A cellular system has a total of 110 reuse groups with 13 cells per group. There

Question

A cellular system has a total of 110 reuse groups with 13 cells per group. There are three channels in each cell for users to make calls. The entire system has 2,760 Erlangs of traffic intensity for the entire system (evenly distributed among all cells in the full system). In the system, the average call is 3 minutes 15 seconds.

A) What is the blocking rate (B) in a cell, assuming this a blocking system?

B) What is the utilization for a single cell, assuming it is a blocking system?

C) If calls were queued in the cell, what would be the average delay (in seconds) for all callers in a single cell?

Explanation / Answer

Given,
1. Number of reuse channels n = 110
2. Number if cells per group c= 13
3. Number of channels available to make calls on each cell a= 3.
4. Traffic intensity = 2760 Erlangs.

Blocking rate:

110/2760= 25.09 Erlang/reuse group

Total number of lines available to call N= a*c = 39 channels.

Using the Erlang B chart

N=39 (number of lines/cell) and
Erlangs=25.09

25.09 falls between 23.65 and 26.53

so 26.53 is used which is a blocking percentage of .5%

b. Utilization of each cell can be given by
25.09 / 39 * 100%
Which is 64.33%.

c. Average delay:

Using the Erlang C chart for 26 Erlangs The average wait time for calls in queue is .077h

.077 * 60*60= 277 seconds.

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