Coffee Vending Machine Essay Sample

The average arrival rate is denoted as λ while the average service rate is denoted as µ. The arrival rate λ is 4 people per minute while the service rate µ is one cup per 10 seconds which can is equivalent to 6 cups per minute.
µ = 60/10
= 6
a)Average number of people waiting in line
Lq = λ2
= 16

6(6-4)

= 16
12
= 1.33
The above procedure is used to determine the number of people who are waiting on the queue. These results can be used by the organization in determining whether there is need to add another coffee vending machine to cater for the customers. Lengthy queues make the customers uneasy, and they may go to a competitor to buy coffee.
b)The average number in the system
Ls = λ
(µ-λ)
= 4
(6-4)
= 4
2
= 2
The above method is used to determine the number of customers in the entire system. It includes both the customers receiving the service and those waiting in the queue. The results can be used to determine the number of customers the organization gets at a particular time (Bhattacharjee, 2014). Such kind of information is important because the company is able to determine the peak times and the low times. The company can add more coffee vending machines during the peak periods so that it does not lose its customers.
c)The length of time an average person wait in line before being served
Wq = λ
µ(µ-λ)
= 4

6(6-4)

= 4
12
= 0.33
The above procedure is used to determine the period of time each person spends on the queue before receiving a service. The organization can use this information to make decisions on whether there is need to add more coffee vending machines or whether the current machine is enough. Such methods can be used by the organization to save on unnecessary costs and to make sure that it does not lose its customers (Bhattacharjee, 2014).

References

Bhattacharjee, B. (2014, Jan 12). Queuing Theory and its Business Applications. Slideshare. Retrieved from: http://www.slideshare.net/BISWAJITorJEET/queueing-theory-29932020