Queue

An overview of the concept of queues in economics, their disciplines, and analytical models.

Background

The concept of a queue is fundamental in both everyday life and economics. It refers to a line or sequence of people, vehicles, or other entities awaiting their turn to receive a good or service.

Historical Context

The study and formalization of queuing theory date back to the early 20th century with mathematical work initiated by Agner Krarup Erlang, primarily to address telecom traffic management. Over time, queuing theory has been extended to various fields including economics, operations research, and service management.

Definitions and Concepts

  • Queue: A number of customers awaiting service.
  • Queue Discipline: The rule or method governing the order in which customers in a queue are served. This can vary widely and include principles like first-come, first-served (FCFS), last-in, first-out (LIFO), random order, or some priority-based system.
  • Queuing Models: These are theoretical models that simulate the behavior of queues to understand and optimize the process of queue management.

Major Analytical Frameworks

Classical Economics

Classical economic frameworks generally do not emphasize queue theory; however, scarcity, supply, and demand implicitly create situations where queues develop as a rationing mechanism.

Neoclassical Economics

Neoclassical economics also tends to focus on equilibrium and efficiency, with queuing arising in markets where supply cannot instantaneously adjust to demand.

Keynesian Economics

Keynesian models might involve queues in scenarios related to employment and resource allocation in aggregate demand contexts.

Marxian Economics

Queues may be interpreted as manifestations of scarcity and resource allocation under capitalism. Inefficiencies and inequities may be highlighted through the examination of who queues, for what, and for how long.

Institutional Economics

This framework examines the rules and norms governing queue disciplines and how different institutions manage and prioritize service.

Behavioral Economics

Behavioral economists may study how perceived fairness and patience (or impatience) influence how individuals interact with queues.

Post-Keynesian Economics

Queues can be important in this framework too, particularly in describing market constraints and efficiencies in response to aggregate demand.

Austrian Economics

Emphases might be placed on how queues form naturally and how they relate to market signaling and entrepreneurship.

Development Economics

Here queues might illustrate issues related to access to goods and services, particularly in developing economies where resources are limited.

Monetarism

Queques might be explored regarding liquidity and closed systems where resources must be controlled and doled out in an organized manner.

Comparative Analysis

By comparing these frameworks, one can see that, while the fundamental nature of queues remains the same, the interpretation and implications vary: from managing scarce resources to exploring human behavior in economic settings.

Case Studies

  1. Grocery Store Lines: Analyzing various queue disciplines—from express lines to first-come, first-served—within retail.
  2. Triage Systems: Examination of priority-based queues in healthcare settings.
  3. Airport Security: The study of random order versus systematic priority boarding processes.

Suggested Books for Further Studies

  1. “Fundamentals of Queueing Theory” by Donald Gross and John F. Shortle
  2. “Queueing Systems” by Leonard Kleinrock
  3. “Queues: A Course in Queueing Theory” by Przemysław Ignaciuk
  • First-Come, First-Served (FCFS): A queue discipline whereby the first person to arrive is the first to be served.
  • Priority Queueing: A system where customers with higher priority are served ahead of those with lower priority.
  • Random Order Queueing: No specific order in which individuals are served, it is entirely random.
  • Simulation Models: Tools used in queuing theory to numerically predict and analyze queue behaviors.

Quiz

### Which of the following describes "First-Come, First-Served" queue discipline? - [ ] Customers with the highest priority served first - [x] The first customer in line is served next - [ ] Customers are served in a random order - [ ] The last customer in line is served next > **Explanation:** First-Come, First-Served means the first customer at the front of the queue is served next. ### What does traffic intensity (\\(\rho\\)) in queuing systems measure? - [ ] Service efficiency - [ ] The number of service channels - [x] Congestion in the system - [ ] Customer satisfaction > **Explanation:** Traffic intensity (\\(\rho = \frac{\lambda}{\mu}\\)) measures the level of congestion in the system, where \\(\lambda\\) is the arrival rate and \\(\mu\\) is the service rate. ### Which of the following terms refers to customers leaving the queue before being served? - [x] Reneging - [ ] Balking - [ ] Prioritizing - [ ] Queue Length > **Explanation:** Reneging describes customers who leave the queue due to prolonged wait times. ### True or False: Last-In, First-Out queue discipline serves the most recent customer first. - [x] True - [ ] False > **Explanation:** True, LIFO means that the most recent customer in the queue is served next. ### What is balking in queuing systems? - [ ] When a customer is served out of order - [x] When a customer decides not to join the queue due to its length - [ ] When a queue has multiple service points - [ ] When there's a random serving sequence > **Explanation:** Balking happens when prospective customers decide not to join the queue upon seeing its length. ### When was the first scientific queuing model developed? - [ ] 1950s during computing research - [x] 1909 by A.K. Erlang - [ ] 1940s during World War II - [ ] 1800s in railway management > **Explanation:** A.K. Erlang developed the first scientific model for queuing in 1909. ### In queuing theory, what does the service rate (\\(\mu\\)) refer to? - [x] Average number of customers served per unit time - [ ] Average number of customers arriving per unit time - [ ] Total wait time of all customers - [ ] Efficiency of queue management > **Explanation:** Service rate (\\(\mu\\)) refers to the average number of customers that can be served per unit time. ### Which queue discipline ensures that customers with higher priority are served first? - [ ] FCFS - [ ] LIFO - [x] Priority Queueing - [ ] Random Order > **Explanation:** Priority Queueing serves customers based on their assigned priority level. ### What is the primary objective of queuing theory? - [ ] To reduce the cost of services - [ ] To predict the exact wait times - [x] To make predictions about queue lengths, waiting times, and service efficiency - [ ] To design faster computational algorithms > **Explanation:** The primary objective of queuing theory is to make predictions about queue lengths, waiting times, and service efficiency. ### Which term describes a mathematical study of waiting lines? - [x] Queuing Theory - [ ] Traffic Management - [ ] Service Efficiency - [ ] Operations Research > **Explanation:** Queuing Theory is the mathematical study focused on analyzing waiting lines and their various attributes.