New York City officials have long been nervous about closing Rikers. Legally mandated to shutter in 2027, the much-maligned island jail complex is to be replaced with lockups in each of the non-Staten Island boroughs. But both Mayor Eric Adams and now-former Department of Correction commissioner Louis Molina have raised questions about whether the borough facilities’ cumulative 3,300-person capacity is enough to detain the city’s jail population safely.

“We think the population in 2024 could be over 7,000,” Molina told the City Council in December 2022. “But I don’t see them being at 3,300 in less than four years if nothing else changes with the administration and adjudication of the administration of justice at the court levels.”

Molina’s 7,000–inmate estimate would be bad news for advocates of the borough-based approach. But what was it based on? Vital City, a New York-based, urban-policy-focused publication (for which I have written) filed a Freedom of Information request with the DOC, and published the seven-page memo, detailing DOC’s estimate, it received in response.

The City, a New York news outfit, wasn’t buying the department’s numbers. One cited expert argued that the DOC’s math was “impossible to fully understand” and that it was failing to take into account city policymakers’ ability to affect the jail population. Neither charge is fair. The memo—though ultimately just a “napkin math” estimate—provides a useful way for people on both sides of the debate to understand the department’s basic capacity problem.

To reach the 7,000 figure Molina cited, the DOC memo’s anonymous authors use something called “queueing theory,” a fancy term for the branch of math that studies the property of waiting lines (“queues,” if you’re British). Queueing theory lets analysts answer questions like how long a line will take to clear, or how many “servers” are needed to service a line of a given length. Queueing theory is widely used in manufacturing and other business enterprises, where it helps illuminate how many widgets can move through a factory in an hour, or how much machinery is needed to process a given number of widgets.

A jail can also be thought of as a big line. Each day, a certain number of people enter it, wait for some period of time, and then exit it. Thinking of a jail in this way allows the DOC to use queueing-theory tools to predict its inmate population.

Specifically, the DOC report uses a basic queueing theorem called “Little’s Law,” which says that the average length of a queue in a given time period is equal to the number of people admitted to the queue in that period, multiplied by the average waiting time over that period. This is usually expressed as a formula—L=λW—where L is average length, λ is the number of admissions, and W is average wait time. Little’s Law is useful because if one knows two of these values, it’s easy to obtain the third. In the case of jails, if one knows the number of admissions on a given day (λ) and the average length of stay in days (W), multiplying one by the other gives the expected average daily population (L).

The DOC’s 7,000 figure comes from this insight. As it turns out, the model has held up pretty well. The table below compares its projections to the actual monthly jail population most recently reported by the New York State Division of Criminal Justice Services. The DOC’s estimates have been within a few hundred people of the actual figure for the months for which data are available. The DOC’s report includes much wider confidence intervals—the 7,300 figure is the middle of a range between 4,400 and 10,300—which makes the model’s accuracy particularly notable.

Critics cited by The City note that the DOC assumes that wait time will remain constant at around three months. Wait times, they argue, have gotten too long, and can be driven down by deliberate city action. The former claim, at least, has merit; as The City notes, wait times are now over 100 days, up from 91 days during the last two years of the de Blasio administration, and 48 days at the lowest point of the Bloomberg administration.

Some of this increase in wait time, I have argued, is driven by decarceration. As low-level cases, which are easily disposed of, are not detained at all, the remaining inmate population is composed mostly of serious offenders, whose cases take longer, driving up average wait time. Bloomberg’s low wait times, in other words, were a function of how many non-serious offenders were being held on Rikers pre-trial.

But even with substantial reductions to wait time, it will be very hard to hit an average daily population that fits in the borough jails. The borough-based jails are designed to hold an average population of 3,300, with an extra 500 beds worth of space to accommodate natural fluctuation. Relative to projected admissions, wait times would need to be reduced to 47 days—shorter than the Bloomberg-era minimum—and never move higher to operate at that level.

This, as I have argued repeatedly, is the basic problem with the borough-based jails plan: the borough facilities simply are not big enough to house plausibly all the people New York City needs to detain. This is because, as I note in my Manhattan Institute report on the topic, 3,300 is an unprecedentedly low figure—lower than almost any figure recorded since Rikers opened, and lower, in jail-to-population-ratio terms, than that of any other major city. The DOC report corroborates this basic fact: the borough facilities do not have enough space.

This does not mean that the city can’t close Rikers. It is possible otherwise to cobble together adequate jail space, through a combination of building more new jails, refurbishing closed ones, and detaining some offenders upstate or on Long Island.

But, despite the obvious problems, many in city government seem uninterested in having such practical conversations. They don’t want to look at the real consequences—for public safety and for the constitutional rights of detainees—entailed by too-small jails. For them, closing Rikers is a matter of principle.

Photo by d EMMANUEL DUNAND/AFP via Getty Images


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