Queuing theory

The queuing theory addresses problems involved in waiting. Typical examples of queuing in business include the lines of people waiting for service at banks and supermarkets and the queues caused by PRODUCTION shutdowns, public transport delays, and slow computer response times. In each of these situations, COSTS and benefits must be weighed. Shorter queues increase customer satisfaction but also are more costly to businesses. Reduced response time on a computer can be compared to the increased cost of hardware or INTERNET service connection. The cost associated with a shutdown of a production line can be compared to the cost of maintaining a supply of parts and machines to restart production quickly. The most typical queuing theory situation is a system where customers arrive and form a line waiting for a service. Analysis of the arrival process includes
• how the customers arrive (singly or in groups)
• how the arrivals are distributed over time (randomly or in segments)
• whether there is a finite population of customers or potentially infinite number
Arrival patterns can include completely regular arrivals (the same constant time interval between successive arrivals), batch arrivals, and time-dependent arrivals. Next, queuing theory analyzes the service mechanism available including
• how long the service will take
• whether the servers are in series (each server has a separate queue) or in parallel (one queue for all servers)
• whether preemption is used (whether customer emergencies move people ahead in a queue)
Queuing theory also includes analysis of queue behavior or discipline. Are people served on a first-come-first-served basis? Do customers decide to not join a queue if it is too long, or leave a queue after waiting? Using formulas or simulating, queuing theory can be used to measure the performance of a system, addressing questions such as
• How long does a customer expect to wait?
• How long will he or she have to wait before a service is completed?
• What is the probability of a customer having to wait longer than a given time interval before he or she is served?
• What is the average length of a queue?