The MM Σ_k=1^K CPP_k/GE/c/L G-queue and its application to the analysis of the load balancing in MPLS networks

The MM CPP/GE/c/L G-queue has been capable of accommodating large batch sizes of arrivals and services with an efficient solution in the Markovian framework. However it suffers from the restriction on the batch size distribution (i.e. geometric batch size distribution). In order to overcome that restriction, to make the model vastly more flexible and also to accommodate the superposition of multiple arrival streams, a new traffic/queueing model, the Markov modulated MM Σ_k=1^K CPP_k/GE/c/L G-queue is introduced. This is a homogeneous multi-server queue with c servers, GE service times and with the superposition of K independent positive and an independent negative customer arrival streams each of which is a CPP, i.e. a Poisson point process with batch arrivals of geometrically distributed batch size.