Case Study – Emergency Department Overcrowding and Patient Flow Redesign

Introduction

Emergency department (ED) overcrowding is commonly framed as an emergency medicine problem, but it is a whole-of-hospital capacity problem that becomes visible in the ED, the only part of an Australian public hospital that cannot refuse work. The Australasian College for Emergency Medicine (ACEM) identifies the dominant driver as access block, where patients requiring admission remain in the ED beyond eight hours because no inpatient bed is available (ACEM, 2021). Access block is an output failure expressed as an input queue, so interventions aimed only at the front door predictably fail (Forero et al., 2011).

This case study examines patient flow at Riverbend Hospital, a hypothetical 400-bed metropolitan public hospital in an Australian capital city, using twelve months of invented data modelled on national patterns (Australian Institute of Health and Welfare [AIHW], 2023a). It defines the problem quantitatively, analyses causes through the input, throughput, output model, proposes an intervention bundle, and specifies an evaluation framework. The argument advanced is that the deficit lies outside the ED.

Case Context and Problem Definition

Riverbend operates a 34-space emergency department serving 310,000 residents. It recorded 68,400 presentations, of which 14,800 (21.6%) arrived by ambulance and 19,494 (28.5%) were admitted. Those admissions represented 19,494 / 27,850 = 70.0% of all hospital separations, so the ED is the hospital’s principal admission pathway.

Three signals prompted executive review. Only 57.9% of presentations were completed within four hours, against a state health target of 80% and the 90% National Emergency Access Target set under the 2011 national health reforms. Access block affected 42.3% of admitted patients, and only 63.5% of ambulance patients reached ED care within 30 minutes. Table 1 disaggregates performance by Australasian Triage Scale (ATS) category (ACEM, 2023).

Table 1: Riverbend Hospital emergency department performance by triage category, twelve-month reporting period

Note. Values are modelled estimates.

Two features of Table 1 are diagnostically important. Median waiting time is longer for ATS 3 (51 minutes) than for ATS 4 (38 minutes), inverting the acuity gradient, because ATS 4 patients are streamed to an ambulatory fast track while ATS 3 patients queue for cubicles occupied by admitted patients. Four-hour compliance for admitted patients (24.6%) is also less than half the discharged rate (71.2%). Both patterns point towards the ED to inpatient interface (Sullivan et al., 2016).

Quantifying the Capacity Deficit

Inpatient occupancy

Of the hospital’s 400 beds, 18 were closed for the year because of nursing vacancies, leaving 382 available. The average midnight census was 361.

Occupancy = occupied beds / available beds × 100 = (361 / 382) × 100 = 94.5%

Simulation shows the probability of a bed being unavailable rises sharply once average occupancy exceeds roughly 85%, and that above 90% a hospital operates in recurrent bed crisis (Bagust et al., 1999). At 94.5% Riverbend holds no buffer, so ordinary seasonal variation transmits directly to the ED.

Average length of stay and Little’s Law

Occupied bed days for the year were 361 × 365 = 131,765, against 27,850 separations.

Average length of stay (ALOS) = occupied bed days / separations = 131,765 / 27,850 = 4.73 days

Little’s Law holds that the average number in a stable system equals arrival rate multiplied by average time in system, L = λW (Little, 1961). For inpatients:

λ = L / W = 361 / 4.73 = 76.3 admissions per day, reconciling with 27,850 / 365 = 76.3

It also converts a target occupancy into a bed requirement:

Required beds = (λ × W) / target occupancy = (76.3 × 4.73) / 0.85 = 360.9 / 0.85 = 425

The shortfall is 425 – 382 = 43 beds. Capital expansion of that scale is neither fundable nor rapid, so the lever is W. Usable capacity at 85% occupancy is 382 × 0.85 = 324.7 beds:

W = L / λ = 324.7 / 76.3 = 4.26 days

Required reduction = 4.73 – 4.26 = 0.47 days, or 11.3 hours per admission, a relative reduction of 0.47 / 4.73 = 9.9%

This is the central finding: a ten per cent reduction in length of stay is arithmetically equivalent to opening 43 beds. Because Australian hospital ALOS has fallen steadily for two decades, that is demanding rather than implausible (AIHW, 2023b).

Emergency department occupancy at peak

Inside the ED, with a mean total ED time of 4.1 hours:

λ = 68,400 / 365 / 24 = 7.81 presentations per hour

L = λW = 7.81 × 4.1 = 32.0 patients, against 34 spaces = 94.2% mean occupancy

Averaged across the day this appears viable, but demand is not uniform. Between 16:00 and 22:00 arrivals rise to 11.4 per hour:

L = 11.4 × 4.1 = 46.7 patients, exceeding 34 spaces by 12.7, an implied occupancy of 137%

Twelve to thirteen patients each evening therefore have nowhere to be placed, the mechanism producing corridor care and ramping. The steady-state assumption does not strictly hold over a six-hour window, so this is an order-of-magnitude estimate.

Ambulance ramping

Of 14,800 ambulance arrivals, 36.5% were not transferred within 30 minutes, with a mean excess delay of 38 minutes:

Patients delayed = 14,800 × 0.365 = 5,402

Crew hours lost = (5,402 × 38) / 60 = 3,421 per year, or 3,421 / 365 = 9.4 per day

Approximately one crew shift of pre-hospital capacity is removed from the road each day at this hospital alone, transferring the deficit onto the state ambulance service and, through delayed responses, onto the community.

Root Cause Analysis: The Input, Throughput, Output Model

The input, throughput, output framework separates causes by the part of the system that owns them (Forero et al., 2011). Figure 1 applies it to Riverbend, including the access block loop through which an output constraint propagates backwards into throughput.

Input factors

Presentations grew 4.1% year on year, consistent with national growth driven by population ageing, chronic disease and constrained after-hours primary care access (AIHW, 2023a). ATS 4 and ATS 5 patients comprise 48.3% of volume, some potentially avoidable general practice type presentations. Input factors nonetheless explain little of the deficit: low-acuity patients achieve 82.1% four-hour compliance and consume ambulatory rather than acute resources, so removing them would move the headline figure only marginally.

Throughput factors

Genuine inefficiencies exist. Senior review occurs after junior assessment rather than at the front of the episode, biochemistry turnaround averages 71 minutes, and formal imaging reporting is unavailable after 22:00. The inverted ATS 3 and ATS 4 waiting times in Table 1 show streaming logic applied to ambulatory patients but not the acute stream. Eliminating every throughput delay would still leave admitted patients waiting for beds that do not exist.

Output factors

Output is the binding constraint. With occupancy at 94.5% and a shortfall of 43 beds, 8,246 admitted patients a year wait more than eight hours in a treatment space unavailable to new arrivals. Discharge timing compounds the mismatch: only 11% of ward discharges occur before 10:00, whereas admission demand peaks between 14:00 and 22:00, so beds are released hours after they are needed. Australian evidence links this to harm, associating overcrowding with increased mortality among patients admitted through emergency departments (Richardson, 2006; Sprivulis et al., 2006), while the Western Australian four-hour rule was later associated with mortality reductions where implemented (Geelhoed & de Klerk, 2012).

Proposed Interventions

The bundle in Table 2 is weighted towards output, in proportion to the causal analysis. Each element specifies a mechanism, not an aspiration, because time targets applied without capacity change produce reclassification rather than flow (Sullivan et al., 2016).

Table 2: Proposed intervention bundle by flow domain, with mechanism, expected effect and supporting evidence

Reducing access block from 42.3% to 25% changes the affected volume from 19,494 × 0.423 = 8,246 patients to 19,494 × 0.25 = 4,874, a reduction of 3,372, or 40.9%. If each spends 3.8 fewer hours in a treatment space, released capacity is 3,372 × 3.8 = 12,814 space hours per year, or 12,814 / 365 = 35.1 hours per day, supporting 35.1 / 4.1 = 8.6 additional episodes daily, equivalent to staffing 1.5 further treatment spaces continuously.

Assuming admitted compliance rises from 24.6% to 45% and discharged from 71.2% to 80%:

Compliant presentations = (19,494 × 0.45) + (48,906 × 0.80) = 8,772 + 39,125 = 47,897

Four-hour compliance = 47,897 / 68,400 = 70.0%, a gain of 12.1 percentage points and a relative improvement of 12.1 / 57.9 = 20.9%

Seventy per cent falls short of the 80% state target, an honest result rather than a failure of ambition. The bundle closes about three-fifths of the gap; the residual requires the 43 beds calculated earlier or substitution through hospital in the home.

Implementation and Evaluation

Implementation is staged across twelve months. Months 1 to 3 establish governance, appoint a patient flow director reporting to the executive, and activate the escalation protocol, which requires no capital. Months 4 to 6 commission the emergency medical unit and extend fast track. Months 7 to 9 roll out predicted date of discharge ward by ward, the element most dependent on medical engagement. Months 10 to 12 open the primary care clinic. Oversight sits within the existing clinical governance structure, which requires systematic monitoring of performance and escalation of deteriorating indicators (Australian Commission on Safety and Quality in Health Care, 2021), with monthly reporting against Table 3 and quarterly peer benchmarking (Productivity Commission, 2024).

Table 3: Evaluation framework showing outcome, process and balancing measures with baselines and twelve-month targets

The balancing measures deserve emphasis, because a four-hour target creates a documented incentive to move patients rather than treat them. Premature discharge would appear as a rise in 48-hour re-presentations and 28-day readmissions. Admitting to the short stay unit purely to stop the clock would show as a conversion rate above 20%. Reclassifying triage categories to flatter the seen-on-time statistic would show as an implausible shift in the ATS distribution, monitored monthly against ACEM implementation guidelines (ACEM, 2023). A bundle that improves outcome measures while degrading balancing measures has moved the problem, not solved it.

Conclusion

The Riverbend case demonstrates that emergency department overcrowding is largely an artefact of inpatient capacity. Four-hour compliance of 57.9% resolves into a discharged rate of 71.2% and an admitted rate of 24.6%, a difference explained by occupancy of 94.5% that leaves no buffer. Little’s Law converts that constraint into two equivalent solutions: 43 additional beds, or a 9.9% reduction in length of stay. The bundle pursues the second, and is projected to lift compliance to 70.0%, cut access block by 40.9%, and return roughly 9.4 ambulance hours a day to the road.

Two conclusions follow for practice. The unit of analysis for crowding is the hospital, not the emergency department, so accountability belongs with the executive rather than the ED director. Targets must also travel with balancing measures, because the Australian record shows time-based targets improve outcomes only when accompanied by capacity reform (Geelhoed & de Klerk, 2012; Sullivan et al., 2016).

References

Australasian College for Emergency Medicine. (2021). Statement on access block. ACEM.

Australasian College for Emergency Medicine. (2023). Guidelines on the implementation of the Australasian Triage Scale in emergency departments. ACEM.

Australian Commission on Safety and Quality in Health Care. (2021). National safety and quality health service standards (2nd ed.). ACSQHC.

Australian Institute of Health and Welfare. (2023a). Emergency department care activity. AIHW.

Australian Institute of Health and Welfare. (2023b). Admitted patient care: Hospital activity. AIHW.

Bagust, A., Place, M., & Posnett, J. W. (1999). Dynamics of bed use in accommodating emergency admissions: Stochastic simulation model. BMJ, 319(7203), 155-158.

Forero, R., McCarthy, S., & Hillman, K. (2011). Access block and emergency department overcrowding. Critical Care, 15(2), 216.

Geelhoed, G. C., & de Klerk, N. H. (2012). Emergency department overcrowding, mortality and the 4-hour rule in Western Australia. Medical Journal of Australia, 196(2), 122-126.

Kelly, A.-M., Bryant, M., Cox, L., & Jolley, D. (2007). Improving emergency department efficiency by patient streaming to outcomes-based teams. Australian Health Review, 31(1), 16-21.

Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383-387.

Productivity Commission. (2024). Report on government services 2024: Public hospitals. Australian Government.

Richardson, D. B. (2006). Increase in patient mortality at 10 days associated with emergency department overcrowding. Medical Journal of Australia, 184(5), 213-216.

Sprivulis, P. C., Da Silva, J.-A., Jacobs, I. G., Frazer, A. R. L., & Jelinek, G. A. (2006). The association between hospital overcrowding and mortality among patients admitted via Western Australian emergency departments. Medical Journal of Australia, 184(5), 208-212.

Sullivan, C., Staib, A., Eley, R., Scanlon, A., Flores, J., & Scott, I. (2016). National Emergency Access Targets metrics of the emergency department-inpatient interface. Australian Health Review, 40(4), 400-405.