Calls handled by 25 servers carrying 5 E

Given: number of servers $n = 25$, total traffic carried $A = 5$ E, mean holding time $h = 4$ min, period $T = 1$ h $= 60$ min.

Traffic in erlang equals the call rate multiplied by the mean holding time:

$$A = \frac{C\,h}{T} \quad\Rightarrow\quad C = \frac{A\,T}{h}$$

Calls put through by the group

$$\begin{aligned} C_{group} &= \frac{5 \times 60}{4} \\ &= 75\ \text{calls per hour} \end{aligned}$$

Calls put through by a single server

Assuming the traffic is shared equally among the 25 servers, each server carries

$$\begin{aligned} A_1 &= \frac{5}{25} = 0.2\ \text{E} \end{aligned}$$

That is, each server is busy 20% of the time, i.e. $0.2 \times 60 = 12$ min in the hour. Number of calls handled by one server:

$$\begin{aligned} C_1 &= \frac{A_1\,T}{h} = \frac{0.2 \times 60}{4} \\ &= 3\ \text{calls per hour} \end{aligned}$$

Check: $25 \times 3 = 75$ calls, which matches the group total.

Interpretation

• Total busy time of all servers in the hour $= 75 \times 4 = 300$ call-minutes $= 5$ erlang-hours, which agrees with 5 E.
• The group occupancy is only $5/25 = 20\%$, so the group is lightly loaded; the blocking will be very small.

Answer: one server carries 0.2 E and puts through 3 calls per hour; the group of 25 servers puts through 75 calls per hour.