A Mathematical Derivation of Erlang Model B and C Formulas Used in the Terrestrial Propagation Mechanisms for Terrestrial Propagation Modeling

In this paper, the author derived the Erlang model B and C formulas mathematically and summed up approximately in/with fifty equations or expressions. The result analysis revealed that using signal to noise ratio (SNR) analysis techniques the noise floor can be predicted–determined. For instance, the two-ray ground model was used to estimate capacity in a spread spectrum cellular mobile system showed excellent results. Further, these model formulas describe the grade of service (GoS) as the probability that an arbitrary user will experience a blocked call in a lost call cleared systems. The likelihood of a call not having immediate access to a channel in a lost call delayed (LCD) system is determined. For LCD systems, the GoS is measured by the probability theory that calls will have delays greater than t seconds. The knowledge of Erlang C formula and service distribution is used to analyze GoS. It was assumed that a nearly ∞ number of users are present in the system, and that all calls in the queue ultimately are serviced. The Erlang C model also assumes a large number of channels and a large number of users with similar calling patterns. The author assumes that, typically five or more channels are considered to be a sufficiently large number of channels