whose state determines the traffic rate at which the source transmits. The class of modulating processes contains e.g. on/off traffic sources with general on and off times (but is considerably broader). We focus on the probability of extreme fluctuations of the resulting traffic rate, or more precisely, we determine the probability of the number of sources being in the on state reaching a certain threshold, given a measurement of the number of sources in the on state $t$ units of time ago. In particular, we derive large deviations asymptotics of this probability when the number of sources is large. These asymptotics are numerically manageable, and it is empirically verified that they lead to an overestimation of the probability of our interest. The analysis is extended to alternative measurement procedures. These procedures allow to take into account for instance more historic measurements than just one, possibly combined with an exponential weighting of these measurements. In the second part of the paper, we apply the asymptotic calculation methods to gain insight into the feasibility of measurement-based admission control (MBAC) algorithms for ATM or IP networks. These algorithms attempt to regulate the network's load (to provide the customers with a sufficient Quality of Service), and at the same time achieve an acceptable utilization of the resources. An MBAC algorithm may base acceptance or rejection of a new request on the measured momentary load imposed on the switch or router; if this load is below a given threshold, the source can be admitted. We investigate whether such a scheme is robust under the possible stochastic properties of the traffic offered. Both the burst level (i.e., the distribution of the on and off times of the sources) and the call level (particularly the distribution of the call duration) are taken into account. Special attention is paid to the influence of the bursts, silences, or call durations having a distribution with a `heavy tail'.