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Queuing Model: Doris Fuller on How Small Changes to Wait Times Can Make Large, Positive Impacts

Stephanie Hepburn is a writer in New Orleans. She is the editor in chief of #CrisisTalk. You can reach her at​

On March 14th, 2015, Doris Fuller lost her daughter, Natalie, to mental illness. Just a few weeks before her 29th birthday, Natalie stepped in front of a train in Baltimore. She’d heard voices that told her to hurt herself and so she did. Fuller describes, in a piece for the Washington Post, what her daughter experienced as “devils that literally hounded her to death, and she did it while laughing, painting, writing poetry, advocating, and bringing joy to the people around her. She was the bravest person I have ever known, and her suicide doesn’t change that.” At that point, Natalie had struggled with bipolar disorder and psychosis for nearly eight years, signs that first became evident during her senior year of college when she had a severe manic episode. After Natalie’s first manic episode, which resolved quickly, she returned to school and experienced another. Fuller’s second introduction to mental illness was when Natalie called from jail. 

Fuller says parents are often thrown into their child’s mental health crisis without any knowledge on what he or she is experiencing. “It’s hard to wrap your mind around it when there’s no family history of mental illness, and you have a teenager or young adult—the typical age of onset—in the midst of a mental health crisis, and you’re just a parent floundering around, wondering ‘What’s going on’ and thinking, ‘Is she using dope?’” During the first episode of psychosis, Fuller says diversion is a term parents haven’t likely heard, and they don’t know the system their child needs to be diverted from. “Parents don’t know what they’re dealing with or the systems involved.” 

Natalie’s experience was a classic case of someone mentally ill who committed a low-level offense: she’d shown up at the home of a boy she had dated, and his roommates got upset because she wouldn’t leave the porch. They called the police who tried to talk her into going home, but she was psychotic, hearing voices that told her she was supposed to be on that porch. The police arrested Natalie but didn’t charge her. As luck would have it, Fuller’s close friend was a neuropsychologist and said, “This sounds like psychosis,” allowing Fuller to step in quickly to advocate for her daughter within the law enforcement system, and it helped. Otherwise, Natalie likely would have ended up languishing in the criminal justice system like so many other similarly situated people experiencing mental illness. 

Knowing what it could have been like for her daughter planted a seed in Fuller’s mind on how it could be different for everyone experiencing mental illness who are triaged to jail instead of treatment. In December 2015, she read a Psychiatric Services paper where the authors applied the queuing model to the problem of Emergency Department boarding in North Carolina counties. “I had a eureka moment and thought, ‘What if the researchers could take this concept and apply it to jail diversion and pretrial inmates waiting for mental health services in the jails?’” Fuller says people with mental illness often spend longer in jail waiting to be assessed for competency to stand trial than it would have taken for them to serve time for the offense they allegedly committed. She wondered if the queuing model could highlight the solution.

Fuller reached out to Kristen Hassmiller Lich, Ph.D., one of the authors, who helped Fuller, who, at the time, was Chief of Research and Public Affairs at the Treatment Advocacy Center, and her colleagues develop a forensic model based on the queuing theory that examined diversion from jail, the length of time people wait in the hospital for competency, and the supply of staffed beds available for pretrial evaluations and/or restoration. They applied the model to five states: Florida, Maine, New Jersey, Texas, and Wisconsin. To determine how changes to these variables could improve the system, the team came up with multiple computational scenarios to answer these three questions:

1) How many fewer inmates would reduce the average bed waits to 3-days or 14-days?
2) How many days would the average hospital length of stay need to be decreased by to reduce the average wait time to 3-days or 14-days?
3) How many beds need to be added to reduce the average wait time for pretrial inmates to 3-days or 14-days?

The common pathway for an arrested person with mental illness is that he or she waits in jail and is then sent to the state hospital for competency assessment, which Fuller says is the most expensive, complicated, and time-consuming route. She says what often happens is that people are restored to competency in 30-days, but hospital administrative hurdles get in the way while someone else who could use that bed waits in jail. “It’s not an efficient system.” What states found is that small adjustment to any of the three key variables had a tremendous impact. Fuller says that by using the queuing model, the state of Texas reduced the average wait for a hospital bed from 2 months to 14 days by decreasing pre-trial average waits for competency services from 189 to 186 days. In Florida, merely diverting two mentally ill offenders per month reduced the average forensic bed wait by 75% (from 12 to 3 days). Wisconsin and New Jersey found that average bed waits fell by more than 50% to less than 14 days by diverting one additional detainee per month. Fuller says it’s no mystery that diverting people experiencing a mental health crisis from the criminal justice system is more cost-effective than putting them in jail and that shorter wait time for competency assessments (or using community-based resources to do so) are more efficient and save money. What’s astonishing, she says, is how small, strategic changes to targeted variables has such a remarkable effect. 

“It’s counter-intuitive that little changes would have a big impact, but the numbers bear out, and it gets stakeholders to examine these problems from a mathematically-based perspective and ask, ‘If we divert and cut forensic bed waits, how much money does that save the state? The savings are staggering, and these changes would improve people’s lives. We don’t want someone arrested for trespassing to sit in jail for a year and then in the hospital for six months. We need a better way.”

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