Approximation of loss calculation for hierarchical networks with multiservice overflows

This paper studies loss calculation in hierarchical networks with multiservice overflows which have different call arrival rates, mean holding times, bandwidth requirements and share a common link. The loss calculation involves two challenging problems: 1) the computation of the two moment characterizations of multiservice overflow traffic over the shared link, 2) the calculation of the loss probabilities for multiservice non-Poisson overflow traffic in hierarchical systems. An efficient approximation method, known as multiservice overflow approximation (MOA), is proposed to enable multiservice networks designs with hierarchical architecture. Two contributions are included in the MOA method. First, an approximation based on blocking probabilities matching is proposed to compute the variances of multiservice overflows over the shared link. Second, a modified Fredericks & Hayward's approximation is used to calculate the loss probabilities of multiservice non-Poisson over flow traffic. The performance of the MOA method is evaluated in a two-tier hierarchical cellular network and compared with an existing approximation method based on multi-dimensional Markov-modulated Poisson process (MMPP). Verified by simulations, the MOA method achieves better accuracy in the general heterogeneous cases at lower computational cost than the MMPP method.