Call-Level Performance Sensitivity in Cellular Networks

The development of analytically tractable teletraffic models for performance evaluation of mobile cellular networks under more realistic assumptions has been the concern of recent works (Corral-Ruíz et al. 2010; Fang a; 2005, Fang b; 2005; Kim & Choi 2009; Pattaramalai, 2009; Rico-Páez et al., 2007; Rodríguez-Estrello et al., 2009; Rodríguez-Estrello et al., 2010; Wang & Fan, 2007; Yeo & Yun, 2002; Zeng et al., 2002). The general conclusion of those works is that, in order to capture the overall effects of cellular shape, cellular size, users’ mobility patterns, wireless channel unreliability, handoff schemes, and characteristics of new applications, most of the time interval variables (i.e., those used for modeling time duration of different events in telecommunications – for example, cell dwell time, residual cell dwell time, unencumbered interruption time, unencumbered service time) need to be modeled as random variables with general distributions. In this research direction, phasetype distributions have got a lot of attention because of the possibility of using the theory of Markov processes1 (Fang, 1999, Christensen et al., 2004). Moreover, there have been major advances in fitting phase-type distributions to real data (Alfa & Li, 2002). Among the phasetype probability distributions, the use of hyper-Erlang distribution is of special interest due to its universality property (i.e., it can be used to accurately approximate the behavior of any non negative random variable) and also because of the fact that it provides accurate description of real distributions of different time variables in mobile cellular networks (Fang, 1999; Corral-Ruíz et al., 2010; Yeo & Yun, 2002). When a probability distribution different to the negative exponential one is the best choice to fit the real distribution of a given time interval variable, not only its expected value but also its higher order moments are relevant. Nonetheless, the study of the effect of moments higher than the expected value has been largely ignored. The reason is twofold: 1) because of the relatively recent use of probability distributions different to the exponential one and 2) because the related works have been focused on developing mathematical models rather than numerically evaluating system performance. In this chapter, the important task of identify and analyze the influence of moments higher than the expected value of both cell dwell time and unencumbered interruption time on