# Literature \ This page summarises how **published ambulance DES** represent key elements of the ambulance system. It builds on the excellent review by Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)), whose clear structure and introduction to ambulance DES have shaped how I organise the sections here. I include the DES from that review, and I have also read and added more recent ambulance DES models. \ # Call arrival timing In all DES studies, call arrivals are modeled using a **Poisson** process, so inter-arrival times are exponential. This is standard for arrival processes in healthcare DES models. Some studies use a **Homogeneous Poisson process (HPP)** with a single arrival rate for the entire simulation period. However, most use a **Non-homogeneous Poisson process (NHPP)** where the arrival rate varies over time (e.g., by hour of day or day of week). > **Note: View studies** > > HPP: > > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > > NHPP by time of day only: > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - by period (00:00-08:00, 08:00-16:00, 16:00-00:00) > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - by 2-hour intervals > > NHPP by time of day and day of week: > > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - by 2-hour intervals and day of week > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) - by hour and weekday/weekend > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - by hour and weekday/weekend > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - by hour and day of week > - Wu and Hwang ([2009](#ref-wu_using_2009)) - by hour, day of week and month > > NHPP incorporating call location: > > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) - by time of day, day of week and zone > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) - by time of day and zone > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) - by node > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) - live data from Baidu Heatmap giving information on number of people in each grid, extracted on a hourly basis, to get representative data for each hour from Monday to Sunday > > Trace-driven: > > - Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) (designed to allow it, but no current access, so reports sampling, as above) \ # Call location Models differ in how they represent where call occur: - Some do **nothing** to represent location. - Some embed location in the **NHPP**, giving each zone its own arrival rate. - Some generate calls first, then **assign each call to a zone** using a probability distribution, with that distribution sometimes time-varying. Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)) note that studies generally assume demand is located at the **centre** of the corresponding zone (though not always). > **Note: View studies** > > Do not represent call location: > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) > > NHPP incorporating call location (as above): > > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) > > Assign zones to generated calls: > > - Wu and Hwang ([2009](#ref-wu_using_2009)) - cluster historical calls into nodes using Nearest Neighbor Hierarchical clustering, then estimate probability a call comes from each node, and use that for a **multinomial distribution** sampling probability of each node. > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - calls are **evenly distributed** among the 4 regions > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - city divided into cells, calls assigned using an **empirical discrete distribution** over cells that **varies by time of day and day of week**, and coordinates drawn randomly within the chosen cell. > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) > - Urgent calls: assign to zone using **discrete distribution** with probability proportional to demographic weight. > - Transfer calls: assigned to hospital (85%) or home (15%) - home coordinates drawn randomly. > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - call locations within each district sampled from an **empirical distribution** for each **4‑hour interval over the week**. > > *Empirical is often used when data doesn't fit well to a distribution. An empirical distribution will divide the data into groups and calculate the probabilities of each.* > > Unclear call location mechanism: > > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) In the studies, call location typically affects **travel times** - but can also influence resource dispatching, hospital selection and shifts. > **Note: View studies** > > From what I can spot (may have missed some): > > - Wu and Hwang ([2009](#ref-wu_using_2009)) - travel time, maybe hospital selection. > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - travel time. > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - travel time to scene (not to hospital). > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - dispatch, travel time, hospital selection, shifts (number of ambulances at base). > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - travel times. \ # Call categories Some studies don't include call categories. Studies that include call categories will sample probability of each, and this can be time-varying. > **Note: View studies** > > No call category: > > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) (USA) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) (USA) > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) (Brazil) > - Lee et al. ([2012](#ref-lee_simulation-based_2012)) (Korea) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) (China) > > Include call category: > > | Study | Country | Categories | How assigned | > |----|----|----|----| > | Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) | UK | C1, C2, C3, C4 | User-supplied frequency distribution which can vary by hour of day | > | Pinto et al. ([2015](#ref-pinto_generic_2015)) | Brazil and UK | All calls receive attributes concerning nature of emergency, category of call, type of ambulance required, RRV requirement, delivery requirement, and whether dispatch will be missed. Basic life support (BLS), Advanced life support (ALS), Mental care support (MCS), Rapid response vehicle (RRV) | Empirical distribution | > | Wu and Hwang ([2009](#ref-wu_using_2009)) | Taiwan | Advanced life support (ALS) or basic life support (BLS) team | Multinomial distribution | > | Gigante and Azevedo ([2022](#ref-gigante_study_2022)) | Brazil | Basic support vehicle or advanced support vehicle | Distribution (95% basic, 5% advanced) | > | Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) | France | \(1\) Primary or secondary (2) Severity (0, 1, 2, 3) | Probabilities | > | Kergosien et al. ([2015](#ref-kergosien_generic_2015)) | Canada | \(1\) Urgent or transfer (2) If urgent, transfer to hospital or not | Probabilities | > | Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) | Singapore | Acuity scores | \- | > | Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) | Canada | Unclear | Unclear | > | Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) | New Zealand | Priority 1 and 2 | Unclear | > | Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) | France | Primary or secondary, and priority levels too | Probabilities | > | Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) | Netherlands | | | As described in Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)), reasons for including include: - Assign **hierachy** to queued calls. - Impact **travel times**. - Impact **activity times** (e.g., time on site, drop off time, in hospital time). - Impact on whether **activities** happen (e.g., whether conveyed). Output metrics may be analysed by category. > **Note: View studies** > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) - care model (hear-and-treat, see-and-treat or see-and-convey), and ED acuity level (1 highest 5 lowest). > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - whether require ambulance, whether call is non-emergency, whether call requires conveyance to hospital, whether call will cause a missing dispatch i.e., care on scene no longer necessary and ambulance makes a missing travel. > - Wu and Hwang ([2009](#ref-wu_using_2009)) - on-scene time, in-hospital time. > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - unclear. > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - order of queued calls, whether require transport to hospital, on-site time, travel time, drop-off time. > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - - > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - on scene treatment time. > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) - appears to be hospital drop-off time and hospital selection. \ # Queue and dispatch policy Normally nearest available vehicle. Some incorporate call priority or possible reassignment to Cat1. Some look for team belonging to specific area first. Some include busy crews, if will finish their job soon. > **Note: View studies** > > **Nearest available vehicle:** > > - Pinto et al. ([2015](#ref-pinto_generic_2015)) > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) > - Wears and Winton ([1993](#ref-wears_simulation_1993)) > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) > - Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) > - Aringhieri ([2010](#ref-aringhieri_integrated_2010)) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > - Lee et al. ([2012](#ref-lee_simulation-based_2012)) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) > > **Nearest available vehicle, conditioned on call priority:** > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) - Queue order by Cat1-4 priority, but if they have waited a long time, they may have their priority increased. There is also balking due to max queue size and reneging for lower priority incidents to drop out entirely or switch to ED attendance path ([source](https://nhsengland.github.io/AmbModelOpen/run/)). > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - Queue order depends on call priority. > - Wu and Hwang ([2009](#ref-wu_using_2009)) - Queue order depends on priority, but lower priority incidents can increase in priority if wait beyond a threshold. Some supply can be marked as holdout so a subset of ambulances is reserved for Cat1 incidents, either alwayds or triggered under certain conditions. > > **Nearest base:** > > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - If no crews available, checks next nearest base. > - Iskander ([1989](#ref-iskander_simulation_1989)) - If no crews available in (or en-route to) nearest or neighbouring bases, it queues at nearest base. > > **Crews/base assigned an area:** Each rescue team or base is assigned a specific area. If assigned team unavailable or all teams of assigned base are busy, then the closest available rescue team/base must take it. > > - Gunes and Szechtman ([2005](#ref-gunes_simulation_2005)) (helicopters) > > **Team with smallest estimated arrival time including crews on a job** (if soon to finish and nearby, they might be smallest): > > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) > > **Nearest available vehicle, but possible to reassign a rescue team serving low priority class to high priority** - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) list two examples, neither are DES. > > **Unclear:** > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) \ # Travel time modelling In Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)), they state that travel times are related to: - Distance travelled - Traffic conditions - rush hour, weekend v.s., weekday, day v.s., night - Weather - Priority of rescue - Traffic accidents - Quality of the roads - Difficulty finding the exact call location. Several different travel time models are used in the literature. Distribution based: 1. Sample from **distribution** 2. Distribution vary by region Or more like…: 3. **As crow flies** multiplied by speed 4. **Pre-computed shortest path** multiplied by speed 5. Divide road into **segments**, calculate travel times for each, sum Or: 6. Any of those three, with **correction factors** for traffic, time of day, etc. Or: 7. Use live travel time data to find estimated travel time for each ambulance > **Note: View studies** > > Several studies talk about the importance of travel time modelling… > > > Henderson and Mason ([2005](#ref-henderson_ambulance_2005)): "The effort we devote to this topic is justified by the great sensitivity of results to travel time assumptions, as noted both by the authors in a preliminary queueing analysis, and by a large proportion of the papers dealing with ambulance planning. For example, Carson and Batta \[17\] describe how the 30% savings predicted by their model turned into a 6% savings in actual tests, primarily due to the model not effectively capturing a certain travel time/distance relationship." > > > > Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)): "Since the performance measures are ambulance response times and utilization levels, travel time estimation forms an important consideration." > > **(a) Distribution based - sample from distribution** > > | Study | Times | Distribution | Varies by | > |----|----|----|----| > | Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) | "Time to scene" and "time to ED site" | Empirical or lognormal (lists various times using these - would need to check code to know exact) | N/A | > | Gigante and Azevedo ([2022](#ref-gigante_study_2022)) | Time of "sending patient to hospital, release of stretcher, cleaning vehicle and returning" | Uniform | N/A | > > **(b) Distribution based - distribution vary by region** > > | Study | Times | Distribution | Varies by | > |----|----|----|----| > | Wu and Hwang ([2009](#ref-wu_using_2009)) | Station to scene, scene to hospital, hospital to station | Unclear | Time (by call arrival time, day divided into segments) and location of activating station (ambulance usually respond within district, each district have more homogeneous traffic patterns than whole city, so calibrate based on district) | > | Gigante and Azevedo ([2022](#ref-gigante_study_2022)) | Travel time to emergency | Triangular | If vehicle doesn't belong to region of ticket, add 5 minutes | > > **(c) As crow flies multiplied by speed** (+ (f) correction factors for traffic, time of day, etc.) > > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - speed differs by time (weekday/weekend), type of unit and area of city - so is corrected with a speed factor > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) > > **(d) Pre-computed shortest path multiplied by speed** (+ (f) correction factors for traffic, time of day, etc.) > > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - Found shortest route between each origin destination pair and found ideal travel times using ArcGIS10 (based on distance and speed limit). Then calculated a correction factor for every pair based on historical ambulance travelling time. Multiple distributions of correction factors were derived by time of day, day of week, ideal travel time span, and nature of trip. > - Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) > > **(e) Divide road into segments, calculate travel times for each, sum** (+ (f) correction factors for traffic, time of day, etc.) > > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - Average travel time assigned to each section of road depending on type (motorway, main road, minor road, local street). For each hour of day, day of week, rescue type and priority, the travel time is calculated by diving the section length by the average speed observed in the GPS data. Travel time is sum of segments that form shortest path between origin and destination > > **(g) Use live travel time data** > > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) - simulation runs in real time, and fetches live travel data via an API > > **Unclear:** > > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) - unclear, but speed depends on location (rural/urban) and time of day. > **Note: View Python options for travel time modelling** > > Ambulance service currently using **igraph** for travel time modelling - described as being like **networkx** but quicker. They have a graph model based on ordnance survey open roads. And that there was some ordnance survey research that gave average travel times for different road types. And they do shortest paths analysis. Working with 500m square grids. It's quite an optimistic model allowing you wrong way down roads and things, but they figured, it maybe helps reflect how blue light they'll get places quicker. > > On HSMA, Sammi taught `openrouteservice` via `routingpy`, but wasn't sure if that was the best option these days. > > Sammi had a first go with `r5py` and was quite impressed. It doesn't do traffic aware routing. But it can work with public transport data (though that's less relevance for us). \ # Processing times 1. Include in **travel times** 2. Assume **0** 3. **Deterministic** varying by location / priority / etc. 4. Sampled from a **distribution**, can then vary by priority / day / etc. 5. **Resource** (time from ED arrival to handover emerging as ED modelled as server with given capacity and LOS) *Note: More aggregation means less scope to explore scenarios where change specific times* > **Note: View studies** > > **(a) Include in travel times** > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - travel to hospital includes everything up to release of vehicle (release of stratecher, cleaning of vehicle and return) > > **(b) Assume 0** > > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - no wait time for calls to be answered by call handler > > **(c) Deterministic varying by location/priority/etc.** > > | Study | Time | Varies by | > |----|----|----| > | Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) | Preparation time | Initial location of vehicles (i.e., at base or on the road) | > | Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) | On-site time | Call location, and whether transport to hospital is required | > | Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) | Drop-off time | Hospital, and call priority | > | Silva and Pinto ([2010](#ref-silva_emergency_2010)) | Time between material replacements | Vehicle type | > > **(d) Sampled from a distribution**, can then vary by priority/day/etc. > > | Study | Time | Distribution | Varies by | > |----|----|----|----| > | Gigante and Azevedo ([2022](#ref-gigante_study_2022)) | "Time for local care and patient preparation for travel" | Triangular | \- | > | Wu and Hwang ([2009](#ref-wu_using_2009)) | On-scene time and In-hospital time | Lognormal | Call type (4 types) and responder (2 skill levels) | > | Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) | Time from allocation to mobilise, time at scene, and time to clear | Empirical or lognormal | \- | > | Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) | Regulation time, preparation time, on site time, DTR time, drop off time | Empirical | Call type (2) and priority level (4) | > | Kergosien et al. ([2015](#ref-kergosien_generic_2015)) | Gamma | Time at scene, discharge time at hospital, and call processing times | \- | > | Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) | Dispatch time and time on scene | Empirical | Patient emergency status and conveyance status | > | Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) | Handover delay | Empirical | Patient emergency status | > | Wang and Hu ([2025](#ref-wang_discrete-event_2025)) | Ambulance preparation delay, on-site delay, and unloading delay | Exponential | \- | > > **(e) Resource** > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) - time from ED arrival to handover is an emerging parameter based on availability of resources… ED is modelled as a server with a given capacity and length of stay, have to queue and wait for resource. > > **Unclear** > > - Pinto et al. ([2015](#ref-pinto_generic_2015)) (time on scene, time at hospital, time to replenish) \ # Hospital selection 1. Not relevant - no choice involved (e.g., one hospital, or simple system with no individual hospital modelling) 2. Use closest hospital 3. Sample from distribution 4. Pre-determined destination by emergency type 5. Trace-driven In Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)), they discuss how it is common to select the closest hospital, but that Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) say 50% of patients are not transported to the closest hospital, and [Savas et al. 1969](http://doi.org/10.1287/mnsc.15.12.B608) say factors include: - Available capacity of hospitals - Hospital having appropriate facilities (e.g., specialists, equipment) - Patient choice due to economic resources - Hospital policy for selectivity Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)) note that hospital selection is more critical in certain scenarios like mass casualty incidents. > **Note: View studies** > > **(a) Not relevant** > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) (one hospital) > > **(b) Use closest hospital** > > - Lee et al. ([2012](#ref-lee_simulation-based_2012)) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > - Pinto et al. ([2015](#ref-pinto_generic_2015)) (closest that supplies the required care for the emergency) > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) (except paediatric or maternity which go to a specialty hospital) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) (based on live travel times) > > **(c) Sample from distribution** > > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) (empirical) > - Wu and Hwang ([2009](#ref-wu_using_2009)) (multinomial - unclear if stratified, but do mention that determinants include distance from scene to hospital and that other factors are also important… but doesn't appear to be stratified, think just describing context) > > **(d) Pre-determined destination by emergency type** > > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) (pre-determined schedule depending on nature and location of case, will be referred to specific centre) > > **(e) Trace-driven** > > - Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) > > **Unclear** > > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) \ # Scenarios Baseline: Estimated timings for given parameters Scenarios: - How that changes with varying **demand** - How many **crew** (add or remove) - How divide crew between **bases** - **Where** bases are - Where crew go after **release** - **Shift** scheduling - working **hours** and **location** *E.g., optimal schedule… avoiding changes during high demand…* Less relevant: dispatching rules (policy change), destination hospital (mass casualty) > **Note: View studies** > > **How that changes with varying demand** > > **How many crew (add or remove), how divide crew between bases, and where bases are** > > - Gunes and Szechtman ([2005](#ref-gunes_simulation_2005)) - extend helicopter operation from 5 to 7 days per week > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) - adding new teams and bases > - Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) - adding new teams and bases > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - 150 or 200 teams, with independent or pooled fleet > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - changing locations > - Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) - vary ambulance allocations between bases > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) > - Lee et al. ([2012](#ref-lee_simulation-based_2012)) > > **Where crew go after release** (Aboueljinane et al. ([2013](#ref-aboueljinane_review_2013)) refer to this as dynamic/multi-period redeployment) > > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) (e.g., system where don't send team to a base that already has one) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) (test different strategies to keep vehicles well distributed) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > > **Shift scheduling** > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - vary times (all shifts start/end at 7, 8, 9, etc.) > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - change start time of private ambulances (7am, 9am, 10am) > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) - test new schdule that avoids shift changes during high demand periods to reduce overtime \ # Shifts Vary between studies. > **Note: View studies** > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) - Shifts are 12 hours, initially 7-7. To represent reduced resources during night shift, half the vehicles will be available. > - Pinto et al. ([2015](#ref-pinto_generic_2015)) - Resourcing levels based on schedule giving number of ambulance of each type at each base during given hour of the week > - Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) - Shifts and overtime are represented. Shift changes occur 6.30-8am, 4.30-6pm, except three units that begin 12h shift at 9am and 3pm - and also model another set of shifts too which mirror variations in call volume over time > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) - Assumes teams work each day on 8h shifts. Total 150-200 teams. Assigned teams and vehicles to time slots to respect standard working constraints (e.g., maximum shift length and lunch breaks). Number of paramedic teams on duty depends on time of day. > - Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) - 10 private ambulances with shifts Monday to Saturday 8am to 8pm. > > Don't mention shifts or explicitly don't include shifts: > > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) \ # Initialisation bias, run length and replications Vary between studies. > **Note: View studies** > > | Study | Initialisation bias | Run length | Replications | > |----|----|----|----| > | Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) | [1 day warm-up](https://github.com/nhsengland/AmbModelOpen/blob/main/docs/config.md) | [14 days](https://github.com/nhsengland/AmbModelOpen/blob/main/docs/config.md) | 10 | > | Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) | "Starts at a time of day when congestion is very low, so no initialisation is necessary" | Unsure | Unsure | > | Wu and Hwang ([2009](#ref-wu_using_2009)) | Unsure | 1 year | 5 | > | Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) | "A simulation run time of 6 months was chosen to ameliorate transient start-up effects" | 6 months | Unsure | > | Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) | 15 day warm-up | 11 months | 10 | > | Gigante and Azevedo ([2022](#ref-gigante_study_2022)) | Unclear | 30 days | 1 | > | Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) | Unclear | 6 months | Unclear | > | Kergosien et al. ([2015](#ref-kergosien_generic_2015)) | 1 day warm-up plus 1 day at end ("to remove the transient states corresponding to the first and last day of the horizon") | 5 days | 20 | > | Pinto et al. ([2015](#ref-pinto_generic_2015)) | 15 days (Figure 8 shows they even reach steady state before then) | 30 days | 10 | > | Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) | Unclear | Several months | Unclear | > | Silva and Pinto ([2010](#ref-silva_emergency_2010)) | Unclear | Unclear | Unclear | > | Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) | Unclear | Unclear | Unclear | > | Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) | Unclear | 2 weeks | 25(?) | > | Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) | Unclear | Unclear | Unclear | > | Wang and Hu ([2025](#ref-wang_discrete-event_2025)) | "Initialized with data" | 1 week | 1 | \ # Sensitivity analysis - Demand - Processing times - Number of resources > **Note: View studies** > > Demand > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) change percentage see and treat and hear and treat > - Silva and Pinto ([2010](#ref-silva_emergency_2010)) evaluate 10-100% increase in demand > - Iskander ([1989](#ref-iskander_simulation_1989)) test 25% reduction in calls > > Processing time > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) reduce time in ED > - Iskander ([1989](#ref-iskander_simulation_1989)) test 50% reduction in dispatching time and 25% reduction in time on scene > > Number of resources > > - Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) increase the number of ambulances > > General > > - Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) "Sensitivity analysis. Constraints and mean data values were varied slightly to determine if the model responded in the expected manner." > > Doesn't mention sensitivity analysis: > > - Kergosien et al. ([2015](#ref-kergosien_generic_2015)) > - Pinto et al. ([2015](#ref-pinto_generic_2015)) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > - Wang and Hu ([2025](#ref-wang_discrete-event_2025)) \ # Verification and validation Verification: - Execution tracing (n=4) - Bottom-up testing (n=2) - Special input testing (n=2) - Assertion checking Validation: - Graphical and statistical comparison with real data (n=6) - Face validation (n=5) - Conceptual model validation (n=3) - Input data validation - Comparison testing - Animation visualisation - Sensitivity analysis > **Note: View studies** > >
> > ### Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)) > > **Verification:** > > - **Execution tracing:** > - Traced calls to check closest available ambulance responded. > > **Validation:** > > - **Conceptual model validation:** > - Checked conceptual model with specialists. > - **Graphical and statistical comparison:** > - Compared to real system - similar mean response time and similar distribution of response times (nice figure, Figure 3, % calls reached by 10min, 15min, 20min, etc.). > - **Face validation:** > - Checked travel times were realistic. > >
> > ### Ingolfsson et al. ([2003](#ref-ingolfsson_simulation_2003)) > > **Verification:** > > - **Execution tracing:** > - Traced all events for 10 simulated hours > - Traced all movements for 3 ambulances for 48 hours > - Checked for apx. 30 calls that the closest available ambulance responded to them > - Checked that the count of the number of available units was incremented and decremented at the appropriate times > > **Validation:** > > - **Input data validation:** > - Checked that call arrival stream generated by model was statistically similar to historical call arrival data at each demand zone and for each hour of the week > - Checked that percentage of calls transported to each hospital was consistent with the data > - **Face validation:** > - Checked that travel times were realistic. > - **Graphical and statistical comparison with real data:** > - Compared response time statistics to real system (nice Figure 3, just like in Aboueljinane et al. ([2012](#ref-aboueljinane_reducing_2012)), showing response time 5 6 7 8 9 10 minutes and % calls reached, compares real times from 2 months with simulated times from 6 months, and finds all within 1.2% of observed). > - Compared average overtime experienced in real system per week with model. > >
> > ### Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) > > **Validation:** > > - **Input data validation:** > - Checked simulated demand by hour and day looked correct. > - **Face validation:** > - Visually inspected relationship between response time and ambulance availability, as "this should be expected to show the trade-off as a non-linear pattern with asymptotic behaviour towards each extreme" (see Figure 6). > - **Graphical or statistical comparison with real data:** > - Checked mean and 90th percentile for response times looked sensible - their pattern (i.e., c1 \< c2 \< c3) and absolute levels (thought not trying to match). Also checked other emerging performance indicators (time to allocate, job cycle time (JCT), ambulance arrivals, handover, vehicle availability). > >
> > ### Wu and Hwang ([2009](#ref-wu_using_2009)) > > **Validation:** > > - **Statistical comparison with real data:** > - Split data into two parts - Jan-Oct for model development and Nov-Dec for validation. T-test comparing response times between DES and real data. > >
> > ### Wei Lam et al. ([2014](#ref-wei_lam_reducing_2014)) > > **Validation:** > > - **Statistical comparison with real data:** > - Compared simulation with historical data for ambulance cycle times, response times, utilisation levels, and other relevant parameters. Appear to look at median, IQR and 90th percentile. > - Other criteria were also validated e.g., call arrival rates per district, daily average call volumes, percentage of conveyance for each PAC class, and conveyance times. > >
> > ### Kergosien et al. ([2015](#ref-kergosien_generic_2015)) > > **Verification:** > > - **Execution tracing:** > - Trace sequence of events for some specific ambulances or demands to make sure implementation is correct. > - **Assertion checking:** > - Implemented functions to check that entity and resource state changes followed valid successions, that ambulance routes were feasible in time and space, and that each demand was handled correctly (right day, plausible time, required transports actually followed by a hospital transport, etc.). > > **Validation:** > > - **Face validation or comparison with real data:** > - Report KPIs for "consistency analysis" against expected - unclear if this is referring to real data, or more about opinion via face validation. > >
> > ### Pinto et al. ([2015](#ref-pinto_generic_2015)) > > **Validation:** > > - **Comparison testing:** > - Compare response time and utilisation with their prior model. > - **Comparison with real data:** > - Mention but not reported. > >
> > ### Henderson and Mason ([2005](#ref-henderson_ambulance_2005)) > > They say they won't describe in full, that the used usual methods from Law and Kelton (2000) Simulation Modeling and Analysis, but provide some examples- > > **Validation:** > > - **Animation visualisation:** > - Identified errors in database of real calls by watching simulated ambulance operations. > - Could also place calls at strategic locations and check that responses were as expected. > - Shortest paths were generated and displayed over the road network to verify the quality of chosen routes. > - **Face validation** > >
> > ### Silva and Pinto ([2010](#ref-silva_emergency_2010)) > > **Verification:** > > - **Bottom-up testing:** > - Modular model where each part of model is implemented and run separately, and each module is analysted to check it behaves consistently with intended model logic. > - **Special input testing:** > - Forced unlikely events and unusual dispatch situations (e.g., call arrives requiring advanced unit but closest unit to incident is basic) and checked decisions. > > **Validation:** > > - **Conceptual model validation** > - With system managers, discussed the conceptual model and simplifications > - With doctors in charge of the system, dicussed variables used to analyse system performance and scenarios to evaluate. > >
> > ### Uyeno and Seeberg ([1984](#ref-uyeno_practical_1984)) > > **Verification:** > > - **Bottom-up testing and special input testing:** > - "Pieces of the model were run separately to monitor the behaviour of each piece. For example, the model was run without any paramedic ambulances. In their absence, utilisation of ordinary ambulances increased and response times to all categories of calls deteriorated as expected." > - **Execution tracing:** > - Could trace individual calls or ambulances, and observe that e.g., ambulances never spent 5 hours on a call, and no calls vanished. > > **Validation:** > > - **Experimentation validation - sensitivity analysis** > - **Conceptual model validation** > - Management personnel reviewed model logic. > - **Comparison with real data** > - **Face validation** > - Management personnel found all experimental results to be acceptable. > >
> > ### Wang and Hu ([2025](#ref-wang_discrete-event_2025)) > > **Verification:** Checked that "all events that occur in the EMS align with the expected assumptions and logic" > >
> > ### Studies that don't mention verification and validation > > - Gigante and Azevedo ([2022](#ref-gigante_study_2022)) > - Buuren et al. ([2012](#ref-van_buuren_evaluating_2012)) > - Maxwell et al. ([2009](#ref-maxwell_ambulance_2009)) > - Berlin and Liebman ([1974](#ref-berlin_mathematical_1974)) > > \ > >
> > # Studies with open code or data > > | Publication | Language & Package | Code | Data | > |----|----|----|----| > | Fonseca et al. ([2025](#ref-fonseca_discrete_2025)) | R simmer | | \- | > | Unpublished | R simmer | Baird ([2020](#ref-baird_bairdjambulance-simmer_2020)) | \- | > | Unpublished | Python SimPy | Pilbery ([2025](#ref-pilbery_richardpilberydaa_des_2025)) | \- | > | Unpublished | Python SimPy | Otles ([2024](#ref-otles_eotlesems_2024)) | \- | > | Lam et al. ([2019](#ref-lam_low-cost_2019)) | Python | and other repositories in | \- | > | Allen et al. ([2021](#ref-allen_developing_2021)) | Python SimPy | | \- | > | Unpublished | Python SimPy | Parajuli et al. ([2021](#ref-parajuli_urmila-mambulance-gis-system_2021)) | \- | > | Bertsimas and Ng ([2019](#ref-bertsimas_robust_2019)) | Python | | | > | Unpublished | Python | | \- | > | Unpublished | Python | | \- | > | Ridler et al. ([2022](#ref-ridler_simulation_2022)) | Julia | | \- | > | Frichi, Jawab, and Aboueljinane ([2022](#ref-frichi_dataset_2022)) - used in Frichi et al. ([2025](#ref-frichi_ambulance_2025)) and Frichi, Jawab, Aboueljinane, Zerka, et al. ([2022](#ref-frichi_assessing_2022)) | \- | \- | | > | Schjølberg et al. ([2023](#ref-schjolberg_comparing_2023)) | Java | | \- | > >
> >
> > ## References > >
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