A cellular hierarchical network with heterogeneous traffic is considered, where calls with shorter (longer) average call-holding time are assigned to the associated lower (upper) layer. The main contribution of this paper is that an efficient and reasonably accurate analytical method is proposed to calculate performance measures of interest, i.e., new call-blocking probability and forced termination probability for conversational services, new call-blocking probability, forced termination probability, and the average number of assigned time slots for streaming services. In particular, a simple two-state MMPP/sup (1,2,...,K)/, that takes into account not only the dependence among overflowed calls of the same class but also the correlation among overflowed calls of different classes, is used to approximate overflowed traffic to reduce computational complexity and improve accuracy. The methods with the multiclass overflowed traffic being approximated as independent Poisson processes and interrupted Poisson processes are also conducted for comparison. Importantly, it is shown via simulation results that the proposed model generates more accurate results than those obtained with the other two approximation methods. Last but not least, the effect of nonuniform traffic density on performance measures is studied via simulation. It is shown that the nonuniform traffic density may have a significant impact on the performance.

A class of loss networks in which each connection specifies a route and a bandwidth requirement is considered. If sufficient bandwidth is not available in one of the links along the route, the connection is blocked and lost. Three schemes are considered for approximating blocking probabilities in the network. For a specific star topology, two of these schemes give blocking probabilities that are very close to the exact values under light, moderate, and heavy traffic. The approximations are shown to be asymptotically correct in a natural limiting regime. The implied costs and their relation to revenue sensitivity are also determined for the approximation schemes. The approximate revenue sensitivities are again very close to the exact values for the specific star topology.>

A reduced load approximation (also referred to as an Erlang fixed point approximation) for estimating point-to-point blocking probabilities in loss networks (e.g., circuit switched networks) with state-dependent routing is considered. In this approximation scheme, the idle capacity distribution for each link in the network is approximated, assuming that these distributions are independent from link to link. This leads to a set of nonlinear fixed-point equations which can be solved by repeated substitutions. The accuracy and the computational requirements of the approximation procedure for a particular routing scheme, namely least loaded routing, is examined. Numerical results for six-node and 36-node asymmetric networks are given. A novel reduced load approximation for multirate networks with state-dependent routing is also presented.>

In a recent paper, Melen and Turner [SIAM J. Comput., 18 (1989), pp. 301–313] determined sufficient conditions for multirate interconnection networks to be strictly nonblocking and rearrangeable. They considered the continuous bandwidth case, which permits the bandwidth of a connection to take an arbitrary value in a given closed interval. In this paper, simple necessary and sufficient conditions for multirate interconnection networks to be strictly nonblocking for both discrete and continuous bandwidth cases are determined. New results for rearrangeable multirate networks with discrete bandwidth requirements are also given.