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Customers arrive at random to the passport center at a rate of 40 customers per hour. Currently, there are 20 clerks, each serving 4 customers per hour on the average.

Estimate the average utilisation of a server and the average number of busy servers. Can we decrease the number of servers?

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Given that

Arrival rate = $\lambda$ = 40 customers / hour

Service rate = $\mu$ = 4 customers / hour

No. of server, $\mathbf{c}$ = 20

Since it is a multi-server system

$\therefore$ Average utilization of servers = $\rho = \frac{\lambda}{c . \mu} = \frac{40}{ 20 \times 4} = 0.5$

and average number of busy servers

$L s=\frac{\lambda}{\mu}=10$

From this we can say that in the long run, a waiter is busy serving customers 50% of its time.

$\therefore$ There is no need for additional servers.

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