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Due Process on Hold: A Queueing Framework for Improving Access in SNAP

This paper proposes a queueing framework that accounts for endogenous congestion phenomena like redials and abandonment to demonstrate how standard staffing models fail to ensure procedural due process in SNAP call centers, offering a data-driven approach to redesign access systems and prevent mass procedural denials.

Original authors: Andrew Daw, Chloe Pache, Angela Zhou

Published 2026-05-15

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Andrew Daw, Chloe Pache, Angela Zhou

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Problem: The "Broken Phone Line"

Imagine a massive, crowded waiting room for a life-saving service. People are desperate to get in, but the door is guarded by only a few tired staff members.

In the real world, this is exactly what happened with the SNAP program (food assistance) in Missouri. People trying to apply for food benefits had to call a hotline to complete an interview. But the lines were so clogged that nearly half of all people were denied benefits simply because they couldn't get through to a human. They didn't fail because they were ineligible; they failed because the phone system was broken. A judge ruled this was unfair and illegal.

The government tried to fix it by hiring more people, but that's expensive and slow. The authors of this paper asked: Is there a smarter way to fix the system without just throwing money at it?

The Old Way of Thinking: The "One-and-Done" Mistake

To understand the authors' solution, we first need to look at how experts usually study phone lines (called "call centers").

Standard math models (like the famous Erlang-A formula) treat a phone call like a customer walking into a store.

The Standard View: If you call, wait too long, and get frustrated, you hang up and leave forever. The store is happy because you're gone, and the line gets shorter.
The Reality of SNAP: If a person hangs up because they are hungry and need food, they don't give up. They call back. And back. And back.
- The Analogy: Imagine a person trying to get a ticket to a sold-out concert. If they can't get in, they don't go home; they stand outside the door and try to push through again five minutes later.
- The Result: Every time someone hangs up, they don't leave the system; they become a new person in line a few minutes later. This creates a vicious cycle where the line gets longer because people are hanging up.

The authors call this "Endogenous Congestion." It's a loop where the system's own failure (long wait times) creates the very traffic that clogs it up (re-dials).

The New Solution: A "Traffic Loop" Model

The authors built a new mathematical model (a "queueing framework") that accounts for this looping behavior. Instead of assuming people leave when they hang up, their model assumes:

Short Loops: People who hang up in frustration call back within hours.
Long Loops: People who get through but need more paperwork, or who successfully get benefits, will call back months later for "re-certification" (checking if they still qualify).

They used a "Fluid Approximation" to solve this.

The Analogy: Imagine trying to count every single drop of water in a rushing river. It's impossible. But if you treat the river as a continuous "fluid" flowing at a certain speed, you can easily calculate how much water is in the river and how fast it's moving.
The Application: Instead of tracking every single phone call, they treated the calls as a flowing stream of water. This allowed them to predict exactly how the system behaves when it is overwhelmed.

What They Found: It's Not Just About Hiring More People

Using data from the court case, they tested different ways to fix the bottleneck. Here is what their "dashboard" revealed:

1. Hiring more staff is expensive and often not enough.
The state of Missouri thought they needed to hire 150+ new people to fix the wait times. The authors' model showed that while hiring helps, it's not the only lever.

2. Fixing the "Process" is a superpower.
The model showed that small changes to how the interview works could have the same effect as hiring dozens of new people.

Speeding up the interview: If agents can talk faster (or use AI tools to handle simple questions), the line moves faster.
Making it easier to succeed: If the interview process is clearer so people don't get stuck needing more paperwork later, fewer people have to call back.
Waiting longer between checks: If the government checks your eligibility once a year instead of every six months, fewer people are calling back at the same time.

3. The "Bundled" Approach is Best.
The paper argues that you shouldn't just hire more people OR just change the rules. You should do a little bit of both.

The Analogy: Imagine a traffic jam. You can try to build a wider highway (hire more staff), but if you also remove a stop sign (speed up the process) and tell cars to take a different route (change the policy), you clear the jam much faster than just building the highway alone.

The Takeaway

The paper proves that the "standard" advice for fixing phone lines (just hire more people) is wrong for social services because it ignores the fact that desperate people keep calling back.

By using this new "traffic loop" model, agencies can see that they don't necessarily need to hire a massive army of new workers. Instead, they can fix the system by making the process faster, clearer, and less frustrating. This ensures that people who are actually eligible for help don't get denied just because they couldn't get through on the phone.

Technical Summary: Due Process on Hold: A Queueing Framework for Improving Access in SNAP

Problem Statement
The paper addresses the operational failure of social safety net call centers, specifically the Supplemental Nutrition Assistance Program (SNAP), where system congestion leads to "procedural denials." In the case of Holmes v. Knodell, Missouri's SNAP call centers were so congested that nearly 50% of application denials were procedural—resulting from applicants' inability to complete required interviews due to long wait times and disconnections, rather than actual ineligibility. The court ruled this a violation of procedural due process.

The core technical challenge is that standard queueing models used in operations research (specifically the Erlang-A model) fail to capture the unique dynamics of social service delivery. Standard models assume that customers who abandon a queue (hang up) are lost to the system forever. However, in SNAP and similar programs, applicants have no private outside options; if they abandon a call, they are highly likely to re-dial. This creates endogenous congestion: abandonment generates future arrivals (re-dials), which in turn worsen congestion, creating a feedback loop that standard models underestimate. Consequently, standard staffing guidance based on Erlang-A fundamentally understaffs these systems, leading to persistent access shortfalls.

Methodology
The authors propose a performance evaluation framework based on a custom queueing model derived from operations research, adapted to capture the specific "orbits" of social service callers.

Stochastic Model: The authors model the call center as a Markovian service network with four distinct states or "orbits" for callers:
- Fresh Arrivals: New applicants seeking enrollment.
- Short Re-dial Orbit: Callers who abandon and return within hours (e.g., same day).
- Long Re-dial Orbit: Callers who abandon and return days later, or those who complete a call but require follow-up documentation.
- Re-enroll/Re-certify Orbit: Successfully enrolled recipients who must return months later for re-certification.
- Lost: Callers who abandon and never return (procedural denials).
The model incorporates parameters for fresh arrival rates ( $\lambda$ ), service rates ( $\mu$ ), abandonment rates ( $\theta$ ), and re-dial rates ( $\delta$ ).
Fluid Approximation: To make the model analytically tractable for large-scale systems (justified by the high call volumes in the Holmes v. Knodell data), the authors derive a deterministic fluid approximation using a system of Ordinary Differential Equations (ODEs). This approximation is proven to converge to the stochastic model under a functional strong law of large numbers (FSLLN).
Parameter Fitting: The model parameters are calibrated using aggregated daily data from four Missouri DSS call centers disclosed in court documents (Exhibit 87). The authors use a robust fitting approach to estimate the fresh arrival rate ( $\lambda$ ) and abandonment parameters by minimizing the Mean Absolute Deviation (MAD) between model-predicted wait times and observed data across a range of plausible behavioral parameters.
Analytical Derivation: Using the steady-state solution of the fluid model, the authors derive closed-form expressions for six key performance metrics:
- Mean number of waiting callers.
- Mean waiting time.
- Average speed to answer (for non-abandoning callers).
- Procedural denial rate (total lost abandonments).
- Endogenous congestion from re-dials.
- Endogenous congestion from re-certification.

Key Results

Model Superiority over Erlang-A: When applied to the Missouri data, the standard Erlang-A model significantly underestimates the required staffing levels. In some scenarios, the Erlang-A model suggests a staffing shortfall of up to 84% compared to the authors' endogenous-congestion-aware model. The Erlang-A model fails because it treats abandonment as a system stabilizer (removing load), whereas the authors' model correctly identifies abandonment as a driver of future load via re-dials.
Comparative Statics: The authors analyze how operational levers affect performance. They find that increasing staffing ( $c$ ), increasing service speed ( $\mu$ ), and increasing the fraction of successful calls ( $p_+$ ) all yield intuitive improvements (reducing wait times and procedural denials).
Elasticity Equivalences: A key finding is that in the overloaded regime, increasing staffing and increasing service speed have identical proportional effects (elasticities) on key metrics like procedural denial rates and waiting times. This suggests that efficiency gains (e.g., via AI or better training) can substitute for hiring, provided the cost-benefit analysis favors the efficiency gain.
Bundled Interventions: The model demonstrates that combining modest staffing increases with system design changes (e.g., reducing Average Handling Time or lengthening re-certification cycles) yields significantly better outcomes than staffing alone. For instance, to reduce wait times below 2 minutes, the authors' model suggests that without hiring, handling time must be reduced by 75%, or re-certification periods extended to one year. With just 50 additional staff, a 50% reduction in handling time suffices.

Significance and Claims
The paper claims to provide the first queueing framework specifically designed to address the "emergent arbitrariness" in social service delivery, where systemic congestion—not a single algorithmic error—violates due process.

Policy Relevance: The framework allows agencies to move beyond "off-the-shelf" Erlang-A guidance, which is shown to be dangerously optimistic for social services. It enables policymakers to conduct ex-ante evaluations of how changes in program design (e.g., interview flexibility, re-certification intervals) and operations interact to affect access.
Systemic Diagnosis: The authors argue that fairness and accuracy in benefits provision are emergent properties of system performance. By quantifying endogenous congestion, the model provides evidence for whether applicants are afforded a "meaningful opportunity to be served," a legal standard for procedural due process.
Practical Tool: The authors introduce a dashboard (based on the fluid model) that allows stakeholders to explore trade-offs between staffing costs and service delivery improvements, offering a data-driven path to remedying the access barriers identified in Holmes v. Knodell.

The paper concludes modestly, noting that while the fluid model offers first-order insights, it is an approximation. A fully probabilistic analysis would be required to study the distribution of individual caller attempts, but the current framework provides a necessary and rigorous foundation for evaluating and improving access at scale.