During the busy evening period at a local supermarket custom

During the busy evening period at a local supermarket, customers arrive at the chek out lines at a rate of 100 customers/hour for 0.5 hours, after which no more customers arrive. The suspermarket has staffed check out lines so that they can serve customers at a rate of 60 customers/hour.

A. Draw a queing diagam for the arriving and served customers at the supermarket check-out lines. Calculate the total time that customers collectively spend waiting.

B. The manager considers hiring additional clerks in order to open up more check out lines and increase th service rate to 80 customers per hour. How much would the total collective delay change as a result of the increased checkout capacity? How much would the longest delay that a customer experiences change?

Solution

(a) As we have from question total no of customers in 1 hour is 100,

So, in 1 minute it is 100/60 customers. This is the frequency of customers every minute.

and for 30 minutes(0.50 hour) it is (100/60)*30 =50 customers.

The capacity of supermarket handling of customers is 60 customers /hour,

It means 1 customer every minute.

So the total time taken by the supermarket to handle 50 customer = 50 *1 = 50 minute

Now the collective time waiting for customers are 50 minute - 30 minute = 20 minute.

(b) Now we have the increased capacity of 80 customers/hour =80/60 per minute,

     So in 30 minutes it is (80/60) * 30 = 40 customers,

   Now, the no. of left out customers after 30 minutes = 50 - 40 = 10 customers,

So, the time taken by supermarket to accomodate 10 customers = (60/80)*10 = 7.5 minutes.

Now the collective delay change as a result od increaed checkout capacity = 20 - 7.5 = 12.5 minures.

And so the longest delay that a customer experiences change is 7.5 minute.