Question

In: Statistics and Probability

Customers enter the camera department of a store with an average of 14 minutes between customers....

Customers enter the camera department of a store with an average of 14 minutes between customers.

The department is staffed by one employee, who can handle an average of 13 customers per hour.

Assume this is a simple Poisson arrival, exponentially distributed service time situation.

Find the following information to help the manager decide if a second employee should be added:

The average number of customers waiting. Please keep 4 decimals.

The average time a customer waits (in minutes). Please keep 4 decimals.

The average time a customer is in the department (in minutes). Please keep 4 decimals.

Solutions

Expert Solution

Customers enter the camera department of a store with an average of 14 minutes between customers.

So, the arrival rate = = 14 per minutes = 60/14 = 30/7 per hour.

The department is staffed by one employee, who can handle an average of 13 customers per hour.

So that the service rate = = 13 per hours = 13/60 per minute.

there are only one service channel

Let

Here we assume that this is a simple Poisson arrival, exponentially distributed service time situation.

So we can use M/M/1 model to find the answer of the following questions.

The average number of customers waiting. Please keep 4 decimals.

average number of customers waiting = Expected average queue length E(m) = Lq

average number of customers waiting = 0.1621 persons.

The average time a customer waits (in minutes). Please keep 4 decimals.

Wait in the queue = Wq = Lq/ = 0.1621*14 = 2.27 minutes.

Wait in the system = W = Wq + 1/µ = 2.27 + 1/(13/60) = 2.27 + (60/13) = 6.88 minutes.

orchestra answered 2 years ago
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