﻿ Queueing Theory: What is it, Elements, History, Examples

# Queueing Theory

## Queueing Theory

In today’s world, efficient resource management is a critical aspect of any successful strategy. Whether it’s waiting in line at a coffee shop or managing customer service enquiries, queues are a universal phenomenon that impact both individuals and businesses. This is where Queueing Theory comes into play. Originating from mathematical principles, Queueing Theory offers valuable insights and strategies for optimising the way resources are allocated to queues.

## What is Queueing Theory?

Queueing Theory is a mathematical discipline that analyses and models the behaviour of queues or waiting lines. It provides a structured framework for understanding how waiting lines form, how they behave, and how resources can be allocated to optimise efficiency. Whether it’s a supermarket checkout, a call centre, or a manufacturing assembly line, Queueing Theory offers valuable tools for streamlining processes and minimising wait times.

Queueing Theory emerges as a powerful tool to enhance efficiency and customer satisfaction. By applying mathematical principles to real-world scenarios, it enables businesses to make informed decisions regarding queue management, staffing, and overall process optimisation. As the global demand for streamlined services and effective resource allocation continues to rise, Queueing Theory remains a cornerstone in shaping strategies that ensure smoother operations and happier customers, bridging the gap between theory and practise.

## Understanding Queueing Theory

Queueing Theory is all about predicting and managing the flow of entities. It addresses these key points:

• Mathematics of waiting: Queueing Theory is a field of mathematics that focuses on the study of queues or waiting lines. It’s not just about standing in line, but it’s about predicting, modelling, and managing those lines efficiently.
• Optimising efficiency: Whether it’s at a grocery store checkout or an airport security line, understanding Queueing Theory helps businesses allocate resources in a way that minimises wait times and enhances overall efficiency.
• Factors in play: Queueing Theory considers various factors, such as how quickly customers arrive, how long it takes to serve them, the number of available servers, and the capacity of the queue itself.
• Strategic insights: By employing Queueing Theory, businesses gain insights into how to strategically manage queues. This includes determining the ideal number of cash registers to open during peak hours or scheduling appointments at a medical clinic.
• Predictive power: Queueing Theory employs mathematical models to predict queue behaviour under different circumstances. This helps organisations prepare for busy periods and allocate resources effectively.

## Elements of Queueing Theory

Queueing Theory comprises key elements that define the dynamics of queues:

• Arrival process: This refers to the pattern at which entities arrive at the queue. The arrival process, often unpredictable, varies between regular patterns and random occurrences. Analysing this element helps businesses anticipate demand and allocate resources effectively.
• Service process: This defines how quickly entities are served by the available servers. Like the arrival process, the service process can also follow different distributions.  The service process directly affects wait times and satisfaction levels.
• Queue discipline: It determines the order in which entities are served from the queue. Common disciplines include First-Come-First-Served, or FCFS, Priority, and Last-Come-First-Served, or LCFS. This universal element shapes the fairness and perceived fairness of waiting lines, impacting customer loyalty
• Queue capacity: This specifies the maximum number of entities that the queue can hold at any given time. Understanding the right queue capacity ensures smooth operations and optimal wait times.

## History of Queueing Theory

The history of Queueing Theory traces back to the early 20th century, marked by a convergence of mathematical innovation and practical challenges. Danish engineer Agner Krarup Erlang played a pivotal role in its inception, applying mathematical concepts to solve complex telephone network traffic problems. His groundbreaking work laid the foundation for understanding the dynamics of queues and resource allocation.

During World War II, Queueing Theory gained further traction as engineers utilised it to optimise military logistics, showcasing its potential to enhance efficiency in real-world scenarios. Post-war, the advent of computing technology facilitated more sophisticated analyses, allowing businesses to explore the impacts of different queue management strategies.

Over time, Queueing Theory’s applications expanded into various sectors, such as telecommunications, manufacturing, healthcare, and service industries. Its evolution has been spurred by advancements in mathematics, computing power, and the increasing need for efficient resource management. Today, Queueing Theory stands as an integral part of strategy development, offering valuable insights into improving processes, reducing wait times, and ultimately delivering enhanced customer experiences.

## Examples of Queueing Theory

Queueing Theory finds application across diverse sectors. Consider a theme park, for instance. Imagine the bustling gates of a theme park, where the convergence of eager visitors creates the potential for long queues and diminished experiences. By employing Queueing Theory, park managers meticulously analyse the influx of visitors per hour and the duration of time each ride takes to accommodate them. This data-driven insight empowers managers to strategically align staffing levels with peak demand, seamlessly kerbing waiting times and elevating the overall visitor encounter

In the healthcare sector, Queueing Theory continues to make a meaningful impact, notably within hospitals. With patient well-being at the forefront, hospitals use it to navigate the intricate web of patient flows, appointment scheduling, and resource allocation. Here, Queueing Theory operates as an indispensable tool, allowing healthcare facilities to streamline the patient journey. By forecasting patient arrivals, assessing the time required for various medical procedures, and gauging the availability of medical staff, hospitals can orchestrate a well-coordinated symphony of care. The result is a reduction in patient wait times, optimised medical resource allocation, and an improved healthcare experience for patients and medical professionals alike.

Queueing Theory is vital for making informed decisions about resource allocation, service levels, and customer satisfaction. It empowers businesses to optimise processes, enhance operational efficiency, and improve overall service quality.

Queueing Theory employs mathematical models to simulate and predict queue behaviour. By manipulating parameters like arrival rates, service rates, and the number of servers, analysts can determine key performance indicators such as average wait time and utilisation rates.

The factors include arrival rates, service rates, number of servers, queue capacity, and queue discipline. These elements interact to shape the behaviour of the queue and the overall system.

Queueing Theory can be broadly categorised into four groups based on characteristics like the arrival process and service process:

• Single-Channel, Single-Phase: One server, one queue.
• Multi-Channel, Single-Phase: Multiple servers, one queue.
• Single-Channel, Multi-Phase: One server, multiple queues.
• Multi-Channel, Multi-Phase: Multiple servers, multiple queues.

The Queueing Theory problem involves analysing and solving challenges related to queues and waiting lines. This includes optimising resource allocation, predicting wait times, and devising strategies to improve system efficiency.

## Category

### Read the Latest Market Journal

#### Navigating the Post-Inflation Landscape in 2024: Top 10 US Markets Key Events to Look out for

Published on Feb 23, 2024 51

#### From Boom to Bust: Lessons from the Barings Bank Collapse

Published on Feb 23, 2024 12

Barings Bank was one of the oldest merchant banks in England with a long history...

#### Decoding FX CFD 2.0

Published on Feb 20, 2024 61

#### Weekly Updates 19/2/24 – 23/2/24

Published on Feb 19, 2024 79

This weekly update is designed to help you stay informed and relate economic and company...

#### Unlock Prosperity with 5 Sure-Fire Financial Instruments!

Published on Feb 14, 2024 187

In Singapore, the concept of guaranteed returns may evoke the spirit of prosperity, reminiscent perhaps...

Published on Feb 13, 2024 69

This weekly update is designed to help you stay informed and relate economic and company...

#### Decoding FX CFD

Published on Feb 7, 2024 97

The foreign exchange market commonly known as the forex or FX market, is a cornerstone...

#### Chinese New Year: Three Cases For CFD Trading

Published on Feb 6, 2024 140

The Chinese New Year is a festive season may be celebrated by some parts of...

POEMS 3 App

• Call Back

• Chat with us

Need Assistance? Share your Details and we’ll get back to you

IMPORTANT INFORMATION

This material is provided by Phillip Capital Management (S) Ltd (“PCM”) for general information only and does not constitute a recommendation, an offer to sell, or a solicitation of any offer to invest in any of the exchange-traded fund (“ETF”) or the unit trust (“Products”) mentioned herein. It does not have any regard to your specific investment objectives, financial situation and any of your particular needs. You should read the Prospectus and the accompanying Product Highlights Sheet (“PHS”) for key features, key risks and other important information of the Products and obtain advice from a financial adviser (“FA“) pursuant to a separate engagement before making a commitment to invest in the Products. In the event that you choose not to obtain advice from a FA, you should assess whether the Products are suitable for you before proceeding to invest. A copy of the Prospectus and PHS are available from PCM, any of its Participating Dealers (“PDs“) for the ETF, or any of its authorised distributors for the unit trust managed by PCM.

An ETF is not like a typical unit trust as the units of the ETF (the “Units“) are to be listed and traded like any share on the Singapore Exchange Securities Trading Limited (“SGX-ST”). Listing on the SGX-ST does not guarantee a liquid market for the Units which may be traded at prices above or below its NAV or may be suspended or delisted. Investors may buy or sell the Units on SGX-ST when it is listed. Investors cannot create or redeem Units directly with PCM and have no rights to request PCM to redeem or purchase their Units. Creation and redemption of Units are through PDs if investors are clients of the PDs, who have no obligation to agree to create or redeem Units on behalf of any investor and may impose terms and conditions in connection with such creation or redemption orders. Please refer to the Prospectus of the ETF for more details.

Investments are subject to investment risks including the possible loss of the principal amount invested. The purchase of a unit in a fund is not the same as placing your money on deposit with a bank or deposit-taking company. There is no guarantee as to the amount of capital invested or return received. The value of the units and the income accruing to the units may fall or rise. Past performance is not necessarily indicative of the future or likely performance of the Products. There can be no assurance that investment objectives will be achieved.

Where applicable, fund(s) may invest in financial derivatives and/or participate in securities lending and repurchase transactions for the purpose of hedging and/or efficient portfolio management, subject to the relevant regulatory requirements. PCM reserves the discretion to determine if currency exposure should be hedged actively, passively or not at all, in the best interest of the Products.

The regular dividend distributions, out of either income and/or capital, are not guaranteed and subject to PCM’s discretion. Past payout yields and payments do not represent future payout yields and payments. Such dividend distributions will reduce the available capital for reinvestment and may result in an immediate decrease in the net asset value (“NAV”) of the Products. Please refer to <www.phillipfunds.com> for more information in relation to the dividend distributions.

The information provided herein may be obtained or compiled from public and/or third party sources that PCM has no reason to believe are unreliable. Any opinion or view herein is an expression of belief of the individual author or the indicated source (as applicable) only. PCM makes no representation or warranty that such information is accurate, complete, verified or should be relied upon as such. The information does not constitute, and should not be used as a substitute for tax, legal or investment advice.

The information herein are not for any person in any jurisdiction or country where such distribution or availability for use would contravene any applicable law or regulation or would subject PCM to any registration or licensing requirement in such jurisdiction or country. The Products is not offered to U.S. Persons. PhillipCapital Group of Companies, including PCM, their affiliates and/or their officers, directors and/or employees may own or have positions in the Products. Any member of the PhillipCapital Group of Companies may have acted upon or used the information, analyses and opinions herein before they have been published.

This advertisement has not been reviewed by the Monetary Authority of Singapore.

Phillip Capital Management (S) Ltd (Co. Reg. No. 199905233W)
250 North Bridge Road #06-00, Raffles City Tower ,Singapore 179101
Tel: (65) 6230 8133 Fax: (65) 65383066 www.phillipfunds.com