Research Journal of Engineering and Technology

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


Affiliations
1 ECE & CSE Dept., SSN College of Engg. & Technology, Ongole, Prakasham-523002, AP, India
2 Dept of ECE, Vathsalya Institute of Science & Technology (VIST) Anantharam (V), Bhongir , Nalgonda Dist. 508116 AP, India
     

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

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Authors

V. Rama Raju
ECE & CSE Dept., SSN College of Engg. & Technology, Ongole, Prakasham-523002, AP, India
R. Vaishnavi
Dept of ECE, Vathsalya Institute of Science & Technology (VIST) Anantharam (V), Bhongir , Nalgonda Dist. 508116 AP, India

Abstract


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.