Queuing theory is a mathematical way of understanding the movement of customers and resources in a process such as in a factory. It is a widely used tool for operations management that studies the interrelationship between customer demand, system capacity, service level, utilization, and costs. Queuing theory helps improve quality of service and reduce operational expenses.

In a queuing system, customers (or items) wait in line for some kind of service or attention. From a mathematical standpoint, queuing theory considers two primary elements: the rate at which service is provided, and how customers are served. This includes determining how quickly customers are served, how long they wait, and the probability that an item will be refused service.

In simple terms, the most important variables in a queuing system are the average number of customers in the system, the length of the queue, and its response time. There are numerous queuing models, some of which are deterministic and others are stochastic. For example, in a deterministic queuing model, the arrivals would be steady over time, and the queue would be operated to process the customers as quickly as possible. On the other hand, in a stochastic queuing model, the arrivals and departures would be random, and the queue would be operated to satisfy the average customer's expectation of waiting time.

In the business world, queuing theory is a tool that managers can use to understand how their operations work, and how to improve service delivery. It helps them to identify under-utilized resources, and to better plan for staffing needs. For example, queuing theory can be used to develop service standards such as response time, throughput, and customer wait time. It can also be used to determine staff levels, identify bottlenecks, and develop strategies for improving service delivery.

The key benefits of queuing theory are its ability to improve efficiency, cost savings, and customer satisfaction. With its help, businesses can evaluate their current queues, determine what changes they need to make, and ensure optimal service delivery. Queuing theory is a powerful tool that managers can use to better manage their business and reduce costs.