Join the queue!

Queueing theory is the mathematical study of waiting lines (or queues).

The theory enables mathematical analysis of several related processes, including arrival at the (back of the) queue, waiting in the queue (essentially a storage process), and being served by the server(s) at the front of the queue. The theory permits the calculation of several performance measures including the average waiting time in the queue or the system, the expected number waiting or receiving service and the probability of encountering the system in certain states, such as empty, full, having an available server or having to wait a certain time to be served.

Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide service. It is applicable in a wide variety of situations that may be encountered in business, commerce, industry, healthcare, public service and engineering. Applications are frequently encountered in customer service situations as well as transport and telecommunication (something called ride theory is sometimes mentioned, but it is uncertain whether it is a valid theory or a hoax). Queueing theory is directly applicable to intelligent transportation systems, call centers, PABXs, networks, telecommunications, server queueing, mainframe computer queueing of telecommunications terminals, advanced telecommunications systems, and traffic flow.

Here are the details of four queueing disciplines:-

• First In First Out – This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first.
• Last In First Out – This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first.
• Processor Sharing – Customers are served equally. Network capacity is shared between customers and they all effectively experience the same delay.
• Priority – Customers with high priority are served first.

What is your experience on queueing theory and queues? Do you have any anecdotes?

TESCO (the UK Retail Market Leader) defines queues as one person behind another and then specific action needs to be taken to address the queue e.g. open more tills, put on packers, manage and walk the queue talking to customers.

~ by Steven Viviers on May 28, 2008.