A manera de introducción

Although relatively scarce, online simulations have been developed for use in healthcare applications; most commonly for modelling patient flows and treatment processes within Emergency Departments, where planning horizons are very short (on the scale of hours).

Hoot et al. (2008) report the development of a generic ED model which uses discrete event simulation to make forecasts of seven performance indicators; including waiting count, waiting time, occupancy level, length-of-stay, boarding count (the number of patients awaiting admission) and boarding time (the time between requesting a hospital bed and receiving it). The authors pay particular attention to validating the model, reporting the use of a “sliding window” technique which partitions their data into fitting and testing subsets which do not overlap. The window contains four weeks of ED data which parameterises the model and moves forward in time in 10-minute increments, updating the simulation parameters as it advances. The outputs generated by the simulation are the mean of 1000 replications compared against their counterparts from the testing subset via their steady-state distributions (independent of time), and Pearson’s 𝑟 coefficient of correlation at 2, 4, 6 and 8-hour forecasts. The correlation coefficient indicates how much of the variation in the testing data can be explained by the simulation model, and each estimate is benchmarked against the autocorrelation at the same intervals from the testing data alone. While this shows that the simulation model is likely to outperform an autoregressive forecasting model, it may be difficult to diagnose issues during development using this statistic. The authors also conduct a residual analysis to show that the forecasts are unbiased, although other properties of the

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distribution of the simulation outputs (such as the variance) are lost if the replications are averaged to obtain a forecast. Additionally, the ability to update the simulation parameters automatically (typically via an auto-validation component) may not be a trivial development for complex simulations. Therefore, the sliding window method may be difficult to apply in a more general context, especially during early stages of development.

Tan et al. (2013) also focus on the Emergency Department, developing a comprehensive model which aims to improve both the supply of ED resources and the management of patient demand. On the supply side, a symbiotic simulation is developed which generates demand forecasts based on the current ED state (or “snapshot”) along with historical data. The snapshot contains current queue conditions, doctors’ availabilities, patients’ statuses and arrival rates. The demand estimates from the symbiotic simulation are used to generate an optimised schedule for the supply of resources, such as doctors, over relatively short planning horizons. The author’s development of an symbiotic simulation which informs an optimisation component (and vice versa) is the only known application of this type in a healthcare setting, although the scope is solely concerned with the Emergency Department.

Marmor et al. (2009) and Espinoza et al. (2014) also develop real-time simulations of Emergency Departments, albeit with slightly different focuses. Since EDs normally have one of the highest throughput rates of any hospital department, both models disaggregate daily arrival rates into hourly rates to facilitate decision making over planning horizons of less that one day. Interestingly, both papers report challenges with initialising the models, due to

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incomplete data to represent the real system’s state at run-time. This is probably to be expected given the frequency at which the models are intended to be run, coupled with manual data entry by ED receptionists. Both models overcome this challenge in a similar way; by running a warm-up period to populate the model first, and then by injecting the information associated with patients who are

observable. Espinoza et al. (2014) refer to models in which the initial conditions are imputed in this way as “mixed input” simulations. Additionally, the authors investigate various levels of data completeness in order to assess the feasability of using their approach in practice. While data availability is clearly an important issue when modelling an ED on time-scales of less than one day, this research is concerned with the management of inpatient beds, where patients typically stay days or weeks before being discharged. On time-scales such as this, data availability issues are not expected to be encountered as regularly.

Bahrani et al. (2013) develop a real-time simulation to aid operational decision making over similar planning horizons (4-8 hours) to Hoot et al. The model focuses on a subsection of the clinical pathway for cardiac patients who arrive as emergencies and uses three metrics to assess the performance of each simulation; patient total waiting time, total hospital cost, and percentage of patients discharged. The performance metrics are computed under different scenarios which can be defined by the user, or from a pre-selected list, including the base case (running under the current configuration of the real system), additional ED staff, additional cardiac staff, additional beds or reductions in these resources. Using a similar approach to Vanberkel et al. (2011), the estimates of the three performance indicators are intended to be judged by

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hospital staff in the light of the criteria considered to be most important at the time, before implementation in the real system.

Finally, Mousavi et al. (2011) report the development of a system for the real- time monitoring of patient quality-of-care throughout a hospital, using a Healthcare Quality Index (HQI) of their formulation. Observed events in the real system are tracked over time, which correspond to parameters in a discrete event simulation model. The simulation is run under the latest parameter values, and the performance statistics which are generated form the basis of the aggregate HQI calculation, to provide a real-time indication of quality-of-care.