Queueing Theory

Waiting to be served

Queueing theory is used to be studied of queueing or waiting in lines to be served by enterprising mathematical tools.When someone is asked “what is queue”, then it’s easy for one to reach of the image of themselves who are waiting for a line to be served in a supermarket on Monday evening.While queue is not targeted only in customers, also can be items, object or information.

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For example, like Gmail, those mail onces customers received in
mailbox according to the server, normally the latest one always in the first line ,that it is waiting to be checked and replied. In warehousing system, the amount of products are waiting to be distributed and input in the inventory system(ERP,CRM etc.).

Cases

Recently, us student were asked to compare Julia and Carmen’s case (FNAC and Apple store in Valencia).Some of us might not notice how exactly these 2 stores treat their customers and how they implement customer experience goal.

Both 2 girls wanted to purchase the targeted article in electronic devices stores. The final result was differentiate by the process of purchase and the way to be treat. Julia didn’t have a good shopping experience and have a lower satisfaction with the store where she had been because she was kept waiting all the time for obtaining information of stock of her wanted item , being told where should she go for the item and was not simplified to get her receipt. On the contrary, Carmen spent a great time in another shop and at the end she got what she desired.

After studying these 2 cases, dropped the attention(checkout line) of when a customer comes to the line , waiting to be charged, but after 30 sec, another customer joins the queue, and after 10  sec…,the cashier are supposed to improve her/his work efficiency,if not, that line will be accumulated with uncountless number. Nevertheless, a discipline of first-comes-first-serve(FCFS) is acceptable and logical rule in a queue .Likewise, last-come-first-serve(LCFS) also is normal when the first queue is overloaded, then the second queue will be appear. Obviously, the last customer in the first queue will be served preferentially.I do believe that the majority of customers are not satisfied with this unfair-treated service because of breaking the rule of FCFS and some might leave for home.

For instance, queueing is dealing with one of the most unpleasant experience of life, waiting to be…Whatever, queueing theory can be summarized that it’s related to arrival process, what will customers act when they are not willing to wait for a long line then to be served,how customers are treated and the rules to be served.

Little’s Law

which was first proven by mathematician John Little, states that the average number of items in a queue can be calculated by multiplying the average rate at which the items arrive in the system by the average amount of time they spend in it.

L = λW

3 input Little’s law is useful in analyzing how a queue has performed over some time.

Eg: Wants to figure out the average number of tequila that are stored in warehouse.

W: Average arrival rate of the tequila(carton) into the warehouse is 5000 per year

λ: Average time the company spend in warhouse is about 3 weeks

Thus, L=5000 x 3