The MM \sum\limits_{k = 1}^K {} CPPk/GE/c/L G-Queue and Its Application to the Analysis of the Load Balancing in MPLS Networks

1. The MM ∑K k=1 CPPk/GE/c/L G-Queue It is well known that the traffic in today’s telecommunication systems often exhibits burstiness i.e. batches of transmission units (e.g. packets) arrive together with correlation among the interarrival times [12]. Several models have been proposed to model such arrival-service processes, queues and networks. These include the compound Poisson process (CPP) in which the interarrival times have generalised exponential (GE) probability distribution [8], the Markov modulated Poisson process (MMPP) and the self-similar traffic models such as the Fractional Brownian Motion (FBM) [11]. The CPP and the ∑K k=1 CPPk traffic models often give a good representation of the burstiness (batch size distribution) of the traffic from one or more sources [7], but not the auto-correlations of the interarrival time observed in real traffic. Conversely, the MMPP models can capture the auto-correlations but not the burstiness [9, 14]. The self-similar traffic models such as the FBM can represent both burstiness as well as auto-correlations, but they are analytically intractable in a queueing context. Often, the traffic to a node is the superposition of traffic from a number of sources, complicating the system analysis further. 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 [2]. 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 flexible and also to accommodate the superposition of multiple arrival streams, a new traffic/queueing model, the Markov modulated ∑K k=1 CPPk/GE/c/L G-queue is introduced [4]. This is a homogeneous multi-server queue with c servers, GE service times and with the superposition of K independent positive and an independent negative1 customer arrival