Abstract
Cell dwell time (DT) and unencumbered interruption time (IT) are fundamental time interval variables in the teletraffic analysis for the performance evaluation of mobile cellular networks. Although a diverse set of general distributions has been proposed to model these time interval variables, the effect of their moments higher than the expected value on system performance has not been reported in the literature. In this paper, sensitivity of teletraffic performance metrics of mobile cellular networks to the first three standardized moments of both DT and IT is investigated in a comprehensive manner. Mathematical analysis is developed considering that both DT and IT are phase-type distributed random variables. This work includes substantial numerical results for quantifying the dependence of system level performance metrics to the values of the first three standardized moments of both DT and IT. For instance, for a high mobility scenario where DT is modeled by a hyper-Erlang distribution, we found that call forced termination probability decreases around 60% as the coefficient of variation (CoV) and skewness of DT simultaneously change from 1 to 20 and from 60 to 2, respectively. Also, numerical results confirm that as link unreliability increases the forced termination probability increases while both new call blocking and handoff failure probabilities decrease. Numerical results also indicate that for low values of skewness, performance metrics are highly sensitive to changes in the CoV of either the IT or DT. In general, it is observed that system performance is more sensitive to the statistics of the IT than to those of the DT. Such understanding of teletraffic engineering issues is vital for planning, designing, dimensioning, and optimizing mobile cellular networks.
Highlights
Cell residence/dwell time (DT), unencumbered interruption time (IT), and unencumbered call-holding/service time (ST) are fundamental time interval variables for the mathematical analysis of cellular networks (CNs). ese telecommunication time variables allow us to compute key parameters of CNs
Note that the label “HErl-2” denotes the hyper-Erlang pdf with two phases and two stages and the label “HExp-2” represents the 2nd order hyperexponential pdf. e following parameters are considered : mean service time (1/μ) is equal to 180 s, total number of channels per cell (S) is equal to 8, offered traffic per cell is equal to 4.4 Erlangs, and total number of channels reserved for handoff prioritization (N(n)) is equal to 1
Despite the fact that the numerical results presented in this work were obtained from particular situations with certain set of system parameter values, these results reveal that there exist important sensitive questions concerning moments higher than the expected value of both DT and IT
Summary
Cell residence/dwell time (DT), unencumbered interruption time (IT), and unencumbered call-holding/service time (ST) are fundamental time interval variables for the mathematical analysis of cellular networks (CNs). ese telecommunication time variables allow us to compute key parameters of CNs (i.e., channel holding time, new session blocking, unsuccessful handoff, forced session termination probabilities, handoff rate, and Erlang capacity, among others). It has been found that the global effect of cellular size/shape, mobility characteristics of users, link unreliability, handoff mechanisms, and behavior of new type of services can be best captured if these time variables are modeled as random variables (RVs) with general probability distribution functions (pdfs) [2,3,4,5,6,7,8,9]. In this sense, some researchers have employed the gamma, log-normal, Pareto, and Weibull pdfs to model cell residence time [10]. When experimental data (that represent certain telecommunication time variable) are best fitted with a general pdf, it is of paramount importance to comprehensively study the influence of moments higher than the expected value of this telecommunication time variable on the system performance [14]. is is the topic of research of the present work
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