Queuing and Waiting Theory Explained in Words and Pictures - Updated Post

“Waiting is frustrating, demoralizing, agonizing, aggravating, annoying, time consuming, and incredibly expensive” (Federal Express)

The Origins of Queuing Theory

The beginning of Queue Theory is often traced back to a study of telephone systems in 1909 by an engineer with Copenhagen Telephone Company. He asked the simple question: "How many trunk or main telephone lines are needed to  adequately service a town?" A nice explanation of this study is given in the YouTube video below by the 'Engineer Guy'. 

In the next video the problem you can see that the problem of passenger loading onto an airplane can also be solved mathematically, but that the psychological and social aspects of human behaviour need to be taken into account to appreciate a queuing problem.





Queuing and Waiting: Characteristics and Definitions

A queue is commonly understood to be a line of waiting customers that require service from one or more servers.

A queue can also consist of a bottleneck of things or information that is unable to be processed in a timely fashion, and is forced to wait idly.   For instance see pictures of queues on my Pinterest collection at Queue Obsession.

A queue forms whenever current demand exceeds the existing capacity to serve.

A queue is a major problem in service delivery because it signifies that waste is occurring - waste of time and  resources.

Of course, as can be seen from the pictures on Queue Obsession, it may also signify that supply cannot meet demand for any number of reasons including rationing (during the war - i.e.  lack of supply) and sometimes queues are deliberately encouraged (e.g. at Harry Potter and Ipad releases) to signify the desirability of a product or service.

Waiting, believe it or not, is a common news story. The frustrations of queuing are shared, and sometimes people can get so angry whilst queuing that violence breaks out.  I have storified some newspaper stories about queuing so you can see how common this phenomena is. You can see this story on storify  here.

Types of Queues Configurations

Below three major types of physical queue configurations are shown: multiple queue, single queue and take-a-number queue.  Queue configuration tells us what a queue looks like.

Some basic queue configurations

A single queue system is sometimes called a snake queue. You often see these at airports.

A multiple queue system is often used at supermarkets and retail outlets.The following 3 minute presentation describes these two common queue configurations:

This queue at the  rugby sevens is a multiple queue.

Rugby Sevens queue at Westpac stadium in Wellington New Zealand

A 'take-a-number' queue is often seen at restaurants/bars, fast food places like Fish and Chip shops, and sometimes also at banks. A take-a-number type queue operates at 'Just Cuts', a franchised hairdressing salon. No appointments are taken, but your name is put into a 'line' on their computer (using the FCFS First-Come-First-Served  rule - see below) and they tell you the approximate wait time so you can go off and do other things while you wait.

Often a combination of queuing configurations can be seen. The above queue at the Rugby Sevens, although a multiple queue, is also like a snake queue. 

Queue Discipline Techniques

Queue discipline techniques are the rules placed over the behaviour of a group that tells the queue components how to behave. These components can be people, attributes of people (e.g. how loyal they are; how sick they are), material things, or information. The figure below illustrates discipline techniques by dividing them into two types; static (FCFS) and dynamic. 

Queue Discipline techniques 

The above diagram shows several techniques used to manage the behaviour of queues. On the right we have a static rule FCFS. This is the 'First come, first served' rule. In this rule, which many service providers abide by, and can be seen in many other systems as well (like hiring and redundancy practices), the organisation simply serves whoever arrives first, and in order of arrival. This is a static queue because the organisation does not actively intercede in queue formation properties. 

Other queue discipline techniques are considered dynamic because organisations do actively intercede in the way that the queue is formed. So, two dynamic options are given for action in the above diagram: selection based on individual customer attributes; and selection based on the status of the queue.  In the 'Selection based on on individual customer attributes' we have three main queue discipline techniques; priority (highest priority served first - e.g. cutting in line, or VIP), preemptive (status is assigned based on how long a task takes and how long a component is queued), and  SPT (or standard processing time).

Organisations dealing with a variety of customer tasks can have long and frustrating queues - post offices are notorious for this - they have multiple customers with different tasks (e.g. registering a car; a complex banking transaction; buying some stamps etc..) that take different amounts of time. This makes managing queues more challenging. Many post offices use preemptive system - e.g. they may have a bank customer only queue, and often now a cashier will intercede in the line to help train customers in how to skip the queue by using self-help facilities (like express deposit boxes for simple transactions).

Source: Uploaded by user via Janet on Pinterest

These rules lend themselves to the use of  mathematical systems which have made computing modelling systems for queuing very popular. Managing queuing is also part of many games like Zoo Tycoon, Theme Hospital and so on (see Note 1 below). Service simulations are explained in another post (to be added to this blog shortly) and managing queues is an essential part of the game-play because it lends itself so well to computer simulation.

As inferred in the first YouTube video about the origins of queuing, queues are not only physical lines of waiting people, but can also be queues on the phone. The following report by The NZ Herald shows the  average response times from common NZ institutions (included times in automated response system).  Like physical queues, waiting on the phone angers and frustrates people. Actually, poor phone communication practices (like not being responsive to customer inquiries) can lead to more expressed anger and frustration because rich interactive communication is missing (you are far less likely to express anger at someone in person that you are on the phone). 

Phone call-time waits at common NZ enterprises  - from the NZ Herald

I have not provided an in-depth discussion of solving queue problems in this post. Wikibooks provides a good introductction to solving queuing problems and also some simple problems. You can find this resource here. Some simple problems are given, with their solutions.

Managing Waiting Lines

There are basically two general ways of dealing with queues: queue management techniques and influencing the experience of queuing.

1. Queue management techniques include such management interventions as:

• understanding how bottlenecks form and solving them as mathematical problems.
• adding servers
• altering queue discipline (the order in which customers are served)
• speeding up serving times 

2. The experience of queuing can also be influenced by intervening to make waits seem shorter and help people become less anxious.

In order to understand the experience of queuing we need to go deeper into the psychology of how and why people wait. The first thing to remember is that TIME IS ELASTIC.

In organisational systems time is almost always treated as uniformly standardised by production and timetables. However time is actually subjectively felt and experienced by living and feeling people.

Waiting is also an outcome of how power operates. Think for a moment about how you feel when you are waiting and you don’t think it is necessary. The distribution of waiting time in a system coincides with the distribution of power – this point is explained further on in this post.

Waiting times limit productive uses of time and in so doing generates distinct social and personal costs. Research shows unequivocally that:

1. Dissatisfaction increases with wait time
2. Perceived waiting time is greater than actual waiting time

But also that

1. There is Inevitable waiting in service/process systems: Waiting results from variations in arrival rates and service rates
2. Also there is an economics of waiting. With high utilization and low cost systems then the purchase includes the price of customer waiting. e.g. low cost airlines

So, as with PERCEIVED quality, we are managing PERCEIVED waiting time

Example of managing PERCEPTION of waiting times:

… a well known hotel group received complaints from guests about excessive waiting times for elevators. After an analysis of how the service might be improved, it was suggested mirrors be installed near where guests waited for elevators. The natural tendency for people to check their personal appearance substantially reduced complaints, although the actually time of waiting was unchanged.

Example of managing EXPECTATIONS:

… some restaurants follow the practice of promising guests a waiting time in excess of the “expected time”. If people are willing to agree to wait this length of time, they are quite pleased to be seated earlier, thus starting the meal with a more positive feeling.

Why does it help to over-estimate waiting time? Because it is very hard to repair initial dis-satisfaction. From a waiter’s perspective, “If they sit down in a good mood, it’s easy to keep them happy” but “If they sit down disgruntled, it’s almost impossible to turn them around. They’re looking to find fault, to criticize.”

A halo effect is created by early stages of encounter. So, if money, time and attention is to be spent, do it on the early stages.

There are several rules that apply when considering how to manipulate the experience of waiting. These are often quoted as below:

1. That Old Empty Feeling: Unoccupied time goes slowly
2. A Foot in the Door: Pre-service waits seem longer that in-service waits
3. The Light at the End of the Tunnel: Reduce anxiety with attention
4. Excuse Me, But I Was First: Social justice with FCFS queue discipline
5. They Also Serve, Who Sit and Wait: Avoids idle service capacity

Disneyland uses the following approaches to controlling customer waiting.

1. Animate: Disneyland distractions, elevator mirror, recorded music
2. Discriminate: Avis frequent renter treatment (out of sight)
3. Automate: Use computer scripts to address 75% of questions
4. Obfuscate: Disneyland staged waits (e.g. House of Horrors)

A further list of guidelines about managing waiting has been generated through Maister’s classic research on waiting and queuing - ‘Ten principles of

1. Unoccupied time feels longer than occupied time

“ Boredom results from being attentive to the passage of time itself”

Restaurant examples: giving out menus before being seated (added bonus of decreasing wait time); turn waiting area into a bar (adds revenue also); posters, reading material, toys, memorabilia.

Telephone examples: muzak (can have opposite effects as unrelated to service activity); menus and bars integrates service into waiting experience; example of sports team playing last week’s game!

Other devices? Windy lines; different queuing systems and movement; medical waiting rooms (take the persons mind off the service - dentist!).

2. Pre-process waits feel longer than in-process waits

A person’s anxiety level is higher waiting to be served, than while being served. Fear of being forgotten. Make first contact human.

Example - triage waiting system. Assessment by a nurse while waiting to see a doctor.

3. Anxiety makes the waits seem longer

People have a fear of being forgotten

The other line always moves faster or, worry that their won’t be enough room (say on a plane)

4. Uncertain waits are longer than known, finite waits

Example: if patient told doctor delayed 30 minutes, will wait happily, but once that time is met, becomes increasingly annoyed.

Important point to note: appointment defines an expectation that must be met.

5. Unexplained waits are longer than explained waits

Any explanation is better than none

eg. plane `technical difficulties’

eg. the sight of a serving person taking a break is a source of irritation

6. Unfair waits are longer than equitable waits

e.g. the situation where someone is felt to be `cutting in front’

FIFO rule - first in, first out - exceptions: emergency cases, table size (frequently resented), express checkout lanes (accepted).

Need to be aware of patrons sense of equity, feelings about status

7. The more valuable the service, the longer the customer will wait

The supermarket example moderated by this point (value of full cart higher than value of lower and so people will wait longer)

Waiting for something of little value is intolerable. Post-process waits the most intolerable (eg. willingness to queue before flight but impatience at baggage handling)

8. Solo waits feel longer than group waits

Promotion of group waiting experiences is beneficial - queuing for music tickets, camaraderie that develops on plane delay, getting to know someone in a queue at Disneyworld.

9. Uncomfortable waits feel longer than comfortable waits

Uncomfortable waits sensitise people to time and poor service

10. New or infrequent users feel they wait longer than frequent users

Know who they are and provide reassurance


Topics for Discussion

1. Suggest some strategies for controlling variability in service times.
2. Suggest diversions that could make waiting less painful.
3. Select a bad and good waiting experience, and contrast the situations with respect to the aesthetics of the surroundings, diversions, people waiting, and attitude of servers.
4. Suggest ways that management can influence the arrival times of customers.
5. What are the benefits of a fast-food employee taking your order while waiting in line?

Useful Tools to Resolve Bottleneck Problems and Innovate

Bottlenecks are places in a service delivery system where queues form. The term bottlenecks includes customers queuing but has a wider meaning incorporating process blockages back-stage as well. When solving bottleneck problems general rules are:

• ensure that only essential work passes through the bottleneck;

• be ruthless in taking away non-essential activates;

• ensure no sub-standard work passes through the bottleneck.

Once you have established where the bottleneck is, devote proportionally more management attention to it to ensure maximum throughput and therefore maximum effectiveness for the process.

A number of useful tools have been developed to help managers understand processes and where bottle-necks occur. Any wait point is a potential fail point in a process because customers can baulk and renege from queues if they don't want to wait. Within a system bottlenecks signal inefficiency and waste in a process.  One useful tool to resolve bottlenecks is the use of service blueprinting. There is an excellent article of service blueprinting by Mary Jo Bitner et al here, and this tool is also discussed in this blog here. Service blueprinting is now often promoted as the first point for service innovation, because it helps service managers visualise a process and then identify where service improvements can be made.

Simple Class Exercise on Queuing 

On Saturday night I went to see Oblivion at Event Cinema in Albany. The movie was scheduled to start at 6.25 pm. We arrived at a bottleneck on the entranceway to the theatres (up the escalators) at 6.20pm. There was already a large number of people milling about, standing, in the entrance area, a large floor area with no seats or signage.  

No-one seemed to know why there was a delay in the screening. One couple were quite anxious as their movie started at 6.15pm and they were already late. Another couple also asked us what was happening as they arrived and we could not tell them as we did not know. The area looked like the diagram below:

The reason given for the delay (I asked the one attendant) was that the previous screening had not yet finished and theaters were not yet ready for use. Identify some techniques Event Cinemas could use to manage managing the waiting experience in this bottleneck. 

Extension Reading - Queues as a Social and Cultural Phenomenon

In many cultures and languages, there is no phenomenon or word for 'queue', signalling immediately that queuing is a cultural and social phenomenon.

Within operations management a plethora of information exists on queuing: there is a science devoted specifically to the mathematics of waiting (for example, see Fitzsimmons and Fitzsimmons 2000; Hall 1991; Dshalalow1995). This literature takes as its unquestioned premise the assumption that efficient queuing is necessary for constructive service interaction between providers and consumers. There is also a literature on the psychology of waiting and how to manipulate the subjective experience of waiting so that time seems shorter than it actually is, or that the time is used by the organization more efficiently to communicate with the customer the organizational commodity (Maister 1985). But very little has been written about the embedded nature of queuing in organizational power relations with the notable exception of Schwartz (1985). He argues that when we wait we are being organized by the organization: the experience of waiting in a queue is the experience of being managed physically (sometimes even violently) and psychologically manipulated in a number of ways. 

A critical perspective emphasizes that queuing and waiting are organized and experienced in the contexts of power. Service experiences occur across a delineated space —there is a social boundary between production and consumption—although this boundary is sometimes blurred. Queuing occurs while one waits for the consumption experience to begin. Consequently while we wait we are in a dissonant condition: we are not doing anything productive, or consuming, and can be in a state of internal conflict. A subject is forced to be in this in-between state, even though it is desire that has led to this state of affairs, and the consumer agrees to it. Desire is at its height when one waits, and it is forced to be in abeyance. At the same time, the cultural heritage of queuing as it is experienced in the American (and other similar cultures) locale needs to be acknowledged as queuing and its antecedent, the organization of time, are experienced differently in different cultures. How queuing can be used to signal the heightened desire for a product or service can be seen below in a picture below showing queues outside a Chinese Apple store. This picture also demonstrates that the phenomenon of the queue is now fully translated into cultures that are not Western and is not solely relevant there.

Queuing is experienced more by those with less power in society: queuing and consumption more generally, like production, is a class issue (Bauman, 1998) as waiting is not a habit of all social classes in Western societies. The higher up the social ladder one climbs the more likely it is that the worker will wait on the consumer (picture the waiter in the high-class restaurant waiting near-by). Who makes who wait is a point where power in its operation in the everyday can be seen to operate. Making others wait is even an aggressive act: waiting can be used consciously to disempower others. The forcing of others to be immobile and passive is a powerful, manipulative act of a person, or regime, over another. To make someone come to you is also, in inter-personal social relations, an example of how ultimate power can be demonstrated. Refusing to serve someone or making them wait for service or communication is also a use of power. “To render oneself motionless for the sake of another has always been one of the most humiliating radical forms of subordination” (Schwartz: 171), and further “The underlying technique for the aggressive use of delay involves the withdrawal or withholding of one’s presence with the intention of forcing another into an interactionally precarious state wherein he might confront, recognize and flounder in his own vulnerability or unworthiness” (38). Deferential self-suspension, that is voluntary passivity, finds its ultimate expression in the apology, a ritual of deference to ameliorate unbalanced social relations.

This picture below is of food queues in Oslo during World War 2; the scarcity of commodities leads to queues, especially necessary commodities like food. Poor people have to queue longer than rich people.

Schwartz also ventures into the terrain of psychoanalysis to explain the ‘regressive possibilities’ of the client service waiting relationship: 

… a sense of inferiority may be amplified because it reanimates sentiments associated with subordinate positions the individual may have occupied in the past … infancy itself, for during this time a child is utterly dependent upon the disposition of a server (parent) for the satisfaction of many of his physical and social needs … his wailing demands for food — is perhaps paradigmatic (though by no means determinative) of the irritation and exasperation of the adult who must wait for the meeting of his needs. (173) 

Psychoanalysts also find anal parallels, as: 

… awareness of the flow of time, especially the ability to measure time, unconsciously is deeply rooted in how often defecation has to take place, at which intervals it has to be done, and how long the process itself should take, how long it may be successfully postponed, and so on. (Fenichel 1945 cited in Schwartz: 174) 

It may seem provocative to complete this brief introduction to the social relations of queuing by raising the issue of anal repression. However, queuing leads to a state of dissonance which places “an attendant strain and a consequent tendency to restructure cognition and activity in such a way as to gain relief from it” (ibid: 168). Theories of repression are often turned to in an attempt to explain how comedy works (for example, see Stewart (1976) about the comedy of Charlie Chaplin) and how people in societies alleviate the tensions inherent in social power structures (Bakhtin, cited in Morson and Emerson 1990). 

References

Bauman, Z. 1998. Work, consumerism and the new poor, Buckingham, Open University Press.

Dawes, J. & Rowley, J. 1996. The waiting experience: Towards service quality in the leisure industry. International Journal of Contemporary Hospitality Management, 8, 16—21.

Durrande-Moreau, A. 1999. Waiting for service: Ten years of empirical research. International Journal of Service Management, 10, 171—189.

Fitzsimmons, J. & Fitzsimmons, M. 2006. Service management: Operations, strategy, information technology, Sydney, McGraw-Hill/Irwin.

Gray, K. undated. The legal order of the queue (Draft). Available: http://www.lse.ac.uk/collections/law/projects/techniquesofownership/tech-gray.pdf [Accessed 4 June 2010].

Heung, V. C. S., Tsang, N. & Cheng, M. 2009. Queuing behavior in theme parks: A comparison between Chinese and Western tourists. Journal of China Tourism Research, 5, 41 —51.

Larson, R. C. 1987. Perspectives on queues: Social justice and the psychology of queuing Operations Research, 35, 895—905.

Leclerc, F., Schmitt, B. H. & Dubé, L. 1995. Waiting  time and decision making: Is time like money? The Journal of Consumer Research, 22, 110—119.

Maister, D. H. 1985. The psychology of waiting lines. In: CZEPIEL, J. A., SOLOMON, M. & SURPRENANT, C. (eds.) The service encounter: Managing employee/customer interaction in service businesses London: Lexington Books.

Mann, L. 1969. Queue culture: The waiting line as a social system. American Journal of Sociology, 75, 340—354.

Schwartz, B. 1975. Queuing and waiting: Studies in the social organization of access and delay, Chicago, University of Chicago Press.

Schweizer, H. 2008. On waiting, London, Routledge.

Weber, M. 1930/1950. The Protestant ethic and the spirit of capitalism London, George Allen and Unwin Ltd. .

Notes

Regarding computer simulations to help with learning about queuing. There are a number of clones and open-source variations of popular games on-line, or you can buy the originals. I have attempted to use these is class, but found students'  orientation to games of this type variable so I tend now to just encourage students to try them out in their own time, or use them for a special project. Other service simulations have been developed for educational use in advanced service management courses, and sometimes come with textbooks (e.g. Fitzsimmons & Fitzsimmons, 2008).