Tag Archives: queuing

Resilient voting systems during the COVID-19 pandemic: A discrete event simulation approach

Holding a Presidential election during a pandemic is not simple, and election officials are considering new procedures to support elections and minimize COVID-19 transmission risks. I became award of these issues earlier this summer, when I had a fascinating conversation with Professor Barry Burden about queueing, location analysis, and Presidential elections. Professor Burden is a professor of Political Science at the University of Wisconsin-Madison, a founding director of the Elections Research Center, and an election expert.

I was intrigued by the relevance of location analysis and queueing theory in this important and timely problem in public sector critical infrastructure (elections are critical infrastructure). I looked into the issue further with Adam Schmidt, a PhD student in my lab. We created a detailed discrete event simulation model of in-person voting, and we analyzed it using a detailed study.

We present an executive summary of our paper below. Read the full paper here: https://doi.org/10.6084/m9.figshare.12985436.v1


Resilient voting systems during the COVID-19 pandemic:
A discrete event simulation approach

Adam Schmidt and Laura A. Albert
University of Wisconsin-Madison
Industrial and Systems Engineering
1513 University Avenue
Madison, Wisconsin 53706
September 21, 2020

Executive Summary

The 2020 General Election will occur during a global outbreak of the COVID-19 virus. Planning for an election requires months of preparation to ensure that voting is effective, equitable, accessible, and that the risk from the COVID-19 virus to voters and poll workers is minimal. Preparing for the 2020 General Election is challenging given these multiple objectives and the time required to implement mitigating strategies.

The Spring 2020 Election and Presidential Preference Primary on April 7, 2020 in Wisconsin occurred during the statewide “Stay-at-home” order associated with the COVID-19 pandemic. This election was extraordinarily challenging for election officials, poll workers, and voters. The 2020 Wisconsin Spring Primary experienced a record-setting number of ballots cast by mail, and some polling locations experienced long waiting times caused by consolidated polling locations and longer-than-typical check-in and voting times due to increased social distancing and protective measures. A number of lawsuits followed the 2020 Wisconsin Spring Primary, highlighting the need for more robust planning for the 2020 General Election on November 3, 2020.

This paper studies how to design and operate in-person voting for the 2020 General Election. We consider and evaluate different design alternatives using discrete event simulation, since this methodology captures the key facets of how voters cast their votes and has been widely used in the scientific literature to model voting systems. Through a discrete event simulation analysis, we identify election design principles that are likely to have short wait times, have a low-risk of COVID-19 transmission for voters and poll workers, and can accommodate sanitation procedures and personal protective equipment (PPE).

We analyze a case study based on Milwaukee, Wisconsin data. The analysis considers different election conditions, including different levels of voter turnout, early voting participation, the number of check-in booths, and the polling location capacity to consider a range of operating conditions. Additionally, we evaluate the impact of COVID-19 protective measures on check-in and voting times. We consider several design choices for mitigating the risks of long wait times and the risks of the COVID-19 virus, including consolidating polling locations to a small number of locations, using an National Basketball Association (NBA) arena as an alternative polling location, and implementing a priority queue for voters who are at high-risk for severe illness from COVID-19.

As we look toward the General Election on November 3, 2020, we make the following observations based on the discrete event simulation results that consider a variety of voting conditions using the Milwaukee case study.

  1. Many polling locations may experience unprecedented waiting times, which can be caused by at least one of three main factors: 1) a high turnout for in-person voting on Election Day, 2) not having enough poll workers to staff an adequate number of check-in booths, 3) an increased time spent checking in, marking a ballot, and submitting a ballot due to personal protective equipment (PPE) usage and other protective measures taken to reduce COVID-19 transmission. Any one of these factors is enough to result in long wait times, and as a result, election officials must implement strategies to mitigate all three of these factors.
  2. The amount of time spent inside may be long enough for voters to acquire the COVID-19 virus. The risk to voters and poll workers from COVID-19 can be mitigated by adopting strategies to reduce voter wait times, especially for those who are at increased risk of severe illness from COVID-19, and encourage physical distancing through the placement and spacing of voting booths.
  3. Consolidating polling locations into a few large polling locations offers the potential to use fewer poll workers and decrease average voter wait times. However, the consolidated polling locations likely cannot support the large number of check-in booths required to maintain low voter wait times without creating confusion for voters and interfering with the socially distant placement of check-in and voting booths. As a result, consolidated polling locations require high levels of staffing and could result in long voter wait times.
  4. The NBA has offered the use of its basketball arenas as an alternative polling location for voters to use on Election Day as a resource to mitigate long voter wait times. An NBA arena introduces complexity into the voting process, since all voters have a choice between their standard polling location and the arena. This could create a mismatch between where voters choose to vote and where resources are allocated. As a result, some voters may face long wait times at both locations.

We recommend that entities overseeing elections make the following preparations for the 2020 General Election. Our recommendations have five main elements:

  1. More poll workers are required for the 2020 General Election than for previous presidential elections. Protective measures such as sanitation of voting booths and PPE usage to reduce COVID-19 transmission will lead to slightly longer times for voters to check-in and to fill out ballots, possibly causing unprecedented waiting times at many polling locations if in-person voter turnout on Election Day is high. We recommend having enough poll workers to staff one additional check-in booth per polling location (based on prior presidential elections or based on what election management toolkits recommend), to sanitize voting areas and to manage lines outside of polling locations.
  2. To reduce the transmission of COVID-19 to vulnerable populations during the voting process, election officials should consider the use of a priority queue, where voters who self-identify as being at high-risk for severe illness from COVID-19 (e.g., voters with compromised immune systems) can enter the front of the check-in queue.
  3. In-person voting on Election Day should occur at the standard polling locations instead of at consolidated polling locations. Consolidated polling locations require many check-in booths to ensure short voting queues, and doing so requires high staffing levels. Election officials should ensure that an adequate number of voting booths (based on prior presidential elections or based on what election management toolkits recommend) can be safely located within the voting area at the standard polling locations, placing booths outside if necessary.
  4. We do not recommend using sports arenas as supplementary polling locations for in-person voting on Election Day. Alternative polling locations introduce complexity and could create a mismatch between where voters choose to go and where resources are allocated, potentially leading to longer waiting times for many voters. This drawback can be avoided by instead allocating the would-be resources at the sports arena to the standard polling locations.
  5. The results emphasize the importance of high levels of early voting for preventing long voter queues (i.e., one half to three quarters of all votes being cast early). This can be achieved by expanding in-person early voting, in terms of both the timeframe and locations for early in-person early voting, adding new drop box locations for voters to deposit absentee ballots on or before Election Day, and educating voters on properly completing and submitting a mail-in absentee ballot.

The results are based on a detailed case study using data from Milwaukee, Wisconsin. It is worth noting that the discrete event simulation model reflects standard voting procedures used throughout the country and can be applied to other settings. Since the data from the Milwaukee case study are reflective of many other settings, the results, observations, and recommendations can be applied to voting precincts throughout Wisconsin and in other states that hold in-person voting on Election Day.

Resilient voting systems during the COVID-19 pandemic: A discrete event simulation approach


waiting is torture, but it’s not so bad if there are mirrors or trees

Operations research is the discipline of making better decisions. We have to solve the right problem to better inform decisions, and sometimes solving the right problem doesn’t involve math.

One of my favorite stories about solving the right problem comes from MIT Professor Dick  Larson (Dr. Queue!). He summarized his story in an article in Slate about queuing theory [Link]:

Midcentury New York featured a rush-hour crisis—not out on the roads, but inside office tower lobbies. There weren’t enough elevators to handle the peak crowds. Complaints were mounting. “One solution would have been to dynamite the buildings and build more elevator shafts,” says Larson. “But someone figured out the real problem isn’t just the duration of a delay. It’s how you experience that duration.” Some buildings installed floor-to-ceiling mirrors near the elevators and, entertained by their own reflections and by the flirting that sometimes ensued, people stopped complaining quite as much about the wait time.

A NY Times article about queuing also contains this story [Link].

A recent article in The Atlantic about how public transit riders perceive waiting times [Link] reminded me of the elevator story. The perception of waiting time is one of many issues involved in incentivizing people to use public transit. If we can understand what makes for acceptable and unacceptable perceived wait times, then maybe we can mitigate what feels like long, torturous waiting times. It turns out that we just need mature trees by bus stops (much like the mirrors by the elevators!):

Riders who waited at stops where there was lots of pollution and traffic significantly overestimated their wait times. The effect was especially pronounced for those who were waiting for longer than five minutes, with those who waited for their rides for 10 minutes in areas that they felt were noisier and dirtier reporting that they had waited for over 12 minutes. Researchers also found a simple mitigating factor: trees. According to the data, the presence of mature trees helped make wait times feel less painful, for both short and long waits, and even in areas where other negative factors were present.

The article is about a paper by Marina Lagune-Reutler, Andrew Guthrie, Yingling Fan, and David Levinson (@trnsprttnst) at the University of Minnesota.

What are your favorite and least favorite transit stops?

Related posts:

operations research at Disney

Kristine Theiler, Vice Present of Planning and Operations Support for Walt Disney Parks & Resorts, gave a talk in the ISyE department at the University of Wisconsin-Madison when being awarded theDistinguished Achievement Award. Ms. Theiler has a BS degree in ISyE from UW-Madison.

She leads an internal consulting team that provides decision support for leadership worldwide. She gave a wonderful talk to the students about industrial engineering at Disney. Her team has more than industrial engineers and is increasingly focusing on operations research. Her team has worked on the following issues:

  • food and beverage (beer optimization!)
  • park operations: attraction performance, operation at capacity, efficiency programs
  • hotel optimization: front desk queuing, laundry facility optimization
  • project development: theme park development, new products and services, property expansion
  • operations: cleaning the rides and park, horticulture planning
  • operations research: forecasting, simulation

Ms.  Theiler showed us her “magic band” – a bracelet that links together the services that a park-goer (a guest) has purchased as well as her room key and possibly her credit card (with a security code) to optimize efficiency. Guests can choose one of seven bracelet colors. This may facilitate personalization aka Minority Report. The magic band is under production.

She also noted that guests at Disney Toyko are willing to wait longer than guests at any other Disney park. Interesting.

Disney works on four key competencies that mesh well with tools in the OR toolbox:

  1. Capacity/demand analysis
  2. Measuring the impact (guest flow, weight times, transaction times)
  3. Process design and improvement
  4. Advanced analytics

The planning for Shanghai Disneyland is underway. Some of the relevant project planning, such as where to locate the park. Once a site is selected, the IEs will plan train lines between locations; how many ticket booths, turnstyles, and strollers will be needed; how to select the mix of attractions and lay them out; how many tables and chairs are needed; what is the right mix of indoor and outdoor tables; how much merchandise space to set aside; how to route parades; how to handles the “dumps” that happen when a show lets out; how to locate your favorite Disney characters (played by actors) for photo ops; how to plan backstage areas to coordinate complex shows; and locate and run hotel services.

Training scheduling optimization for the cruise lines was one of the more technical projects. There are many side constraints and stochastic issues for the 1500 people that may need to be trained at any given time. There include precedence constants (fire class 1 must be taken before fire class 2), time windows (fire drills can only be run on Tuesdays from 9-11), attendance randomness (employees and class leaders get sick), so contingency plans are a must.

Operations research and industrial engineering are obviously valuable at Disney. One of the main benefits of using advanced analytical methods is that they bring an unbiased perspective. It’s much easier to bring up a difficult issue when you discuss it from a numbers perspective rather than first stating your opinions. Analytics also provides a way to “connect the dots” between services: more people attending a show may lead to an increased need for merchandise space near the show’s exits.

Shanghai Disney

queuing, cutting in line, and social justice

Page Six ran a story about wealthy Manhattanites who hire “black-market Disney guides” for $130 an hour (or $1,040 for an eight-hour day) to cut in line for the rides at Disney World. The guides are people with disabilities who, according to Disney rules, are allowed to take up to 6 people to the front of the ride lines.

At face value, this may seem like a good trade – people who pay do not have to wait in line. People who do not pay more have to wait. But of course, this is not how we really feel about queuing.

This story became popular because hiring guides with disabilities violates the social justice principle we associate with queues. First come first served, no exceptions! This is especially important since single line FIFO queues, like the ride queues at amusement parks, have the highest expectations of social justice. We are someone less concerned with grocery store lines with multiple servers and multiple lines, where a late-comer to one line can be served before someone who has been waiting longer in another line. We reluctantly accept the Law of Lines.

I blogged about the psychology of queuing long ago based on Dick Larson’s research on the intersection of operations research and psychology [Link]. Dr. Larson and his collaborators found that people are willing to wait longer on average to ensure that no one gets special treatment. Special treatment means that someone violates the first-come-first-serve queuing rule. Multiple servers with a single queue preserve social justice.

In reality, we accept many deviations from FIFO/FCFS queues. For example, frequent fliers can register with the TSA and pay an annual fee to get expedited screening at many hub airports. We accept this. Frequent fliers skipping the security queue is not unlike the wealthy people who purchase a “guide” at Disney to avoid waiting. The difference is that the TSA expedited screening is an official way for cutting in line whereas the Disney guides are working around the way the rules are intended to work (cutting via a technicality).

What are your favorite ways to avoid queuing?


pumpkin patches and queuing theory

This weekend, my family and I went to a pumpkin patch. Everyone else had the same idea. The line stretched out of the pumpkin patch gates and through the parking lot.  We waited in line for ten minutes and then balked. When we left, about 90% of those that were leaving did not have pumpkins. We arrived in the morning on Sunday. It was only going to get busier. I cannot imagine the amount of revenue that was lost. We found out later that it took nearly two hours to get through the line.

During our short wait and on our drive to another orchard, we discussed queuing and pumpkin patches.

First, the pumpkin patch could make money by moving the long line inside  of the gates. Quite a few people left only because they could see how long the line was from their cars as they drove in. If they committed to at least getting out of their cars, they might have stayed long enough to buy pumpkins. Queuing in the parking lot was also a safety issue–nearly everyone in line had small children.

The long line was caused by the wait for the hayrides to the pumpkin fields. We couldn’t see the pumpkin fields from the front of the line.  It is a long walk, which is hard with small children and large pumpkins. The only bottleneck was for the hayrides. The traffic outside of the pumpkin patch was not too congested and the parking lot was not nearly full. The pumpkin patch hired people to make sure there was no gridlock in the parking lot (there wasn’t), but overlooked the bottleneck for the hayrides.

There was plenty to do at the pumpkin patch aside from picking pumpkins. There was a store, haunted house, and a restaurant. If people had been given tickets for a scheduled FCFS hayride (with a time of when the hayride would be leaving), they could spend money while they waited for their turn. Waiting two hours for a pumpkin isn’t so bad if you are enjoying donuts and cider.

The queue leveled off and seemed to reach steady state. The rate out only equaled the rate in because so many balked at the long line. For those of you who study queues, is this typical?

Picking pumpkins should be modeled as an infinite server queue, and in practice, this assumption should be a good approximation. (An infinite server queue can model self-service). Maybe this could happen if pumpkins are planted closer to the entrance, so some people could bypass the hayrides and walk instead. This should be somewhat achievable: when we pick apples, many more people can pick at the same time.

There are real constraints that would ultimately limit the pumpkin patch throughput, even if they had a continuous stream of tractors to and from the pumpkin fields. This can be contrasted with, say, an amusement park or stadium, where a large number of people can be served in a short amount of time (even stadiums have their limits).

  • The country road that leads up to the pumpkin patch is a two lane highway. It can only accommodate so many cars per unit of time.  Having someone direct traffic on busy weekends could help if it gets bad (the apple orchard we went to does this).
  • The parking lot was on grass. People drive slow and awkwardly on grass. The pumpkin patch isn’t profitable enough to warrant paving a huge lot to improve throughput. Amusement parks have many lanes so people can park in a short amount of time. That wouldn’t work in agricultural settings. Some congestion in the parking lot seems inevitable.
  • Ultimately, there is a choke point at these types of orchards, where everyone goes through some central area to pay. Even with many makeshift registers set up outside the barn, paying for pumpkins would get pretty chaotic if it got too busy, even if the registers are well-staged. The places I have seen that efficiently coordinate a huge number of cash registers are well-designed and inside.

So now that I figured out how to efficiently run a pumpkin patch, should I open my own?

pumpkin patch

OR and H1N1

This is the second of three posts about the INFORMS Annual Meeting.

I enjoyed a talk by Dr. Richard Larson of MIT about the timely topic of H1N1 and operations research.  I tuned out much of the alarmist news prior to the conference (to keep my sanity) and instead adopted a rigorous handwashing regimen.  Larson’s talk highlighted the many opportunities for addressing H1N1 issues using operations research, including:

  • Queuing for vaccinations.
  • Reneging on vaccinations (some health care workers are refusing required vaccinations).
  • Timing the vaccinations (before the prevalence peaks) is important for reducing risks, since youths are particularly susceptible to dying from H1N1..
  • Locating facilities to manage surge capacity when the epidemic hits.
  • Correctly diagnosing and isolating cases of H1N1.
  • Supply chains for vaccinations.

Larson and his collaborator Dr. Stan Finkelstein takes a different kind of focus, looking at personal choices, such as hand washing, coughing into sleeves, avoiding handshakes, and avoiding crowds.  They examine this issue through non-pharmaceutical interventions.  Someone infected with H1N1 infects about 1.5 people in the next 24 hours (on average).  This value is the mean of a random variable, which depends on personal choices (like handwashing).  He examines the conditions under which the average number of infections decreases below 1.0, when the virus essentially dies out (Similar to my reasoning on vampire populations).

Finkelstein, a medical doctor, discussed some of the policy results.  Initial reports suggested that H1N1 has a fatality rate of about 50% (Spanish flu has a FR of 3%).  After an initial panic, flu fatigue set in.  And the first wave of H1N1 resemble seasonal rather than pandemic flu.  But after the recent panicking, many of us simply have not been motivated to improve our personal choices to reduce H1N1 transmission.  Case in point, elbow bumping pictured below (instead of hand shaking) did not catch on at the conference as I had hoped. And the anti-bacterial hand gel was not located in useful places at the conference, so I used my own personal stash of anti-bacterial lotion after shaking hands.

I hope some of this research is used to lessen the impact of H1N1 this year before I am transformed into a germ-a-phobe.

Link:  Flu101@MIT

Karima Nigmatulina, after successfully defending the first PhD thesis on our flu research project, bumps congratulatory elbows with advisor Richard Larson as Anna Teytelman looks on. 	 	 CESF Venn CESF embraces problems operating at the Venn diagram intersection of ‘traditional engineering,’ management (broadly interpreted) and social science.

Karima Nigmatulina, after successfully defending the first PhD thesis on our flu research project, bumps congratulatory elbows with advisor Richard Larson.