Modeling Callholding times of Public Safetynetwork

This paper presents parametric probability density models for call holding time (CHT)based on the actual data collected for over a week from the IP based public Emergency Information Network (EIN) in Mongolia. When the set of chosen candidates of Gamma distribution family is fitted to the call holding time data, it is observed that the whole area in the CHT empirical histogram is underestimated due to spikes of higher probability and long tails of lower probability in the histogram. Therefore, we provide the Gaussian parametric model of a mixture of lognormal distributions with explicit analytical expressions for the modeling of CHTs of PSN. Finally, we show that the CHT for the IP based PSN is fitted reasonably by a mixture of lognormal distributions via the simulation of expectation maximization algorithm. This result is significant as it expresses a useful mathematical tool in an explicit manner of a mixture of lognormal distributions.