High School

A service counter employs 5 servers. Each server can serve 14 customers per hour and customers arrive at the counter at the rate of 13 per hour. Both service rate and arrival rate follow a Poisson distribution.


The servers work 7 hours per day (excluding lunch time). What is the idle time, in hours, of a server in one day? Round your answer to one decimal.

Answer :

The idle time of a server in one day is 0 hours.

To calculate the idle time of a server in one day, we need to consider the service rate, arrival rate, and the total working hours.

Number of servers (n) = 5

Service rate (λ) = 14 customers per hour

Arrival rate (μ) = 13 customers per hour

Working hours per day = 7 hours

The idle time of a server can be calculated using the following formula:

Idle time = 1 - (λ / μ)

Substituting the given values, we have:

Idle time = 1 - (14 / 13)

Idle time = 1 - 1.0769

Idle time = -0.0769

The idle time cannot be negative. A negative value indicates that the arrival rate is higher than the service rate, resulting in a backlog of customers and no idle time.

In this case, since the idle time is negative, it means that there is no idle time for the server. The server is continuously occupied with serving customers during the working hours.

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