Subject: Mobile Communication System

Topic: Fundamental of Mobile Communication

Difficulty: Medium

Grade of Service is a measure of ability of user to access a trunk system busiest hour.

The Erlang B formula determines the probability that a call is blocked, and is a measure of the GOS for a trunked system that provides no queuing for blocked calls. The number of busy channels is equal to the number of busy users, and the probability of blocking is given as:

$P_r[Blocking] = \frac{(\frac{A^C}{C!})}{{\sum_{k=0}}^{C} \frac{A^K}{K!}} $

Where: C is the number of trunked channels, and A is the total offered load to the trunked system.

The Erlang C formula is derived from the assumption that a queue is used to hold all requested calls which cannot be immediately assigned a channel. The Erlang C formula is given by:

$P_r [call \ delayed] = \frac {A^C} {A^C + C! (1 - \frac{A}{C})\sum_{k=0}^{C} \frac{A^K}{K!}} $