tag:theconversation.com,2011:/us/topics/queues-38460/articlesQueues – The Conversation2023-02-20T16:32:43Ztag:theconversation.com,2011:article/1992312023-02-20T16:32:43Z2023-02-20T16:32:43ZHow queuing leads to city centre violence and what our research says about preventing night-time brawls<p>People go out at night because they want to socialise, drink and be entertained. Unfortunately, all too often that leads to violent behaviour in our towns and city centres. But the events that lead to such violence are poorly understood. </p>
<p>We set out to explore some of the possible explanations of night-time violence using data on Cardiff city centre footfall (the number of people in the city centre) and assault-related attendances at the nearby University Hospital of Wales. <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9779416/">We found</a> that a break down in the unwritten etiquette of queuing may be one of the reasons behind increases in violence at night.</p>
<p>When revellers gather to enjoy themselves at night, they often drink alcohol and possibly take drugs. This typically sets the activity apart from other places where people gather, such as transport centres or places for other commercial activity such as shopping. </p>
<p>People are attracted to night-time environments based on the <a href="https://journals.sagepub.com/doi/abs/10.1177/004728759303200204">total number of social opportunities they provide</a>, whether it’s going clubbing or visiting pubs. So, while entertainment venues compete against one another for trade, they also collectively market to attract patrons from near and far.</p>
<p><strong>The relationship between footfall and assault related injuries</strong></p>
<figure class="align-center ">
<img alt="A graph showing days of the week on the horizontal axis and numbers on both vertical axes. A line loops up and down." src="https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/508108/original/file-20230203-2880-nenoi7.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=424&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">A graph showing the relationship between footfall and assault related injuries.</span>
<span class="attribution"><span class="source">author provided</span></span>
</figcaption>
</figure>
<p>There has been plenty of research into what reduces or promotes night-time violence in city centres. One of the clear signals of danger is that the larger the footfall in the area, <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9779416/">the larger the chance for assaults to occur</a>. </p>
<p><a href="https://www.sciencedirect.com/science/article/pii/S1359178908000451?via%3Dihub">Crowding</a> and <a href="https://link.springer.com/article/10.1057/cpcs.2012.12">noise</a> are associated with increases in violence in city centres at night. And, in Australia, it has been shown that when <a href="https://www.tandfonline.com/doi/full/10.1080/10826084.2021.2019772">trading hours are restricted</a> there is a <a href="https://onlinelibrary.wiley.com/doi/10.1111/dar.12123">decrease in violence</a>.</p>
<p>But our research shows the correlation between footfall and assault is not linear. In other words, if we double the footfall, we do not simply double the number of assaults. The relationship between these two factors is more complicated, so we decided to investigate what could account for that.</p>
<h2>Queue etiquette</h2>
<p>One particular aspect we considered was the role drunkenness has to play because it <a href="https://royalsocietypublishing.org/doi/full/10.1098/rstb.2008.0028?casa_token=m93tA6ou_hwAAAAA:BprjJMUf5LNgIp6ftJlEBAnpBA-rAIQMvv6gvvCh4-wtDDkZFtYAN8LRNdVRDs2CCS7U8EkiV4PzGQ">affects how people cooperate</a>, for example when queuing. Queues are a social response to resource competition, whether that resource is nightclub entry, a pint of beer or a taxi. </p>
<p>However, since queuing is a social phenomenon, the people waiting in line have <a href="https://pubsonline.informs.org/doi/abs/10.1287/opre.35.6.895">expectations about how others should behave</a>, such as not skipping to the front. </p>
<p>When a violation of those unwritten rules occurs, people queuing in an orderly fashion will seek to defend the queue’s order, with the most vocal complaints stemming from those who are <a href="https://psycnet.apa.org/buy/1987-04011-001">closest to where the person jumps into the line</a>. Although even those ahead of the intrusion <a href="https://onlinelibrary.wiley.com/doi/full/10.1111/j.1559-1816.2008.00396.x?casa_token=xrR27tjG5jcAAAAA%3A-ub-j1Onmr9Senw4N2aGVljAgfifCQvqv_qWTGqPbTm437LilyojU30Mq1vyB2X_lOv3A_KMxLiSPo8">may also react to the injustice</a>. </p>
<p>However, whether there’s a queue violation or not, waiting in line makes people stressed. This increases <a href="https://link.springer.com/article/10.1177/0092070396244005">the longer they believe they have been waiting</a>. In turn, such stress can lead to aggression.</p>
<p>To understand the role queues play in the relationship between footfall and assault, we used a mathematical model to help predict what would happen in a variety of night-time scenarios. </p>
<p>We assumed the average arrival time of people into a queue is constant. We also assumed the rate at which they are served and leave the queue is constant, but also rises and falls in line with the number of servers, such as bar staff, taxi drivers or similar. </p>
<p>We also adjusted the models to take account of various other factors, such as weather, bank holidays and whether there were Six Nations or other international rugby matches being played at Cardiff’s Principality Stadium.</p>
<p>We found there was a significant relationship between the number of people in the city centre and the number of assaults recorded in the hospital’s accident and emergency department. The relationship relating footfall with assaults we saw from our queuing models performed better than the simple linear relationship. This is why doubling footfall does not double assaults.</p>
<p>Our study also found events such as bank holidays and rugby matches led to an increase in violence, beyond what might be expected from the impact of footfall alone. Additionally, warmer weather also increased the likelihood of assaults but more rain did not have a significant effect.</p>
<h2>Cutting city centre violence</h2>
<p>Our mathematical models show that by reducing queuing time, stress and related violence drops too. The average waiting time drops dramatically as the number of servers increases. So when pubs, taxi services or similar are understaffed, that increases the competition between people queuing.</p>
<p>The <a href="https://www.legislation.gov.uk/ukpga/2003/17/contents">UK Licensing Act 2003</a> places a duty on licensed premises to prevent crime and disorder and to maintain public safety. But there are no provisions on how licensed activity should increase as the number of patrons increases. </p>
<p>If further research confirms our observations, then there is a need to address the design and operation of night-time services, not only of bars, but of other areas where queues of revellers might form, such as taxi ranks and fast food outlets.</p><img src="https://counter.theconversation.com/content/199231/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>James White receives funding from the NIHR, MRC, Health and Care Research Wales, Scottish Chief Scientist Office, and Department for Education. </span></em></p><p class="fine-print"><em><span>Simon C Moore receives funding from NIHR, Youth Endowment Fund, ESRC, MRC. </span></em></p><p class="fine-print"><em><span>Thomas Woolley does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Recent research shows how the relationship between alcohol consumption, queuing and crowds can lead to violent behaviour in city centres at night.Thomas Woolley, Senior Lecturer in Applied Mathematics, Cardiff UniversityJames White, Chair professor, Cardiff UniversitySimon C Moore, Professor of Public Health Research, Co-Director of Crime and Security Research Institute and Director of the Violence Research Group, Cardiff UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1910592022-09-21T02:18:43Z2022-09-21T02:18:43Z‘An obsession with order, hierarchy, and one’s place within it’: what The Queue says about Englishness<p>As we have seen from coverage of “The Queue” – capitalised and thus now, apparently, a proper noun – the English are proud of their queuing prowess.</p>
<p>The Queue for the queen lying in state is <a href="https://www.washingtonpost.com/world/2022/09/15/queen-queue-coffin-westminster/">portrayed</a> as testament to the English ideals of civility, duty and sacrifice. </p>
<p>David Beckham’s 13-hour wait in the crowd was widely praised, while TV hosts Holly Willoughby and Phillip Schofield’s <a href="https://www.news.com.au/entertainment/celebrity-life/royals/british-tv-hosts-holly-willoughby-and-phillip-schofield-address-claims-they-skipped-queue-to-see-queen-lying-in-state/news-story/b90ebcf98b827c8a5b9f694d3ec127da">alleged (although denied)</a> “push-in” has been admonished.</p>
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<p>But The Queue is part of a bigger picture. Like class, the English propensity to celebrate queuing illuminates a peculiar national obsession with order, hierarchy, and one’s place within it.</p>
<h2>Queueing as a form of ceremony</h2>
<p>Let’s address something important: are we talking here about Britishness or Englishness? What is seen to define an English person, British person or person
of the United Kingdom is a matter of considerable debate. Our choice of the word “English” over “British” in this article reflects the fundamental Englishness of the British national project, to which the monarchy is central.</p>
<p>The English proclivity for queuing has been the subject of cultural commentary for decades. </p>
<p>In 1946 Hungarian humourist George Mikes reportedly <a href="https://www.psychologytoday.com/au/blog/slightly-blighty/202209/the-psychology-queuing-pay-respects-the-queen">noted</a>:</p>
<blockquote>
<p>An Englishman, even if he is alone, forms an orderly queue of one […] [queueing is] the national passion of an otherwise dispassionate race. </p>
</blockquote>
<p>British anthropologist Kate Fox, author of <a href="https://www.bookdepository.com/Watching-the-English-The-International-Bestseller-Revised-and-Updated-Kate-Fox/9781444785203?redirected=true&selectCurrency=SEK&w=AF7YAU9611TN4FA8VT6K&gclid=EAIaIQobChMI8Nisqb6i-gIVEZpmAh3FuAt1EAAYAiAAEgIEJfD_BwE">Watching the English</a>, wrote that in the 2011 London riots:</p>
<blockquote>
<p>I witnessed looters forming an orderly queue to squeeze, one at a time, through the smashed window of a shop they were looting.</p>
</blockquote>
<p>Queueing as a form of ceremony, such as seen in London this week, is perhaps a particular type of queue.</p>
<p>In defiance of the typical English reservedness, The Queue has been credited with fostering cameraderie and even <a href="https://www.independent.co.uk/life-style/love-sex/queen-elizabeth-ii-queue-romance-b2169693.html">chance meetings</a>.</p>
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Read more:
<a href="https://theconversation.com/queen-elizabeth-ii-capturing-the-worlds-most-photographed-woman-in-life-and-death-190490">Queen Elizabeth II: capturing the world's most photographed woman in life and death</a>
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<h2>Queuing in England and around the world</h2>
<p>Of course, it’s not only the English who queue. Regulating the flow and order of people is a universal human need. </p>
<p>Saving space in densely populated urban milieu, Japanese people form tight zig-zags. </p>
<p>In Spain, the penultimate person to arrive for a bus merely nods to the last person to let them know whom to follow. </p>
<p>In both cases, what appears to be anarchy is, in fact, tightly regulated.</p>
<p>However, there is something culturally distinctive about the English queue. The English seem to have a fondness for publicising their queuing ability.</p>
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<h2>Queuing and deficiency</h2>
<p>While much of the recent coverage has emphasised the egalitarianism of The Queue, researchers such as <a href="https://academic.oup.com/tcbh/article-abstract/16/3/283/1698382?redirectedFrom=fulltext">Joe Moran</a> have noted queuing has endured a chequered past.</p>
<p>In economically impoverished postwar Britain, food queues became a source of national resentment.</p>
<p>Many felt the queue was an unfair method of distribution – especially for older people, mothers with young children or working women, who faced more difficulty to wait in line for essential items.</p>
<p>In the late 1940s and early 1950s Winston Churchill seized on the unpopularity of queues to <a href="https://www.academia.edu/20514598/The_Oratory_of_Winston_Churchill">argue</a>:</p>
<blockquote>
<p>We [The Conservatives] are for the ladder. Let all try their best to climb. They [Labour] are for the queue. Let each wait in his place till his turn comes.</p>
</blockquote>
<p>Queues, he <a href="https://academic.oup.com/tcbh/article-abstract/16/3/283/1698382?redirectedFrom=PDF">argued</a>, were socialist, and that, should a Labour government have its way, the country could become “Queuetopia”. </p>
<p>In the 1960s and ‘70s the English faced recurrent queues at banks and post offices. The queue was widely depicted as a symptom of inefficiency of the national economy, something one might expect on the other side of the Iron Curtain, but not appropriate for Britain.</p>
<p>Throughout the late 1970s and the 1980s, associating queues with incompetence and disorganisation was a constant theme in politics. </p>
<p>Advertising firm Saatchi and Saatchi <a href="https://www.open.edu/openlearn/people-politics-law/howe-labour-isnt-working-did-the-job-the-conservatives">produced</a> a 1978 election poster for the Conservatives depicting a queue outside the unemployment office and the slogan: “Labour isn’t working”.</p>
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<h2>Queues and queue-jumping</h2>
<p>More recently, as <a href="https://disaster-sts-network.org/system/files/artifacts/media/pdf/strangers_in_their_own_land_anger_and_mourning_on_the_american_right_by_arlie_russell_hochschild_z-lib.org_.pdf">observed</a> by sociologist Arlie Russell Hochschild, the queue and queue-jumping have been weaponised in political discourse regarding minorities. </p>
<p>As one of us (<a href="http://notebooks.drustvo-antropologov.si/Notebooks/article/view/55/40">Andrew Dawson</a>) has noted, many of Britain’s white working class perceive the British policy of multiculturalism as a relegation of their status. </p>
<p>The benefits that flow to immigrant ethnic minorities are often presented as an unfair “push-in” for the social mobility ladder, allowing them to effectively “jump” Britain’s class queue. </p>
<p>That queuing for social occasions such as the queen’s death has been reimagined in recent years as a positive phenomenon is curious.</p>
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<p>Whether in a queue or a ladder, however, such appeals to social organisation are about knowing one’s place – a particularly English preoccupation.</p>
<p>Ask any Englishperson about their position in society. Depending upon their class, they may be embarrassed or affronted by the question, but they will have an answer, whether they share it with you or not (determined, again, by their class).</p>
<p>To this end, the reaction to Willoughby and Schofield’s alleged transgression speaks to the ability of this class system to reassert itself in the face of celebrity and fame. </p>
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<a href="https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="People queue to see the queen lying in state." src="https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=353&fit=crop&dpr=1 600w, https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=353&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=353&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=443&fit=crop&dpr=1 754w, https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=443&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/485758/original/file-20220921-22-2g7jll.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=443&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">People queued for hours to see the queen lying in state.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
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<p>Perhaps The Queue helps to explain why Meghan Markle, Duchess of Sussex, has experienced such hostility upon entering British society. Not just because of discriminatory and racist attitudes based on her biracial, divorcee, actress status, but also because she is American.</p>
<p>Queuing is seen by some as <a href="https://www.washingtonpost.com/business/is-there-anything-more-british-than-the-queue/2022/09/16/3da02baa-357d-11ed-a0d6-415299bfebd5_story.html">antithetical</a> to America’s rampant individualism – where your place is often imagined as malleable rather than rigid, dependent on achievements, popularity and wealth. </p>
<p>Australians also may recoil at suggestions of one’s place in society, with some insisting that in contrast to the stuffy British “motherland”, we are a classless society.</p>
<p>While “The C-word”, as the Australian author <a href="https://www.themonthly.com.au/issue/2013/december/1385816400/tim-winton/c-word#mtr">Tim Winton called class</a>, of course very much exists in Australia, we have far less of a vocabulary or understanding of class than the English.</p>
<p>While it may be less obvious in Australia, or railed against in America, many English people continue to embrace these systems even as the wider world moves on in seemingly disordered ways.</p>
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Read more:
<a href="https://theconversation.com/how-does-class-impact-on-australians-love-lives-new-research-brings-a-complex-issue-into-the-open-163893">How does class impact on Australians' love lives? New research brings a complex issue into the open</a>
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<img src="https://counter.theconversation.com/content/191059/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Cynthia Sear receives funding from the Australian Government Research Training Program (RTP) Scholarship Grant. </span></em></p><p class="fine-print"><em><span>Andrew Dawson does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Appeals to social organisation are about knowing one’s place, a particularly English preoccupation.Cynthia Sear, PhD Candidate, The University of MelbourneAndrew Dawson, Professor and Chair of Anthropology, The University of MelbourneLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1552772021-03-11T13:28:50Z2021-03-11T13:28:50ZSkipping the vaccine line is not only unethical – it may undermine trust in the rollout<figure><img src="https://images.theconversation.com/files/388850/original/file-20210310-24-1hes64d.jpg?ixlib=rb-1.1.0&rect=8%2C8%2C5455%2C3628&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Waiting in line for a vaccine at the Balboa Sports Complex in Encino, California.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/thomas-zisfain-of-woodland-hills-2nd-from-left-covers-up-to-news-photo/1230839506?adppopup=true">Mel Melcon/Los Angeles Times via Getty Images</a></span></figcaption></figure><p>The rollout of the COVID-19 vaccine has been <a href="https://mynbc15.com/news/spotlight-on-america/vaccine-cheats-at-risk-americans-wait-as-rich-and-connected-skip-ahead-for-covid-19-shots">accompanied by reports of line-jumping</a> as people farther down the list attempt to get ahead of those deemed higher priority.</p>
<p>In late February, for example, one health provider, <a href="https://www.npr.org/2021/02/24/970176532/high-end-medical-provider-let-ineligible-people-skip-covid-19-vaccine-line">One Medical</a>, was <a href="https://www.cbs8.com/article/news/health/coronavirus/one-medical-investigated-after-reportedly-vaccinating-ineligible-people/509-6d1edb1f-44dd-4d6e-824e-283eef01e24e">stripped of its vaccine allocation</a> after allegedly allowing people connected to the company and those paying for its “concierge medical service” to have the shots – despite not being eligible. Likewise in January, hospitals in <a href="https://www.forbes.com/sites/tommybeer/2021/01/27/seattle-hospital-offered-major-donors-invite-only-covid-19-vaccine-appointments/?sh=47cd37ef641a">Washington state</a> and <a href="https://www.miamiherald.com/news/coronavirus/article248323565.html">South Florida</a> faced criticism for offering invitation-only vaccine slots to private donors. More recently, <a href="https://www.texastribune.org/2021/03/09/texas-coronavirus-vaccine/">Texas has come under scrutiny</a> for allowing people to be vaccinated without proving eligibility.</p>
<p>The resulting unfairness of practices such as these has compounded other <a href="https://www.cdc.gov/coronavirus/2019-ncov/community/health-equity/race-ethnicity.html">inequalities highlighted by the pandemic</a>. As a law scholar who has <a href="https://blog.harvardlawreview.org/examining-the-interface-between-rights-and-queues/">studied queuing</a>, I consider building trust in the fairness of the line, alongside trust in the vaccine itself, to be important for the success of the immunization program. Those who skip the line not only displace those waiting behind them, they flout the informal rules of fair play that, with appropriate priority rules, make the rollout fairer than any market or lottery-based alternatives. </p>
<h2>First come, first served</h2>
<p>Historically, first come, first served has often been the default when it comes to queuing. The “<a href="https://core.ac.uk/download/pdf/188095001.pdf">first-in-time, first-in-right</a>” principle goes at least as far back as the 17th century, when it served to settle property disputes in <a href="https://doi.org/10.1016/S1574-0730(07)01003-1">English common law</a>. In wartime Europe, first come, first served was used to allocate rationed goods. And the <a href="https://www.qminder.com/queues-in-ussr/">bread lines in communist Eastern Europe</a> became a symbol of the erosion of trust when systems fail to match supply and demand.</p>
<figure class="align-center ">
<img alt="Dozens of people in Moscow stand in a food line on an icy street waiting to buy bread" src="https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=398&fit=crop&dpr=1 600w, https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=398&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=398&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=501&fit=crop&dpr=1 754w, https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=501&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/388870/original/file-20210310-18-87pahn.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=501&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Bread lines became a metaphor for the decline of Communism.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/dozens-of-people-in-moscow-stand-in-a-food-line-on-an-icy-news-photo/612577394?adppopup=true">Shepard Sherbell/Corbis via Getty Images</a></span>
</figcaption>
</figure>
<p>Nowadays, first come, first served is often replaced by scheduling algorithms that can triage priority. And waiting lists differ in other respects. Sometimes the lines are winner-take-all, in which one’s position can determine whether or not one gets the goods or services. Other times, placement determines only your wait time.</p>
<p>The COVID-19 vaccine phased allocation falls somewhere in between the two – not quite winner-take-all, but a little more than affecting
just wait time, given the stakes of COVID-19 infection. </p>
<p>Because demand for COVID-19 vaccines has outstripped supply, there has had to be a rationing of supplies. In determining who is eligible for a vaccine and when, a series of <a href="https://www.cdc.gov/mmwr/volumes/69/wr/mm695152e2.htm">ethical principles</a> have been drawn up to help determine priority, alongside considerations of epidemiology and ease of implementation.</p>
<p>These ethical goals include reducing deaths and hospitalizations among high-risk groups, as well as promoting solidarity and <a href="https://www.atsdr.cdc.gov/placeandhealth/svi/index.html">protecting against systemic unfairness</a> disadvantaging vulnerable populations.</p>
<p>As the COVID-19 vaccine has rolled out across America, each state has established its own priority lists and timelines. As a general rule of priority – <a href="https://www.cdc.gov/coronavirus/2019-ncov/vaccines/recommendations.html">endorsed by the Centers for Disease Control and Prevention</a> – health care workers and long-term care residents have been given the highest priority, followed by those age 75 and over and front-line essential workers, with people at high risk of serious COVID-19 illness next in line.</p>
<p>Many states have added groups or tweaked the list. <a href="https://www.kff.org/coronavirus-covid-19/press-release/states-set-different-covid-19-vaccination-priorities-for-people-with-high-risk-conditions/">Sixteen states now give priority to smokers</a>, for example, and <a href="https://www.edweek.org/policy-politics/where-teachers-are-eligible-for-the-covid-19-vaccine/2021/01">44 have moved to provide teachers</a> with early eligibility. With so much variety and changeability in vaccine priority, and the different speed of each state’s rollout, some people might question whether the line deserves adherence. </p>
<h2>Skipping the line</h2>
<p>Each state has also made various official exceptions that allow people to jump the queue. Permission to skip the line has been given in cases of expiring doses, where vaccines would have to be disposed of if not injected into people’s arms. </p>
<p>In Los Angeles, expiring doses have been opened up to so-called “<a href="https://www.reuters.com/article/us-health-coronavirus-vaccine-chasers/covid-19-vaccine-chasers-hunt-wait-and-hope-in-los-angeles-idUSKBN2A91BY">vaccine chasers</a>,” who wait at clinics or vaccination sites and receive end-of-day shots. Meanwhile in Massachusetts, doses have been reserved for “<a href="https://www.mass.gov/doc/massachusetts-75-caregiver-covid-19-vaccine-eligibility/download">companions</a>” who accompany persons age 75 and over to a mass vaccination site. </p>
<p>But there have also been, as the One Medical case has shown, scandals involving line-cutting by the wealthy or politically connected. This is not restricted to the U.S. Several politicians in Peru, Argentina and Ecuador have been <a href="https://www.nytimes.com/2021/02/25/world/public-dismay-turns-to-anger-as-south-american-officials-jump-the-line-for-vaccines.html">forced to resign</a> after getting vaccines for friends and family, and scandals involving both the wealthy and the politically connected have been reported in <a href="https://www.wsj.com/articles/in-brazil-people-illicitly-snag-vaccines-and-brag-about-it-11613563201">Brazil</a>, <a href="https://abcnews.go.com/International/wireStory/canadian-couple-condemned-allegedly-jumping-vaccine-line-75518010">Canada</a> and the <a href="https://www.bbc.com/news/uk-wales-55803134">U.K.</a> This compounds the inequality of vaccine access between, as well as within, countries.</p>
<p>Cases of people jumping the line are entirely predictable; the special treatment of the rich and powerful has a long history when it comes to queuing. And line-jumping may be <a href="https://doi.org/10.1093/acprof:oso/9780195391572.003.007">more frequent in already unequal societies</a>, scholars have suggested.</p>
<h2>Concierge services</h2>
<p>This imbalance affects both the number of lines people have to join and the length of time they wait.</p>
<p>America’s poor often encounter more <a href="https://blog.harvardlawreview.org/examining-the-interface-between-rights-and-queues/">unavoidable lines</a> for basic services, and can spend days, weeks, months or even years waiting for housing, schools, health care or immigration services.</p>
<figure class="align-center ">
<img alt="A long line of people waiting for polio vaccines in Illinois in 1959" src="https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=348&fit=crop&dpr=1 600w, https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=348&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=348&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=437&fit=crop&dpr=1 754w, https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=437&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/388868/original/file-20210310-13-u5u8oj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=437&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Lines for vaccines aren’t new. This one is for a 1959 polio shot.</span>
<span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/PolioVaccine1959/b2247f40913d4aa1850f1699821ea728/photo?Query=lines%20AND%20vaccine&mediaType=photo&sortBy=arrivaldatetime:asc&dateRange=Anytime&totalCount=34&currentItemNo=0">AP Photo</a></span>
</figcaption>
</figure>
<p>Lines are prolific for specific vulnerable populations, such as those within the U.S.’s extensive prison system, welfare recipients or people caught up in an extreme weather disasters. This results in a cost to those affected in their time, but also in other ways. Studies have shown that an uncertain delay – one in which you are not sure how long you will be waiting for a service – can <a href="https://ssrn.com/abstract=3428718">reinforce subordination and political resignation</a> on the part of those already vulnerable. </p>
<p>Wealthier Americans do not have to encounter many of these lines. And in the ones they do join, they are more likely to be able to skip to the front. Common examples can be seen in air travel, where VIP lanes are opened for those who can afford them, or <a href="https://doi.org/10.1111/lsi.12256">recreational goods</a> – such as for sports games or theme parks, where you can pay more to bypass those lining up.</p>
<p>But the ability to pay to line-jump also extends to more basic goods, including health care. </p>
<p>Concierge medicine services – such as the ones that have allowed some people to get illegitimate early access to vaccines – allow paying patients the <a href="https://heinonline.org/HOL/Page?handle=hein.journals/stanlp17&div=12&g_sent=1&casa_token=u0vKjxMDO3cAAAAA:awze_K_yc1T9pMHMqaXUKHIH4dZ0RJEfp_df3bIrNQkZ3ugL5mUGAoReYs6vwFjFYtgcfA&collection=journals">first access</a> to a suite of time-sensitive resources, ranging from priority scheduling to eliminating waiting rooms. </p>
<p>They have been increasingly <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1625036">prevalent</a> in the U.S. and are <a href="https://doi.org/10.1016/j.amjmed.2017.03.031">presented</a> both as a workaround for wealthy patients and a way for doctors experiencing burnout to practice outside an overburdened primary care system. </p>
<p>Such practices have been justified by their supporters as a way to cut wait times. In reality, such VIP lines in health care can make health care more <a href="http://doi.org/10.1001/virtualmentor.2013.15.7.ecas3-1307">inaccessible</a>. Given the overall scarcity of primary doctors, and the premiums demanded for such services, such systems can <a href="https://doi.org/10.7326/M15-0366">displace</a> lower-income, minority and Medicaid patients.</p>
<p>They also <a href="https://www.theatlantic.com/magazine/archive/2012/04/what-isnt-for-sale/308902/">inject market forces</a> into a sphere generally governed by other ethical principles, such as the rights of all patients to health care. Skipping the line undermines this commitment. It also exposes line-jumping to be both a symptom and a cause of inequality.</p>
<p>This is the concern when it comes to the rollout of the COVID-19 vaccine. The <a href="https://www.cdc.gov/coronavirus/2019-ncov/vaccines/recommendations-process.html">CDC</a> and the different <a href="https://www.health.state.mn.us/diseases/coronavirus/vaccine/phase1b1c2.pdf">states</a>’ phased allocations have prioritized equality and mutual responsibility. Illegitimate line-jumping is a direct threat to these principles and works more insidiously to undermine them.</p>
<p>[<em>Over 100,000 readers rely on The Conversation’s newsletter to understand the world.</em> <a href="https://theconversation.com/us/newsletters/the-daily-3?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=100Ksignup">Sign up today</a>.]</p><img src="https://counter.theconversation.com/content/155277/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Katharine Young does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>No one likes a long line. But privileging the rich and powerful – as has often been the case – may undermine trust in the vaccine rollout.Katharine Young, Professor of Law, Boston College, Boston CollegeLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1054762018-11-16T15:48:51Z2018-11-16T15:48:51ZWhy is this line so long?<figure><img src="https://images.theconversation.com/files/245982/original/file-20181116-194491-np2wnk.jpg?ixlib=rb-1.1.0&rect=594%2C172%2C4418%2C3065&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A long line might actually be the quickest line.</span> <span class="attribution"><a class="source" href="http://www.apimages.com/metadata/Index/Black-Friday/8374145f19d0430fa4f9c8c34b345c2b/7/0">AP Photo/Michael Dwyer</a></span></figcaption></figure><p>Warning: After reading this article, you will never again stand in a line without thinking about how to make your wait time shorter. And as an expert in operations management, I’m here to spread the word that sometimes a longer line may actually be a good thing.</p>
<p>My family is used to my preaching. On a recent shopping excursion, we overheard an impatient customer blurt out, “Why is this line so long?” To which my daughter responded, with a glare in my direction, “Don’t even consider telling him about queuing theory.”</p>
<p>It did take considerable restraint not to answer his question. But I was just happy realizing that my daughter knows the difference between single-server and multiple-server queuing models.</p>
<p><a href="https://doi.org/10.1007/978-0-387-73699-0_5">Queuing theory</a> is the mathematical science behind why the line is so long. A queue is just another word to describe a line of things waiting their turn – whether it’s people waiting to get a free ice cream cone or a new car moving through the assembly line.</p>
<p>Prepare to arm yourself with some queuing theory basics to help you brave the throngs while holiday shopping.</p>
<h2>When the line reaches around the block</h2>
<p>Of course there can be many reasons for a long line.</p>
<p>Maybe a retail manager is spiteful and wants to see every customer get angry. But that’s not a good business strategy and probably an unlikely reason for a long line.</p>
<p>Another possibility is that the manager puts more value on her costs to provide a service – in this case, staffing adequately to ring up your purchase speedily – than on your time waiting for that service. This scenario is a more likely reason, but still not a good long-term business strategy. Even though it’s easy to assume some version of this is at the root of your line-waiting woes, it’s typically not the reason.</p>
<p>Or perhaps you’re waiting for a service that is highly sought after by many people. In this case, the line might indicate just how smart you are to be waiting in it for your share of whatever’s at the other end. This sounds promising, but is rarely the case. It’s not often you camp out for front-row tickets or to be the first to get some new gadget.</p>
<p>The most likely scenario is that you’re misunderstanding how the line is designed. Seeing a line snake back and forth across the width of a store three times can be deceiving as to how long you may actually have to wait. In what may appear to be a very long line, the service rate can be so good that the line moves very quickly.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=382&fit=crop&dpr=1 600w, https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=382&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=382&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=480&fit=crop&dpr=1 754w, https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=480&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/245984/original/file-20181116-194519-gzqg5w.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=480&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">One line spreads the risk of slowdowns out over the whole group.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/jacksonville-floridafebruary-5-2018-travelers-waiting-1029446116">James R. Martin/Shutterstock.com</a></span>
</figcaption>
</figure>
<h2>Getting to the math of the matter</h2>
<p>This concept of system design rests on a mathematical theorem called Little’s Law. It’s named after its creator, John Dutton Conant Little, an MIT professor who specializes in operations research.</p>
<p>Little’s Law provides the math that a researcher like me can use to check out different system designs employed in various instances of waiting lines. It states that over time, the number of customers in a system is equal to their rate of arrival multiplied by the average time they spend in that system.</p>
<p>Some lines have service times that vary – like at the post office. Some have service times that are fixed – like a mechanized car wash. Unique formulas apply to each scenario to help operations managers design the best system for their business.</p>
<p>With the Little’s Law equation and my own stopwatch, I’ve proven over and over again that a longer line may actually be a better line. Let me explain.</p>
<p>Imagine a situation where you have many shorter lines, each being served by its own cashier. Call it the grocery store model, or the single-server model, more officially. You can get out of there quickly only if you correctly guess which line will move the quickest. And if you’re anything like me, you’re bound to bet on the wrong line.</p>
<p>But a single, longer line, being served by multiple employees – think banking, the motor vehicle department or airport security – is actually faster for everyone, even though it looks much longer than what you’re used to seeing in other systems.</p>
<p>The main reason is that if there’s a price check, a return or some other very slow customer, that delay affects only that cashier directly dealing with the situation. The rest of the line continues to move along. The delay at one cashier gets distributed across the entire system in the multiple-server model, instead of completely stalling out just that one line, as in the single-server model we see in the grocery stores.</p>
<p>So even if you see a very long line, as long as it’s the only option, you should be pleased. You don’t have to guess which line to get in. Little’s Law means a single long line is the fairest way to get everyone out of there as fast as possible.</p><img src="https://counter.theconversation.com/content/105476/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Joost Vles does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Don’t despair if, once you’ve gathered your shopping items, you’re met by a single line that looks a mile long. Queuing theory suggests this is likely the fastest way to get you rung up and moving on.Joost Vles, Adjunct Instructor of Management, University at BuffaloLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/925142018-06-04T20:28:34Z2018-06-04T20:28:34ZFed up with always being in the slow queue? That’s why queues are being ‘designed out’<figure><img src="https://images.theconversation.com/files/208792/original/file-20180304-65529-12e8sjq.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C5076%2C3381&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Businesses are weighing up the costs of queuing and using innovative ways to do away with queues, or at least make the perceptions of waiting less painful.</span> <span class="attribution"><a class="source" href="https://unsplash.com/photos/1O77vgBVkXQ">Michal Parzuchowski/Unsplash</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span></figcaption></figure><p><em>This is the second article in our new series, <a href="https://theconversation.com/au/topics/moving-the-masses-54500">Moving the Masses</a>, about managing the flow of crowds of individuals, be they drivers or pedestrians, shoppers or commuters, birds or ants.</em></p>
<hr>
<blockquote>
<p>Remember that time is money. <strong>– Benjamin Franklin, 1748</strong></p>
</blockquote>
<p>Whether it is lining up to pay for your groceries, making a bank transaction, or waiting for a table at a trendy restaurant, time costs money. As businesses become aware of the direct and indirect costs of waiting, they are looking at innovative ways to reduce these expenses by “designing out” queues. The challenge for anyone serving the public in a way that involves waiting is that they must manage people’s perceptions as well as optimising the rate at which they are served. </p>
<h2>People are not ships</h2>
<p>In a logistics context, say stevedoring, managers can to some extent <a href="http://www.deshlergroup.com/portclosure/">predict delays or weather conditions</a> that have impacts on efficiency. They have historical data about how long it takes to unload a ship, normal volumes of containers and how much labour is required. Using this data, they can set delivery windows so that ships can deliver quickly. Less queuing takes place and therefore less time and money is lost. </p>
<p>These <a href="http://www.inboundlogistics.com/cms/article/cutting-transportation-costs/">delivery window times and optimised routes</a> are communicated to pilots. Accordingly, they sail into ports “just in time” to be unloaded. </p>
<p>Unfortunately, unlike ships, people enter queues randomly, which creates a problem in providing optimal service. Companies cannot control this type of customer demand. </p>
<p>For example, people don’t consistently arrive at the supermarket checkout area in five-minute increments, with exactly six items. If they did, retailers could <a href="http://people.revoledu.com/kardi/tutorial/Queuing/Arrival-Distribution.html">mathematically determine</a> exactly how many staff to employ, and when to employ them, to maximise service levels and minimise costs. </p>
<h2>Hitting the queuing ‘sweet spot’</h2>
<p>Businesses face the challenge of identifying the <a href="https://www.isixsigma.com/industries/retail/queuing-theory-and-practice-source-competitive-advantage/">optimum point</a> where the costs of providing the service equal the costs of waiting. People in queues behave in ways that create direct and indirect costs for businesses. Sometimes customers will <em>baulk</em> and simply refuse to join the queue. Or they join the queue but <em>renege</em>, leaving because wait times are too long. </p>
<p>This behaviour leads to <a href="https://www.emeraldinsight.com/doi/pdfplus/10.1108/09604520710735182">measurable costs</a>. These costs are both direct, like abandoned carts, and indirect, like perceptions of poor service quality, increased dissatisfaction and low levels of customer loyalty. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=415&fit=crop&dpr=1 600w, https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=415&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=415&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=521&fit=crop&dpr=1 754w, https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=521&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/207990/original/file-20180227-36686-10b17x1.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=521&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The inverted curve describes the optimum balance between the costs of providing service with the costs of making customers wait.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Queuing theory and the evolution of the queue</h2>
<p>Queuing theory evolved from the work of Danish engineer A.K. Erlang. In 1909 he experimented with fluctuating demand in telephone traffic. By the end of the second world war, Erlang’s early work had been extended to more general problems and business applications, such as <a href="https://hal.archives-ouvertes.fr/hal-00263072/document">airports</a>. Queuing theory is now widely used to examine arrival characteristics, waiting behaviours and queue performance to <a href="https://www.analyticsvidhya.com/blog/2016/04/predict-waiting-time-queuing-theory/">predict waiting times</a>. </p>
<p>Airports have also sought to reduce the waiting time for luggage collection by moving the carousel further away from the arrival gate. Passengers <a href="https://www.nytimes.com/2012/08/19/opinion/sunday/why-waiting-in-line-is-torture.html">spend their time walking instead of waiting</a>.</p>
<p>The nature of a queue has changed and will continue to change, as <a href="https://www.aph.gov.au/About_Parliament/Parliamentary_Departments/Parliamentary_Library/pubs/BriefingBook43p/futurepopulation">populations increase</a> and consumers become increasingly time-poor. In a retail context, the traditional grocer, who would hand-select products for customers in a first-come-first-serve manner, has given way to self-service supermarkets since the first such store, <a href="https://australianfoodtimeline.com.au/first-self-service-grocery-store/">Piggly Wiggly</a>, opened in Memphis, Tennessee, in 1916. Promoting lower prices and better value, these supermarkets were the first to provide “checkout stands” where shoppers lined up after selecting their own products.</p>
<p>The original “grid-style” checkout allowed retailers to serve multiple shoppers at multiple checkouts while also presenting them with a small range of impulse items, such as chocolates, soft drinks and magazines. Known as a <a href="http://www.zainbooks.com/read.php?i=chapter-4--relational-models-qualitative-methods-analysis-theory-effective-management-decision-making&b=177&c=4">single-channel, single-phase system</a>, this is still the dominant format. </p>
<p><img src="https://cdn.theconversation.com/static_files/files/151/single_single_v2.gif?1528081550" width="100%"> </p>
<p>However, more and more retailers are moving to a longer single line, with customers being served by multiple devices. An example is banks of self-serve checkouts. This is referred to as a multi-channel, single-phase system. </p>
<p>These longer “snake” single lines achieve three things:</p>
<ol>
<li>they provide the illusion that the line is moving faster because it is always moving forward</li>
<li>they enable retailers to present even more tempting “impulse” treats in a longer linear flow</li>
<li>they reduce <a href="https://www.nytimes.com/2012/08/19/opinion/sunday/why-waiting-in-line-is-torture.html?pagewanted=all&_r=0">customer anxiety and frustration</a>.</li>
</ol>
<p><img src="https://cdn.theconversation.com/static_files/files/150/single_multiple_v2.gif?1528081550" width="100%"></p>
<p>The reason for the third benefit is that with two or more queues, versus a single queue, you don’t know which one is going to move faster. This creates an unpleasant feeling and a sense of inequity, which the multiple-channel format seeks to diminish.</p>
<p><img src="https://cdn.theconversation.com/static_files/files/149/multiple_multiple_v2.gif?1528081549" width="100%"></p>
<h2>Why does your queue always seems slower?</h2>
<p>Two interrelated theories explain this perception. <a href="http://psychology.iresearchnet.com/social-psychology/decision-making/illusory-correlation/">Illusory correlation</a> refers to an error in human judgment when a person perceives a relationship between two salient variables that are not in fact correlated. Consider washing your car and it starts to rain – we might think washing the car “causes” it to rain. Or we might think red cars attract more police attention – there is an “association” between driving a red car and getting a speeding ticket. In a queuing context, two important variables are at play, “speed of queue” and “your time”. </p>
<p>Added to this is amplification theory. This draws on <a href="http://assets.csom.umn.edu/assets/71516.pdf">research</a> published in 2001 that proposed that “bad is stronger than good” and “bad memories have a more powerful psychological impact on us than do good events”. In other words, <a href="http://www.bbc.com/future/story/20130827-why-other-queues-move-faster">we are more likely to remember slow queues</a> than times when we have been in faster queues. </p>
<p>In addition, unoccupied time always seems to pass more slowly than occupied time. This is why businesses are increasingly <a href="https://www.business.com/articles/simple-ways-to-improve-your-customers-waiting-experience/">giving you something to do while you queue</a>. There may be magazines close at hand, or a TV screen mounted on the wall in a bank.</p>
<p>The most obvious solution is to keep you moving. It’s a strategy used at festivals and tourist attractions where “snake” lines are common. The snake line also helps free up space, makes everything appear more orderly and equitable and prevents queue-jumping. People prefer movement, so standing still or waiting in a queue with nothing to do can create a <a href="http://onlinelibrary.wiley.com/doi/10.1111/j.0021-9029.2006.00078.x/abstract">negative experience and negative evaluations of service</a>. </p>
<h2>Moving beyond the queue</h2>
<p>Many sectors are designing out the queue altogether, or at least the perception of queuing. For example, in many banks, government departments, libraries, retail stores and airports, the queue is beginning to disappear. </p>
<p>At <a href="https://digitalscholarship.unlv.edu/cgi/viewcontent.cgi?article=2054&context=thesesdissertations">airports</a>, check-in kiosks have replaced queues and counters. The kiosks are dispersed widely throughout the terminal, thus providing travellers with <a href="http://www.emeraldinsight.com/doi/abs/10.1108/IJRDM-08-2013-0153">perceptions of spatial convenience</a>. In retail and service landscapes our perception of convenience diminishes the further we have to walk, so clustering of essential services, including check-in kiosks and retail outlets, is replacing the traditional linear design of airports. Spatial convenience gives people the <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5511147/">perception of less crowding, no queues, ease of access and mobility</a>. </p>
<p>Retailers are <a href="https://unita.com.au/work-category/retail/">playing with innovative layouts</a> and removing the queue altogether. Bank queues are also becoming <a href="https://thefinancialbrand.com/52315/future-banking-concept-branch-design-showcase/all/">a thing of the past</a>; a new <a href="http://publicdesigngroup.com/">Bank of Queensland branch fit-out</a> invites customers to “take a seat” rather than line up for service.</p>
<h2>So, are we still queuing?</h2>
<p>Well, yes and no. We still have to wait, but the ways in which we wait, especially the perception of how we wait, is definitely changing.</p>
<p>The new <a href="https://www.amazon.com/b?ie=UTF8&node=16008589011">Amazon Go store</a>, for instance, has completely removed all the checkouts. This ensures customers will never have to queue for service. The only problem now is <a href="http://www.news.com.au/finance/business/retail/the-future-of-shopping-amazon-go-launches-cashless-supermarket-with-no-cashiers-lines-or-registers/news-story/43bc168c8d47cd9fb2e65bcd0c629642">the long line-up</a> to actually get inside the store! </p>
<hr>
<p><em>You can find other articles in the series <a href="https://theconversation.com/au/topics/moving-the-masses-54500">here</a>.</em></p><img src="https://counter.theconversation.com/content/92514/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Businesses are weighing up the costs of queuing and using innovative ways to minimise these costs by doing away with queues.Gary Mortimer, Associate Professor in Marketing and International Business, Queensland University of TechnologyLouise Grimmer, Lecturer in Marketing, Tasmanian School of Business and Economics, University of TasmaniaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/766472017-05-07T18:27:59Z2017-05-07T18:27:59ZThere’s a mathematical formula for choosing the fastest queue<figure><img src="https://images.theconversation.com/files/168079/original/file-20170505-21007-yfd4iq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p>It seems obvious. You arrive at the checkouts and see one queue is much longer than the other, so you join the shorter one. But, before long, the people in the bigger line zoom past you and you’ve barely moved towards the exit.</p>
<p>When it comes to queuing, the intuitive choice is often not the fastest one. Why do queues feel like they slow down as soon as you join them? And is there a way to decide beforehand which line is really the best one to join? Mathematicians have been studying these questions for years. So can they help us spend less time waiting in line?</p>
<p>The intuitive strategy seems to be to join the shortest queue. After all, a short queue could indicate it has an efficient server, and a long queue could imply it has an inexperienced server or customers who need a lot of time. But generally this isn’t true.</p>
<p>Without the right information, it could even be disadvantageous to join the shortest queue. For example, if the short queue at the supermarket has two very full trolleys and the long queue has four relatively empty baskets, many people would actually join the longer queue. If the servers are equally efficient, the important quantity here is the number of total items in the queue, not the number of customers. But if the trolleys weren’t very full but the hand baskets were, it wouldn’t be so easy to estimate and the choice wouldn’t be so clear. </p>
<p>This simple example introduces the concept of service time distribution. This is a random variable that measures how long it will take a customer to be served. It contains information about the average (mean) service time and about the <a href="http://www.mathsisfun.com/data/standard-deviation.html">standard deviation</a> from the mean, which represents how the service time fluctuates depending on how long different customers need.</p>
<p>The other important variable is how often customers join the queue (the arrival rate). This depends on the average amount of time that passes between two consecutive customers entering the shop. The more people that arrive to use a service at a specific time, the longer the queues will be. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/168080/original/file-20170505-20986-35dd45.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Never mind the queue, I picked the wrong shop.</span>
<span class="attribution"><span class="source">Shutterstock</span></span>
</figcaption>
</figure>
<p>Depending on what these variables are, the shortest queue <a href="http://www.columbia.edu/%7Eww2040/DecidingWhichQ1986.pdf">might be the best</a> one to join – or it might not. For example, in a fish and chip shop you might have two servers both taking orders and accepting money. Then it is most often better to join the shortest queue since the time the servers’ tasks take doesn’t vary much.</p>
<p>Unfortunately, in practice, it’s hard to know exactly what the relevant variables are when you enter a shop. So you can still only guess what the fastest queue to join will be, or rely on tricks of human psychology, such as joining the leftmost queue because most right-handed people <a href="https://www.nytimes.com/2016/09/08/business/how-to-pick-the-fastest-line-at-the-supermarket.html?_r=0">automatically turn right</a>.</p>
<h2>Did you get it right?</h2>
<p>Once you’re in the queue, you’ll want to know whether you made the right choice. For example, is your server the fastest? It is easy to observe the actual queue length and you can try to compare it to the average. This is directly related to the mean and standard deviation of the service time via something called the <a href="https://books.google.co.uk/books/about/The_Mathematical_Theory_of_a_Stationary.html?id=OJhNOAAACAAJ&redir_esc=y">Pollaczek-Khinchine formula</a>, first established in 1930. This also uses the mean inter-arrival time between customers. </p>
<p>Unfortunately, if you try to measure the time the first person in the queue takes to get served, you’ll likely end up feeling like you chose the wrong line. This is known as Feller’s paradox or the <a href="http://www.columbia.edu/%7Eks20/stochastic-I/stochastic-I-RRT.pdf">inspection paradox</a>. Technically, this isn’t an actual logical paradox but it does go against our intuition. If you start measuring the time between customers when you join a queue, it is more likely that the first customer you see will take longer than average to be served. This will make you feel like you were unlucky and chose the wrong queue. </p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/Jd1wNizPjoE?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
</figure>
<p>The inspection paradox works like this: suppose a bank offers two services. One service takes either zero or five minutes, with equal probability. The other service takes either ten or 20 minutes, again with equal probability. It is equally likely for a customer to choose either service and so the bank’s average service time is 8.75 minutes. </p>
<p>If you join the queue when a customer is in the middle of being served then their service can’t take zero minutes. They must be using either the five, ten or 20 minute service. This pushes the time that customer will take to be served to more than 11 minutes on average, more than the true average for the of 8.75 minutes. In fact, two out of three times you encounter the same situation, the customer will want either the 10 or 20 minute service. This will make it seem like the line is moving more slowly than it should, all because a customer is already there and you have extra information. </p>
<p>So while you can use maths to try to determine the fastest queue, in the absence of accurate data – and for your own peace of mind – you’re often better just taking a gamble and not looking at the other options once you’ve made your mind up.</p><img src="https://counter.theconversation.com/content/76647/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>There’s also one that explains why you always think you’ve picked the wrong queue.Enrico Scalas, Professor of Statistics and Probability, University of SussexNicos Georgiou, Lecturer in Mathematics, Probability and Statistics, University of SussexLicensed as Creative Commons – attribution, no derivatives.