Calls handled by 30 servers carrying 15 E

Traffic (Erlang) definition: traffic intensity $A = C\,h / T$, where C = number of calls in period T and h = mean holding time. So the number of calls is $C = A\,T/h$.

Given: N = 30 servers, A = 15 E, h = 3 min, T = 1 h = 60 min.

Calls by the group as a whole

$$\begin{aligned} C_{group} &= \frac{A\,T}{h} \\ &= \frac{15 \times 60}{3} \\ &= 300\ \text{calls per hour} \end{aligned}$$

Calls by a single server

Assuming traffic is shared equally, each server carries

$$\begin{aligned} A_1 &= \frac{15}{30} = 0.5\ \text{E} \end{aligned}$$

i.e. each server is busy 50% of the time = 30 min in the hour.

$$\begin{aligned} C_1 &= \frac{A_1\,T}{h} = \frac{0.5 \times 60}{3} = 10\ \text{calls per hour} \end{aligned}$$

Check: $30 \times 10 = 300$ calls.

Answer: a single server handles 10 calls/hour; the group handles 300 calls/hour.