Cell traffic load is typically characterised has the two important distributed parameters.
- Average number of mobile stations requesting the service (average call arrival rate (λ).
- Average length of time the mobile stations requiring the service (average holding time T).
The offered traffic load is defined as
a= λT.
For example, in a cell with 100ms, on average, if 30 requests are generated during an hour with an average holding time of T=360 seconds then the average call arrival rate is.
λ =
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/1-1.jpg)
A servicing channel that is kept busy in an hour is quantitatively defined as one ERLANG.
Here the traffic load offered for the example by ERLANG is
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/2-1.jpg)
= 3 Erlang.
The average arrival rate is λ and the average departure rate is µ. Therefore all the channels are busy, for this arriving call is turned away. An M/M/S/S queuing model of the system can be analyzed. Since M/M/S/S is a special case of M/M/S/∞, steady-state probabilities p(i) for these systems have the same form as those for states i=0…S in the M/M/S/∞ model. Therefore, S is defined as the channels in a cell. Thus we have
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/3.jpg)
Where a= λ/µ is the offered load and
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/4.jpg)
Therefore the arriving call probability p(s) blocked is equal to the probability of all the channels are busy, which is
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/5.jpg)
The above equation is called the Erlang B formula and is denoted by B(s, a). B(s, a). Therefore it also called blocking probability of rejection, or probability of loss.
From the old example, if S is given as 2 with a=3, the blocking probability is
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/6.jpg)
Therefore, a fraction of 0.529 calls is blocked, and that we got to reinitiate the decision. Thus the entire number of blocked calls is about 30*0.529=15.87. The efficiency of the system is often given by.
![](https://www.webvidyalayam.com/wp-content/uploads/2021/03/7.jpg)