Uniform Approximations for Multirate Loss Systems with State Dependent Arrival Rates

摘要

A multirate loss system with complete sharing is investigated, in which multiple classes of customers arrive as a state dependent Poisson processes. This arrival process includes the Bernoulli-Poisson-Pascal (BPP) and the batched Poisson process with geometric distributed batch sizes. Asymptotic uniform approximations to the blocking probabilities are derived, when the capacity and a parameter of the arrival processes are commensurately large. The results are obtained with the saddle-point method of integration and the approximation uniformly holds across all traffic regimes, where the blocking probabilities may vary by several order of magnitude. Moreover, a numerically stable representation of the approximation is given, which gives accurate results also for the critical traffic region. Numerical results show that while prior asymptotic approximations are quite accurate, the new approximations are very accurate.