How can you apply queuing theory in real-world situations?

1 What is a queue?

A queue is a collection of entities that arrive at a system and wait for some service or resource. This could be anything from people, vehicles, machines, packets, jobs, or other items requiring attention. The system could be a bank, hospital, factory, network, server, or other process providing service or resource. Queues have three main characteristics: the arrival pattern, the service pattern, and the queue discipline. The arrival pattern describes how frequently and randomly entities arrive at the system and can be deterministic or stochastic; for example, customers at a supermarket checkout are stochastic while trains at a station are deterministic. The service pattern describes how long and randomly the system takes to serve each entity and can also be either deterministic or stochastic; for example, the service time of a cashier is stochastic while the service time of a machine is deterministic. Lastly, the queue discipline describes the order in which entities are served by the system and can be first-in-first-out (FIFO), last-in-first-out (LIFO), priority-based, random, or any other rule; for example, the queue discipline of a supermarket checkout is FIFO while an emergency room is priority-based.

2 What is a queuing model?

A queuing model is a mathematical representation of a queue that captures its main characteristics and allows you to calculate various performance measures. The notation for the most common queuing models is A/B/c/K/N/D, where A is the arrival pattern (Markovian, Poisson, deterministic, or general), B is the service pattern (Markovian, Poisson, deterministic, or general), c is the number of service channels or servers in the system, K is the maximum number of entities allowed in the system (or infinity if there is no limit), N is the size of the population (or infinity if there is no limit), and D is the queue discipline (FIFO, LIFO, or priority). For example, a M/M/1 queue has Poisson arrivals and services, one server, no limit on entities or population size, and FIFO discipline.

3 What are some performance measures?

A queuing model can be used to calculate several performance measures, such as the average number of entities in the system (L) and queue (Lq), the average time an entity spends in the system (W) and queue (Wq), the utilization or traffic intensity of the system (Rho), and the probability that there are n entities in the system (Pn). Depending on the queuing model, different formulas or methods are used to calculate these performance measures. For instance, a M/M/1 queue has formulas for L, Lq, W, Wq, Rho, and Pn.

4 How can you apply queuing theory in real-world situations?

Queuing theory can be utilized in real-world situations to solve various problems and make better decisions. For instance, it can be used to design and optimize the service capacity and layout of a system, manage and control the demand and behavior of entities, or evaluate and improve the performance and quality of a system. To apply queuing theory, one must first identify and define the problem and objectives they want to achieve or optimize. Then, data must be collected on the characteristics of the queue, such as arrival pattern, service pattern, queue discipline, and performance measures. After selecting a suitable queuing model that matches the data and assumptions of the queue, performance measures can be calculated from the model and compared with objectives and constraints. Finally, different scenarios or solutions based on the queuing model can be tested and implemented to evaluate their impacts and trade-offs.

5 What are some examples of queuing theory applications?

Queuing theory has many applications in various fields and industries, such as health care, manufacturing, transportation, telecommunications, and service. In health care, queuing theory can help design and manage the capacity and flow of patients, staff, and resources in hospitals, clinics, or pharmacies. For instance, it can help determine how many beds, nurses, doctors, or equipment to have, how to prioritize patients, or how to reduce waiting times and improve quality of care. In manufacturing, queuing theory can help design and optimize the production and inventory systems. It can minimize the idle time, downtime, or backlog of machines or workers; or maximize the throughput, efficiency, or profitability of the system. In transportation, queuing theory can help design and manage the traffic and congestion of vehicles, passengers, or goods in roads, airports, or ports. It can determine how many lanes, toll booths, or gates to have; how to allocate them; or how to reduce the delays, queues, or emissions. In telecommunications, queuing theory can help design and optimize the network and communication systems. It can balance the load, bandwidth, or latency of the network or system; or prevent the loss, blocking, or congestion of the packets. Finally in service sectors such as retail banking hospitality and entertainment queuing theory can help design and improve customer service and satisfaction. It can reduce customer waiting time frustration abandonment; or increase customer loyalty retention or revenue.

6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?