Development of a Digital Twin to Analyse Waiting Lists in a Sleep-Disordered Breathing Unit

1. Introduction

Sleep disorders are a significant health problem, affecting an estimated 10–30% of the global population (Chattu et al., 2019; Haba-Rubio et al., 2016; Morin et al., 2006; Song et al., 2024; Young et al., 2002). Within this group, respiratory sleep disorders are particularly relevant, with obstructive sleep apnoea (OSA) being one of the most prevalent and impactful entities. OSA is associated with marked impairment in quality of life (Chalet et al., 2024), increased cardiovascular risk (Craciun et al., 2025) and a higher likelihood of road traffic accidents (Karimi et al., 2015). Its high prevalence, together with the need for specific diagnostic tests, generates substantial care pressure, and many specialist units accumulate long waiting lists that in some settings exceed one year (Flemons et al., 2004; Santos-Jaén et al., 2022).

To address this challenge, several strategies have focused on organisational redesign and resource optimisation (Naiker et al., 2018), including improved scheduling, better coordination across care levels and enhanced management of patient flows. In parallel, growing data availability and technological advances have fostered digital solutions that combine simulation models with artificial intelligence (AI) approaches. In respiratory sleep medicine, AI-based screening and risk-stratification models have been proposed to identify patients at higher probability of OSA and prioritise their access to diagnostic tests (Casal-Guisande et al., 2025; Ferreira-Santos et al., 2022). While these tools can improve allocation of diagnostic resources, they do not capture the global dynamics of the care system, as they fail to explicitly model the interaction between arrivals, installed capacity and process-time variability, which jointly determine waiting times and resource utilisation.

In this setting, discrete-event simulation (DES) offers a particularly suitable framework for analysing and redesigning healthcare processes. DES models represent real systems through entities, events and resources, enabling computational analysis of complex dynamics that are difficult to assess using conventional approaches alone (Forbus & Berleant, 2022a). In healthcare, DES has proven useful for anticipating trends, evaluating multiple improvement scenarios and detecting bottlenecks (Van Lent et al., 2012; Vanbrabant et al., 2019), with applications mainly in emergency departments (Gartner & Padman, 2020), clinics (Hribar et al., n.d.; Sauer et al., 2016; Yakutcan et al., 2021), critical care services (Williams et al., 2020) and surgical services (Lenin et al., 2015), with aims such as optimising patient flow, resource allocation and appointment configuration. More recently, some of these DES models have been described as operational digital twins of healthcare services, providing virtual replicas that support safe testing of organisational changes before real-world implementation.

Despite the growing interest in DES in healthcare (Álvarez-Vázquez et al., 2025; Dehghani et al., 2017; Doudareva & Carter, 2022a; Forbus & Berleant, 2022b; Gjerloev et al., 2024; Günal & Pidd, 2010; Liu et al., 2020; Ouda et al., 2023; Vázquez-Serrano et al., 2021; Zhang, 2018), its use in certain specialties remains limited, and sleep units are a representative example of this gap. To our knowledge, only one prominent patient flow model has been reported for a multidisciplinary sleep centre in Calgary (Pendharkar et al., 2015), underscoring the scarcity of studies in dedicated sleep units.

Against this background, the present study aims to develop a DES model specifically tailored to the Sleep-Disordered Breathing Unit of the Pneumology Department at Álvaro Cunqueiro Hospital in Vigo, Spain. This unit is characterised by heterogeneous patient profiles, multiple coexisting care pathways and constrained diagnostic resources. During the study period, waiting time for respiratory polygraphy exceeded one year for non-urgent patients, highlighting the need for analytical tools that can describe operational dynamics and evaluate improvement options without intervening directly in clinical practice.

This work makes three main contributions:

• Propose a DES model that structurally represents patient flow, resources and operational rules in the unit, allowing analysis of system behaviour under alternative organisational scenarios.
• Identify and quantify, using real historical data, the main bottlenecks and operational inefficiencies that drive the formation and persistence of waiting lists.
• Conduct a formal validation of the model, establishing its potential as a prospective tool for evaluating improvement scenarios and supporting strategic decision making.

2. Materials and Methods

2.1. Study Design

A retrospective simulation study was conducted to model patient flow in a Sleep-Disordered Breathing Unit. The aim was to develop and validate a DES model capable of reproducing the real behaviour of the unit and providing a methodological basis for prospectively evaluating alternative organisational scenarios. Figure 1 summarises the overall simulation scheme.

The study adopted a four-stage design. First, the patient flow to be modelled was defined by in-situ mapping of the unit, identifying the main clinical stages of the care process. Second, the data required for model parametrisation were extracted and pre-processed from the hospital information system from the year 2024. Third, a computational DES model was created in MATLAB, specifying entities, resources, queues and referral logic and generating indicators such as mean waiting time and queue length at each stage. Finally, the model was calibrated and validated using pre-defined error metrics against observed queue and waiting-time data from the end of 2025, and the resulting structure was retained as the simulation model for subsequent analyses.

To ensure reproducibility and methodological transparency, model documentation was structured according to the STRESS (Strengthening the Reporting of Empirical Simulation Studies) guidelines (Monks et al., 2019), summarized in Table 1.

2.2. Patient Flow Definition

The study was conducted in the Sleep-Disordered Breathing Unit of the Pneumology Department at Álvaro Cunqueiro Hospital (Vigo, Galicia, Spain). The unit provides a dedicated diagnostic–therapeutic pathway for these conditions, with OSA as the predominant entity and an annual workload of nearly 2,000 patients assessed for suspected disease. All patients referred from Primary Care (PC) and other specialties during 2024 were included, without restrictions on age, sex or clinical profile, in order to reproduce the unit’s real case mix.

From a clinical-organisational perspective, diagnostic capacity is structured mainly around respiratory polygraphy (PLG) as the standard test, with polysomnography (PSG) reserved for complex cases and overnight pulse oximetry (POX) used as a screening tool in low-to-moderate suspicion. After PLG or PSG, results are communicated in a follow-up consultation, where treatment is decided, with CPAP as the reference therapy for moderate-to-severe OSA and alternatives such as mandibular advancement devices or conservative measures in selected cases.

For modelling purposes, the care pathway was represented using six stages: e-Consultation, face-to-face consultation, POX, PLG, PSG and follow-up consultation, as shown in Figure 2.

Once the patient flow had been defined, the central element of the simulation—a state-transition matrix describing movement probabilities between stages—was parameterised by combining analysis of historical records with direct observation and expert input from the Unit Head, including a small probability of direct discharge at each stage to reflect non-protocolised pathways, as detailed in Table 2.

2.3. Data Collection and Processing

Data for DES parametrisation and validation were obtained from a retrospective observational study spanning form 1st January through 31st December 2024. Information was extracted from the information systems of Álvaro Cunqueiro Hospital and integrated from two main sources: appointment-scheduling systems (daily capacity, arrival and discharge rates, waiting lists and unannounced no-shows) and internal operational logs (effective professional availability). Using a full calendar year allowed both seasonal variation in demand and fluctuations in service capacity to be captured.

The model relied on a set of input parameters describing the operational logic and constraints of the real system, which are summarised numerically in Table 3. To assess the model’s ability to reproduce waiting list dynamics, a retrospective validation scheme was defined using data from the end of 2025, comparing simulated values with the actual status of queues and accumulated demand.

The study complied with current data-protection regulations and the principles of the Declaration of Helsinki, using only aggregated administrative and management data without access to identifiable clinical records.

2.4. Model Construction

Once the care pathway had been defined and operational parameters estimated, the conceptual model was implemented in MATLAB R2025b using Simulink and SimEvents. A modular architecture was adopted, with each stage represented as an interconnected functional block, modelling patients as dynamic entities and clinical units as finite-capacity servers with associated queues. Routing between stages was governed by the previously parameterised state-transition matrix (Table 2).

The model incorporated four main structural components: differentiated demand generation according to referral source, dynamic capacity management based on estimated daily service rates, probabilistic modelling of no-shows as decision nodes within queues, and time-varying resource availability according to the real work calendar, including weekdays, weekends and periods of reduced activity. Figure 3 displays the high-level Simulink/SimEvents block diagram, showing entity flows, queues and resource allocation across the care pathway.

Definition of Key Performance Indicators (KPIs)

After implementing the operational logic, the model was instrumented to automatically record two quantitative performance metrics at each care stage. The first was the mean waiting time in queue, quantifying the average delay from a patient’s arrival at a stage to the start of service, computed as the mean time spent in waiting buffers by all processed entities. To ensure this metric reflected steady-state behaviour, data from the initial warm-up period, during which the system evolves from initial conditions to a stable regime, were excluded.

The second KPI was the mean queue length, representing the average occupancy of waiting lists and obtained as the time-weighted average number of entities in queue. This indicator supports continuous identification of saturation points and dynamic bottlenecks at each stage.

2.5. Validation Metrics

Model fidelity in reproducing real-world system dynamics was assessed using a retrospective validation scheme with a two-year simulation horizon, from 1st January 2024 through 31st December 2025. Ten independent replications with different random seeds were run to capture stochastic variability in the care process. Outputs were collected at 10 temporal cut-off points (the final simulation date and the preceding nine weeks), recording for each care stage the two predefined KPIs. At each cut-off, average values across replications were compared with hospital historical data for the corresponding dates.

To quantify model–data agreement, three predictive performance metrics were used: Relative Percent Difference (RPD), to characterise over- or under-estimation from a management perspective; Root Mean Squared Error (RMSE), as a global measure of accuracy sensitive to large deviations; and Mean Absolute Error (MAE), providing a direct estimate of average error in the original units of each indicator. These metrics were computed both by care stage and at global level for the full patient pathway.

3. Results

Results were analysed at three levels: individual stage, overall system and complete patient pathway. As PSG is scheduled and managed by the Neurology Department rather than Pneumology, validation results for this stage are not reported and the analysis focuses on the stages directly operated by the Sleep-Disordered Breathing Unit.

3.1. Validation of Waiting Times

Table 4 summarises the waiting-time validation results for each of the five modelled care stages.

A marked heterogeneity in model fit was observed across stages. PLG showed the best performance, with an RMSE of 5.48 days, an MAE of 4.34 days and an RPD of 2.9%, indicating high fidelity in reproducing delays in this critical diagnostic phase. e-Consultation and POX presented an intermediate error (RPD 21.1% and 28.1%, respectively), whereas face-to-face consultation and, particularly, the follow-up consultation showed larger discrepancies (RPD 44.5% and 73.7%, respectively), suggesting the influence of prioritisation decisions and organisational factors not explicitly captured by the model. At system level, the weighted mean waiting time showed a moderate fit (global weighted RPD 34.6%), and the full patient pathway yielded an RPD of 10.4%, indicating that the model reasonably approximates the overall time spent in the circuit despite local errors.

The stage-specific fit for waiting times is summarised in Figure 4. Figure4a compares observed and simulated mean waiting times at the 10-validation cut-offs for each stage; points close to the identity line indicate better agreement, which is most evident for PLG and clearly worse for the follow-up consultation. Figure 4b displays a heatmap of the three-error metrics by stage, making the contrast between the low relative error of PLG and the high discrepancies of the follow-up consultation visually apparent. Weekly time-series comparisons and replication-variability plots are provided in the Supplementary Material.

3.2. Validation of Number of Patients in Queue

Table 5 presents the validation results for the mean number of patients in queue at each care stage.

The fit was generally better than for waiting times. PLG again showed a good performance with an RMSE of 28 patients, an MAE of 24.53 patients and an RPD of 2.7%, and both the face-to-face consultation and POX exhibited very low relative discrepancies (RPD 1.9% and 3.1%, respectively), reflecting a good ability of the model to reproduce workload at these stages. In contrast, e-Consultation (RPD 16.9%) and the follow-up consultation (RPD 14.7%) showed larger errors, consistent with their higher variability and with non-explicit organisational decisions. Overall, the weighted RPD for the number of patients in queue was 3.6%, and 3.5% for the full patient pathway, indicating that the model consistently reproduces throughput and the aggregate service pressure of the unit, providing a solid basis for evaluating reorganisation scenarios.

Figure 5 provides a graphical synthesis of these results. Figure 5a compares observed and simulated numbers of patients in queue at the 10-validation cut-offs for each stage. Figure 5b shows a heatmap of the three-error metrics by stage, visually highlighting the low errors for face-to-face consultation, POX and PLG and the higher discrepancies for e-Consultation and follow-up. Weekly time-series comparisons and replication-variability plots are provided in the Supplementary Material.

4. Discussion

The Sleep-Disordered Breathing Unit at Álvaro Cunqueiro Hospital faces increasing demand for sleep studies, particularly PLG, leading to long waiting lists and clinically relevant diagnostic delays. The DES model offers a quantitative representation of current operations and estimates how queues and waiting times evolve along the care pathway.

Validation shows very good agreement for workload (number of patients in queue) and moderate agreement for waiting times: PLG exhibits low relative errors for both indicators, whereas follow-up consultation concentrate the largest discrepancies, likely reflecting prioritisation and organisational decisions not recorded in information systems. Overall, the model reproduces aggregate service pressure and mean total time in the system with limited deviation, despite local misestimation at some stages.

The model is not intended to predict the exact waiting time of individual patients, but to compare organisational scenarios consistently. Changes in PLG capacity, consultation schedules or prioritisation rules can therefore be explored to estimate the direction and approximate magnitude of their impact on waiting lists and workload, in a conservative way that avoids underestimating system pressure. In line with Box’s dictum (Box & Draper, 1987) that “all models are wrong, but some are useful”, the value of this model lies in supporting “what-if” analyses and guiding planning and reorganisation decisions in the unit.

4.1. Comparison with the Literature

Table 6 positions this DES model alongside previous applications in outpatient, diagnostic and critical care contexts, where simulation has been used to identify bottlenecks, test capacity changes and avoid unintentionally harmful interventions before real-world implementation. The only earlier model focused on a sleep centre, developed in a multidisciplinary setting, used patient flow simulation to explore access constraints and prioritisation policies, showing that intuitive changes did not always shorten time to clinically meaningful outcomes. Other DES studies have addressed intensive care bed occupancy, endoscopy throughput or chronic disease pathways such as COPD, often relying on commercial software and validation based mainly on face validity or high-level indicators.

Against this background, the present work extends the role of DES from a general decision-support tool to a quantitatively validated engine for “what-if” analyses in a monographic Sleep-Disordered Breathing Unit. It is, to our knowledge, one of the first models specifically tailored to this type of unit, implemented in MATLAB to facilitate adoption in settings where this software is already available, and subject to formal retrospective validation using MAE, RMSE and RPD. These features complement the model’s demonstrated ability to reproduce aggregate workload and support scenario comparison, helping to bridge the current gap in modelling of sleep units and offering a transferable methodological reference for centres facing similar waiting list pressures.

4.2. Study Limitations

In line with other DES studies in healthcare, the present model must be interpreted in light of several limitations that partly explain the heterogeneous validation results. A first constraint concerns the state-transition matrix: because detailed routing information could not be directly extracted from hospital information systems, transition probabilities were derived by combining administrative data with clinicians’ expert judgement, which captures uncoded operating rules but inevitably introduces subjectivity and possible bias.

Moreover, the lack of structured urgency fields in corporate systems prevented formal priority queues from being implemented, likely contributed to the greater errors observed in stages with more intense clinical triage, such as the follow up consultation. Finally, the study is single centre and reflects the specific configuration of one pneumology based sleep unit; although the modelling and validation approach is transferable, direct generalisation to other settings should be made cautiously and requires tailored reparameterization.

4.3. Practical Implications and Future Work

Despite these limitations, the model remains a useful tool for understanding the global behaviour of the unit and for analysing organisational scenarios at the aggregated level for which it was designed. Its ability to approximate overall workload and key stages such as PLG supports its use as a virtual testbed to evaluate increases in diagnostic capacity, redistribution of weekly schedules, fast-track circuits for selected profiles or changes in the role of e-Consultation in initial triage. Rather than describing individual trajectories, the model provides robust estimates of the relative impact of planning decisions on waiting lists and system pressure and, in practice, behaves as an operational digital twin that mirrors the unit’s performance under alternative configurations.

Future work will focus on “what-if” scenarios in which AI-based risk-stratification tools modulate referral and prioritisation flows, while keeping the simulation aggregated. For example, redirecting low-risk OSA cases to lower-intensity circuits or prioritising high-risk patients for PLG. It will also be important to represent urgency or clinical-severity strata as aggregated patient classes with differentiated priorities and demand patterns, and to conduct prospective validations in which model-based predictions are compared with the outcomes of real organisational interventions.

5. Conclusions

This work presents a DES model applied to the Sleep-Disordered Breathing Unit of Álvaro Cunqueiro Hospital, using real-world data to reproduce the care pathway and quantify its performance. The model developed has proved both methodologically feasible and operationally useful; despite heterogeneous accuracy across stages, it approximates the global system workload well and shows particularly strong agreement in key stages such as PLG, making it suitable for comparative “what-if” analyses of organisational scenarios. In this sense, the model functions as an operational digital twin of the unit, providing a virtual representation that can be used to explore alternative configurations without disrupting routine care.

The discrepancies observed in stages highlight structural limitations in activity recording, notably the absence of explicit clinical-urgency stratification and the lack of traceability for certain organisational decisions, which constrain both model accuracy and the ability to monitor the care process appropriately. At the same time, these limitations point to clear areas for improvement in the unit’s information systems.

Finally, this study provides one of the first documented DES applications in a dedicated sleep unit and lays the groundwork for future work aimed at incorporating urgency stratification and aggregated clinical attributes, as well as deploying the model as a decision-support tool to reduce waiting lists and improve access to diagnosis and treatment for OSA.