Abandonment and Access

The System Sheds Load Before You Notice

When a patient calls a behavioral health clinic, gets told the next available appointment is six weeks out, and never calls back, that is not a no-show. It is not non-compliance. It is not low motivation. It is abandonment — a queueing event with a precise mechanical cause: the system’s offered wait exceeded the patient’s patience threshold.

Queueing theory has modeled this since Conny Palm’s 1937 work on impatient customers. The concept is straightforward. Every person who enters a queue carries a patience distribution — a maximum time they will wait before leaving. When the system’s delay exceeds that threshold, the customer abandons. In telephony, the caller hangs up. In healthcare, the patient disappears from the data entirely.

This distinction matters because abandonment is invisible by default. The patient who leaves does not generate a chart note, a billing record, or a complaint. They simply stop appearing. And when your measurement systems only count people who complete service, you systematically undercount demand and overestimate access.

Abandonment Is a System Property, Not a Patient Property

The instinct in healthcare operations is to treat abandonment as a patient behavior problem. No-show policies punish patients. Referral drop-off gets attributed to “patient engagement.” Prescription abandonment is filed under non-adherence. Each of these framings locates the failure inside the patient and leaves the system unexamined.

Queueing theory says otherwise. Abandonment rate is a function of three system parameters: arrival rate, service rate, and the number of servers. Given those three inputs, the abandonment rate is determined. You can change it by changing the system. You cannot change it by lecturing patients.

The Erlang-A model (Palm’s extension of the Erlang-C queue to include impatient customers) formalizes this. In an M/M/s+M queue — Poisson arrivals, exponential service times, s servers, exponential patience — the abandonment probability is a calculable function of offered load and patience rate. The model shows that abandonment rises steeply as utilization approaches 1.0, following the same nonlinear curve that governs wait times. This is not coincidence. It is the same mechanism. Long waits cause abandonment. High utilization causes long waits. The system’s capacity ratio drives both.

Five Types of Healthcare Abandonment

Abandonment in healthcare is not one phenomenon. It is at least five, each occurring at a different stage of the care pathway and each with different dynamics.

1. LWBS — Left Without Being Seen. The patient arrives at the emergency department, is triaged, and leaves before being evaluated by a provider. National LWBS rates historically sat around 2%, but post-2020 data from multiple systems shows sustained increases, with some high-volume urban EDs reporting 5-10%. The Emergency Department Benchmarking Alliance treats LWBS above 2% as a performance flag. LWBS is the most visible form of abandonment because the patient was physically present and then was not — but it still underestimates the problem because it does not count patients who saw the waiting room and never registered.

2. No-Shows in Scheduled Care. The patient has an appointment and does not appear. In primary care, no-show rates typically run 15-30%. In community mental health, the numbers are worse: studies document initial-appointment no-show rates of 40-60%, with one intervention study reporting a baseline of 52% no-shows when wait-to-appointment was 13 days, dropping to 18% when the wait was eliminated. The relationship between wait time and no-show probability is not subtle. It is roughly monotonic and well-documented.

3. Referral Drop-Off. A primary care provider refers a patient to a specialist. The patient never schedules, never appears, or never completes the referral loop. The ASPN Referral Study and subsequent analyses show that roughly 50% of specialty referrals are completed in typical practice. In rural systems with limited specialist access and long travel distances, completion rates fall further. A referral that is placed but never completed is a system loss — the patient entered the queue (was referred) and abandoned before service (the specialist visit).

4. Prescription Abandonment. The provider writes a prescription. The patient never fills it. Primary medication non-adherence — prescriptions written but never picked up — runs around 20-30% across populations. When prior authorization is required, abandonment escalates: data from the CoverMyMeds Medication Access Report shows that 37% of prescriptions requiring prior authorization that are denied are subsequently abandoned entirely. Cost is the other driver: abandonment rates for specialty drugs can reach 75% when out-of-pocket cost exceeds $100.

5. Prior-Authorization Abandonment. This is provider-side abandonment. The provider initiates a prior-authorization request, encounters delays or denials, and either gives up or routes the patient to a less-appropriate alternative that does not require authorization. Nearly half of pharmacists and 4 in 10 prescribers report that prior authorization regularly leads to treatment abandonment. This is the system abandoning the patient, not the reverse — though it shows up in no one’s abandonment metrics.

Loss Systems: When There Is No Queue at All

Most healthcare queues allow waiting — the patient can sit in the ED, remain on a waitlist, or hold a future appointment. But some healthcare resources operate as loss systems: if no capacity is available at the moment of need, the arrival is turned away. There is no queue. The patient is simply lost.

The Erlang-B formula models this. In an M/M/s/s system (s servers, no waiting room), the probability that an arriving customer finds all servers busy — and is therefore lost — is given by Erlang’s loss formula. The probability depends only on offered load (arrival rate times service time) and the number of servers.

ICU beds are a loss system. When all ICU beds are occupied, the patient requiring ICU-level care is either held in a less-appropriate setting (ED boarding, PACU hold), transferred out, or — in the worst case — receives a lower level of care. Surgical suites operate similarly during peak demand: if no OR slot is available, the case is postponed or cancelled. Psychiatric crisis beds in many communities are loss systems where a patient in acute psychiatric crisis who presents when no beds are available may be boarded in an ED for days or discharged with inadequate follow-up.

The Erlang-B result has a counterintuitive property that matters for capacity planning: loss probability is highly sensitive to the number of servers when offered load is near capacity. Adding one ICU bed to a 10-bed unit running at high occupancy can cut the blocking probability substantially — not by 10%, but by a much larger factor. Conversely, losing one bed (to staffing shortages, equipment failure, infection control) can spike blocking rates disproportionately. Kortbeek et al. demonstrated this in their analysis of coupled operating-theater and ICU systems, showing that Erlang loss bounds accurately bracket ICU rejection probabilities.

True Demand = Served + Abandoned

This is the core measurement problem. If your access metrics only count patients who completed care, you are measuring throughput, not demand. When a community mental health center with a six-week waitlist reports “stable caseload,” the stability may be an artifact of abandonment. Half of referrals may be dropping off before conversion. The schedule looks full because the system shed exactly enough demand to fill exactly the available supply.

Little’s Law (L = lambda W) tells you how many people are in the system at steady state. But lambda in Little’s Law is the effective arrival rate — the rate of customers who actually enter and are served. If arrivals balk (never enter the queue) or abandon (enter and leave), the observed lambda is lower than the true demand rate. The gap between true demand and observed throughput is the abandonment shadow.

This matters operationally because capacity planning based on observed demand will always undersize the system. If you build capacity for the patients you see, you will never have enough capacity for the patients you do not see — because they left before you could count them.

Behavioral health example. A community mental health center operates with 8 therapists, each carrying 25 active clients. The schedule is full. The waitlist is 6 weeks. Monthly referrals average 40. Monthly intake completions average 20. The center reports stable demand and adequate capacity. But 20 referrals per month are evaporating — people who were told “six weeks” and never called back, or who called back once, got voicemail, and gave up. True demand is not 20 intakes per month. It is 40. The system needs 16 therapists to meet actual demand, not 8. The apparent stability is abandonment masquerading as equilibrium.

Rural referral example. A critical access hospital refers patients to a regional medical center 90 miles away for cardiology, orthopedics, and general surgery. The hospital tracks referrals placed but not referrals completed. When someone finally audits the loop, completion rates are 45% for cardiology, 38% for orthopedics, and 55% for general surgery. More than half of orthopedic referrals — patients whose PCP determined they needed specialist evaluation — never arrived. The referral network is not a functioning queue. It is a loss system with a 50%+ blocking rate, except the “blocking” is invisible because the patient quietly gives up rather than being formally turned away.

Product Implications

Software that supports healthcare operations must treat abandonment as a first-class metric, not an afterthought.

Track abandonment by stage. Instrument each transition in the care pathway: referral placed to referral scheduled, scheduled to attended, attended to follow-up completed. Measure conversion rates at each stage. The stage with the lowest conversion rate is the binding constraint for access.

Measure time-to-abandonment. Do not just count how many patients abandon. Measure when they abandon. If most no-shows occur when the wait-to-appointment exceeds 10 days, that is a designable threshold. If most referral drop-offs happen within 72 hours of referral (before the patient ever contacts the specialist), the failure is in the handoff, not the wait.

Alert on abandonment rate shifts. A rising LWBS rate is a leading indicator of ED throughput failure — it signals that delays have crossed the patience threshold before boarding hours or door-to-provider times fully register. A rising referral abandonment rate signals network degradation. These are earlier signals than utilization or wait-time metrics because abandonment responds to the tail of the wait distribution, not the mean.

Calculate true demand. Every access dashboard should display both served volume and estimated true demand (served + abandoned + balked). Without this, capacity planning will always chase observed demand and never close the access gap.

Warning Signs

• Stable demand despite known access barriers. If wait times are growing but volume is flat, abandonment is absorbing the excess demand. The system is not in equilibrium. It is shedding load.
• No-show rates above 20% treated as a patient problem. If the response to high no-shows is reminder calls and cancellation fees rather than wait-time reduction, the organization is optimizing around the wrong variable.
• Referral completion not tracked. If the system measures referrals placed but not referrals completed, it literally cannot see half the access problem.
• Prior-auth denial rates without treatment completion follow-up. A denial that results in the patient receiving no treatment is a system failure, not an administrative outcome.
• Loss-system resources without blocking probability monitoring. If ICU beds, crisis beds, or OR suites are managed without calculating rejection rates from Erlang-B or equivalent models, capacity decisions are being made blind.

Integration Hooks

Human Factors M3 (Pattern Recognition). Abandonment is a non-event. The patient who did not show, the referral that was never completed, the prescription that was never filled — these are absences, not presences. Human pattern recognition is systematically poor at detecting non-events. This is why abandonment persists as a blind spot: the signal is the dog that did not bark. Product design must compensate by making the invisible visible — surfacing abandonment counts, not just service counts.

Workforce M2 (Turnover as Workforce Abandonment). Employee turnover follows the same queueing logic. A nurse or therapist who tolerates six months of mandatory overtime, inadequate support, or stagnant wages is a customer in a queue — waiting for conditions to improve. When the wait exceeds their patience threshold, they leave. Organizations that measure only retention (the employees who stayed) and not departure timing and reasons (the abandonment signal) will underestimate workforce demand exactly the way clinics underestimate patient demand. The mechanism is identical. The math is the same.