The problem of aggregating different stochastic process into a unique one that must be characterized based on the statistical knowledge of its components is a key point in the modeling of many complex phenomena such as the merging of traffic flows at network nodes. Depending on the physical intuition on the interaction between the processes, many different aggregation policies can be devised, from averaging to taking the maximum in each time slot. We here address flows averaging and maximum since they are very common modeling options. Then we give a set of axioms defining a general aggregation operator and, based on some advanced results of functional analysis, we investigate how the decay of correlation of the original processes affect the decay of correlation (and thus the self-similar features) of the aggregated process.

The aim of this contribution is to take a further step in the study of the impact of chaos-based techniques on classical DS-CDMA systems. The problem addressed here is the sequence phase acquisition and tracking which is needed to synchronize the spreading and despreading sequences of each link. An acquisition mechanism is considered and analyzed in depth to identify analytical expressions of suitable system performance parameters, namely outage probability, link startup delay and expected time to service. Special chaotic maps are considered to show that the choice of spreading sequences can be optimized to accelerate and improve the spreading codes acquisition phase.

In this paper we consider a tensor-based approach to the analytical computation of higher-order expectations of quantized trajectories generated by Piecewise Affine Markov (PWAM) maps. We formally derive closed-form expressions for expectations of trajectories generated by three families of maps, referred to as (n,t)-tailed shifts, (n,t)-broken identities and (n,t,π)-mixing permutations. These families produce expectations with asymptotic exponential decay whose detailed profile is controlled by map design. In the (n,t)-tailed shift case expectations are alternating in sign, in the (n,t)-broken identity case they are constant in sign, and the (n,t,π)-mixing permutation case they follow a dumped periodic trend.

A self-similar behavior characterizes the traffic in many real-world communication networks. This traffic is traditionally modeled as an ON/OFF discrete-time second-order self-similar random process. The self-similar processes are identified by means of a polynomially decaying trend of the autocovariance function. In this work we concentrate on two criteria to build a chaotic system able to generate self-similar trajectories. The first criterion relates self-similarity with the polynomially decaying trend of the autocovariance function. The second one relates self-similarity with the heavy-tailedness of the distributions of the sojourn times in the ON and/or OFF states. A family of discrete-time chaotic systems is then devised among the countable piecewise affine Pseudo-Markov maps. These maps can be constructed so that the quantization of their trajectories emulates traffic processes with different Hurst parameters and average load. Some simulations are reported showing how, according to the theory, the map design is able to fit those specifications.