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Queuing Theory

Project 6 - Team 6

Joshua S

on 27 April 2014

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Transcript of Queuing Theory

Queuing Theory

- Queuing is the foundation that helps keep companies efficient and organized. At any time there may be more people that need assistance or help than an organization can handle. Queues assist employees to track, prioritize, and deliver services and transactions. Without queues organizations will not run smoothly or efficiently.

Provision for reservations
Making waiting a comfortable and less painful activity
Reducing perception of actual waiting and increasing expectation of waiting -- do not underestimate the likely period of wait rather overstate and make real wait to be less than expected so that a way of protective thinking is to be brought in the customer
Queuing Theory
Queuing theory deals with waiting times.

“Businesses often utilize queuing theory as a competitive advantage” and is described as “the mathematical study of waiting in lines” (Sherman, 2010).
Queuing Theory Advantages
Some possible ways of circumventing problems of waiting lines based on theory and psychology of waiting lines are:

The first to develop a viable queuing theory.
Created a distribution function to describe the probability of a prescribed outcome after repeated iterations of independent trials.
The distributions he used could be applied to any situation where excessive demands are made on a limited resource.

History of Queuing Theory
S.D. Poisson (1781 - 1840)

The impetus for the development of queuing theory was the burgeoning telephone industry in the early 1900’s.
The limitations of manual switching of telephone calls became obvious as the number of subscribers quickly outstripped the ability of operators to accurately place their calls every time.

Tore Olaus Engset and Agner Krarup Erlang are the first developers of queuing theory as applicable to the telephone industry.
Danish engineer who worked for the Copenhagen Telephone Exchange.
Published his first paper on queuing theory in 1909.

A.K. Erlan (1878 – 1929):
T.O. Engset (1865 – 1943):

Norwegian mathematician and engineer.
His formulations were not known until 1918.
His main work was not in queuing theory and traffic engineering and his contributions are not as well known.

Swedish electrical engineer.
Made several contributions to teletraffic engineering and queuing theory.
Published his first paper on queuing in 1936.
Was the first to introduce the concept of reneging (or queuing abandonment) in 1937.

Conrad “Conny” Palm (1907 - 1951):

Do not underestimate the likely period of wait -- overstate and make real wait to be less than expected so that a way of protective thinking is to be brought in the customer
If customers are walking away disgusted because of insufficient customer support personnel, the business could compare the cost of hiring more staff to the value of increased revenues and maintaining customer loyalty (Sherman, 2010).
The cost of waiting in line is at a maximum when the organization is at minimal service capacity.

The Cost of Waiting in Line
The problem in almost every queuing situation is a trade-off decision.
Abilla, P. (2011, August 13). Applying Little's Law to Business. Retrieved from Shmula.com: http://www.shmula.com/littles-law/8035/

Agner Krarup Erlang, Danish mathematician, c 1915. (n.d.). [Online image]. Retrieved April 20, 2014, from http://www.ssplprints.com/image/89051/unattributed-agner-krarup-erlang-danish-mathematician-c-1915

"A Queuing System." Introduction to Queuing Theory Part 1. N.p., n.d. Web. 23 Apr. 2014. <http://www.math.wm.edu/~rrkinc/queue_intro.ppt‎>.

CHYDZINSKI, A. (2010). Optimization problems in the theory of queues with dropping functions. University of Technology. Retrieved on April 18, 2014, from http://researchwebshelf.com/uploads/92_a_26.pdf
Dictionary.com. (n.d.) Queue. Retrieved on April 20, 2014, from http://dictionary.reference.com/browse/queue
Fundamentals of Queuing Theory. (1998). [Online image]. Retrieved April 20, 2014, from http://ebookee.org/Fundamentals-of-Queueing-Theory-Wiley-Series-in-Probability-and-Statistics-_2744.html

Hlynka, M. (2013). History of Queuing Theory. University of Winsdor. Retrieved April 20, 2014, from http://web2.uwindsor.ca/math/hlynka/qhist.html

Jfried09. (2012). History of the Queue. Queuing Theory. Retrieved April 20, 2014, from http://queuingtheory.wordpress.com/2012/04/26/iframe-widt/

Jfried09. (2012). Switchboard. [Online image]. Retrieved April 20, 2014, from http://queuingtheory.wordpress.com/2012/04/26/iframe-widt/

Manske, M. (2010). Conny Palm. [Online image]. Retrieved April 20, 2014, from http://commons.wikimedia.org/wiki/File:Conny_Palm_%286979247547%29.jpg

Pandey V., Tulsian P.C. (2006). Quantitative techniques: theory and problems. Pearson Education India. Retrieved on April 16, from, http://my.safaribooksonline.com/book/math-and-science/9789332512085/9dot-queuing-theory/ch9sec18_xhtml#X2ludGVybmFsX0h0bWxWaWV3P3htbGlkPTk3ODkzMzI1MTIwODUlMkZjb3B5cmlnaHRfeGh0bWwmcXVlcnk9
Queuing Systems. (n.d.). [Online image]. Retrieved April 20, 2014, from http://tomsosu.blogspot.com/2012/07/internet-history-plus-businessweek-on.html

"QUEUING THEORY DISCUSSION." Queuing Theory Discussion. N.p., n.d. Web. 21 Apr. 2014. http://home.snc.edu/eliotelfner/333/quethry.htm
Reid, R. Dan, and Nada R. Sanders. Operations management: an integrated approach. 4th ed. Hoboken, NJ: John Wiley, 2010. Print.

S. D. Poisson. (n.d.). [Online image]. Retrieved April 20, 2014, from http://xoomer.virgilio.it/vannigor/Poisson.htm

Sherman, P. (2010). Queuing theory and practice: a source of competitive advantage. iSixSigma. Retrieved on April 18, 2014, from http://www.isixsigma.com/industries/retail/queuing-theory-and-practice-source-competitive-advantage/
Sherman, P. (2010, July 25). Queuing Theory and Practice: A Source of Competitive Advantage. Retrieved April 21, 2014, from http://www.isixsigma.com/industries/retail/queuing-theory-and-practice-source-competitive-advantage/
Sinley, J. (n.d.). Queuing Theory. Reference for Business. Retrieved April 20, 2014, from http://www.referenceforbusiness.com/encyclopedia/Pro-Res/Queuing-Theory.html

Sridhar, M. S. (2001). Service Quality and Customer Satisfaction. Retrieved April 21, 2014, from http://www.researchgate.net/publication/Waiting_Lines_and_Customer_Satisfaction%2Ffile%2Fd912f50a3d915e080f.pdf
The Single Server Queue. (n.d.). [Online image]. Retrieved April 20, 2014, from http://www.amazon.com/Single-North-Holland-Applied-Mathematics-Mechanics/dp/0444894829/ref=la_B0034NI1HE_1_1/192-5978962-8197717?s=books&ie=UTF8&qid=1398268095&sr=1-1

Werenskiold, E. (2014). Portrait of Director Tore Olaus Engset. [Online image]. Retrieved April 20, 2014, from http://www.telenor.com/art-collection/theme-work.php?gid=7&id=461&aid=1689

"Why Is Queuing an Important Issue in a Company's Operations?." Small Business. N.p., n.d. Web. 21 Apr. 2014. <http://smallbusiness.chron.com/queuing-important-issue-companys-operations-18269.html>.
Woeppel, M. (2013). Little's Law - The one thing you can do to improve process performance. Retrieved from Pinnacle Strategies: http://pinnacle-strategies.com/littles-law-the-one-thing-you-can-do-to-improve-process-performance.html
References (Continued)
The cost of waiting in line is at a maximum when the organization is at minimal service capacity.
As service capacity increases, there is a decrease in the number of customers in the line and in their wait times, which reduce queuing cost.

Service Capacity
‘Customers’ do not always have to be humans, they can be anything that is waiting to receive service - a piece of data, a car waiting to be repaired, a train car waiting to be unloaded, etc.
Queues should be within the control of the system management and design
Managers must decide the best way of servicing these customers in a timely, cost-effective manner.
Managing Queuing

“Any time there is more customer demand for a service than can be provided, a waiting line occurs.”
Single Vs Multiple Lines
Regarded as equitable by the people in the line.
There is no way to be penalized for picking the wrong line
It eliminates jockeying (switching lines to improve service time)
It generally has better performance time than a multiple-line system.

Queuing Systems
Two common ways of servicing customers are the models of single line and multiple line.

Banks typically have single-line systems. Customers wait in a single line until they are served by an available server (a teller in the case of a bank).
Other industries that use a single-line system are airline or rental car counters, restaurants, amusement parks, and call centers.
Multiple-line systems are used by industries such as grocery stores. Customers enter individual lines for each server.

Advantageous when specialized servers are needed, or when the required space is too large for a single-line system.
This system also allows for service differentiation, such as an express lane in a supermarket or a high roller line in a casino.
Many small lines are more inviting for a customer than a single long line (reduces balking).

Single Lines:
Multiple Lines:
Queuing theory helps to determine the right amount of inventory that should be on hand or even the amount of employees that should be on duty at particular times to ultimately reduce wait time and increase profits. This can be true in many situations, such as the following:
Inventory levels
Improving customer satisfaction
Managing costs associated with lines
Assigning resources
Staffing tellers at a bank
Determining landing times for airplanes
Determining the number of hospital rooms that should be constructed
“In the classic single-server FIFO queue we cannot control the performance of the system. Given the input and service process parametrization, all we can is compute the queue size, the waiting time, their average values, distributions, etc. However, we cannot control these values at all” (Chydzinski, 2010).
Queuing Theory Disadvantages
"There is not a great deal one can do to account for stationary without complicating the mathematics enormously" (Pandey, 2006).
Population of customers served may be finite
Queue discipline may not be first come first serve
Jeffrey Tsang
Joshua Simon
Katrina Gadwood
Olesya Blanchard

Benjamin Knickelbine
Britnee Houtz
Damaris Martis
Eric Mendenhall

Inventory, also the total amount of work in a system
Que time or waiting time
Little's Law
Three characteristics that govern process behavior. A change in one affects the others.
Reduce inventory and you change queue times
Lower queue times and you change inventory
Do either and you change throughput
To improve process performance you just have to change any of the three factors:
Average Inventory = Throughput X Ave Queue Time
Little’s Law can be used to estimate wait times, plan inventory times, and reducing work-in-process.
Hospitals use the law to plan for staffing, budgeting, and wait time of patients.
Must be careful of work-in-progress explosion (WIP), if process utilization reaches 100% then WIP can explode and the queue time will reach infinity.

Uses of Little's Law
The manager must consider the added cost of providing more rapid service (i.e., more checkout counters, more production staff) against the inherent cost of waiting.
If employees are spending their time manually entering data, a business manager or process improvement expert could compare the cost of investing in bar-code scanners against the benefits of increased productivity.
Arranging some absorbing or interesting activity during waiting
Avoiding visibility of long lines
Some of the preliminaries of service delivery process be done during the waiting
Providing attention, concern and necessary information for reducing uncertainty and anxiety (Sridhar,2001).
- The analysis of queues (or waiting lines) where customers wait to receive a service.
Developed models that accounted for callers that dropped due to frustration from waiting for an operator and for those that were patient enough to wait for their call to be connected.
His models were first used by traffic engineers to develop better systems.
The optimal total cost is found at the connection between the service capacity and waiting line curves. (Sherman, 2010)
Waiting space may be limited.
Arrival rate is state dependent -- long lines scare customers away
Arrival process is not stationary
Peak periods and slack periods during which the arrival rate is higher and lower respectively than the overall average
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