# Queuing

Automobiles arrive at the drive-through window at a post office at the rate of 4 every 10 minutes. The average service time is 2 minutes. the Poisson distribution is appropriate for the arrival rate and service times are exponentially distributed.

(A) what is the average time a car is in the system?

(b) what is the average number of cars in the system?

(c) what is the average time cars spend waiting to receive service?

(d) what is the average number of cars in line behind the customer receiving service?

(e) The probability that there are no cars at the window is given by.

(f) The percentage of time the postal clerk busy is given by.

(g) The probability that there are two cars in the system is given by.

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#### Solution Preview

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Solution

The given system is an M/M/1 queuing system.

It is given that,

The arrival rate, λ = 24 per hour

The service rate, µ = 30 per hour.

a) The average time a car is in the system is given by,

1 = 1/(u - lamba) = ...

#### Solution Summary

The solution determines various aspects of a Queuing problem.