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Abstract
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The authors regret to inform that, for reasons out of their control, the initial published version was not the final version. The final version of the refereed work, now named "How Do Traffic and Demand Daily Changes define Urban Emergency Medical Service (uEMS) Strategic Decisions? A multi-period survival approach", has an improved state of the art, a more detail description of the simulation model, a new subsection to assess solution robustness, and an overall improvement of the wording and figures. The final version is below.
How Do Traffic and Demand Daily Changes define Urban Emergency Medical Service (uEMS) Strategic Decisions? A multi-period survival approach
Abstract
This paper presents a methodology to locate vehicle base stations using a scenario based optimisation to address daily traffic and demand changes, which are due to what we define as city dynamics. The model allows us to understand better how these daily changes affect an urban emergency medical service (uEMS) response system.
The methodology incorporates two steps. The first step uses scenario-based optimisation and survival function theory to locate vehicle base stations, whereas the second step uses agent-based simulation to assess the solution performance and compare it with average-period and non-survival prone solutions. The proposed models are tested for different situations using real data from the city of Porto.
The results of the sensitivity analyses show the importance of understanding the dynamics of cities and how they impact uEMS response systems. Useful insights regarding the number of stations and the average response time are addressed together with the minimum number of stations required for different maximum response time limits and different survival coefficients.
Finally, we conclude that a multi-period solution improves response time because it accounts for city dynamics and that a heterogeneous survival-based approach benefits victims' by properly measuring the system response concerning the victims' outcome.
Keywords Emergency medical service; Scenario-based optimisation; Simulation; City dynamics; Survival functions; Multi-period approach
1. Introduction
1.1. Background, motivation, and contribution
The study of road crashes, their implications and how to minimise their impact, is of high interest within the transport research community. This is particularly true for those that focus on road safety by studying the post-crash response of the emergency medical service (EMS).
Moreover, the World Health Organisation presented in 2011 a global plan of action for road safety for the decade 2011-2020 (Who, 2011). This plan indicates that researchers should focus on the post-crash response through activity 7 of pillar 5 of the document, where it reads: "Encourage research and development into improving post-crash response". One way of improving post-crash response is by studying the EMS response and assess where improvements can be made.
Some researchers have worked to create models for planning EMS solely to assist road crashes in a city (Kepaptsoglou et al., 2012) or in a specific road network (Zhu et al., 2012). However, emergency medical services usually respond to all types of medical emergencies, and no separate service may exist to assist just one type of medical emergency. One can argue that there are moral issues when resources are available and cannot be used in an active emergency because they are exclusive to another type of emergency. Moreover, Amorim et al. (2017) show that general planning of the emergency medical service generates a similar road crash response performance when compared to an EMS planned to prioritise road crashes. Therefore, from a transportation research perspective, it makes sense to study the emergency medical service as a whole.
In recent works, the focus of EMS response research has been on dynamic EMS, where vehicles are dynamically allocated, dispatched or routed to be prepared for the upcoming hours (Vasić et al., 2014; Zhang, 2012; Panahi and Delavar, 2009), and on the fact that emergency medical calls are heterogeneous - i.e. response time affects victims' survival differently (Mccormack and Coates, 2015; Erkut et al., 2008; Blackwell and Kaufman, 2002).
This work aims to study the importance of city dynamics when planning an urban emergency medical service (uEMS) response system. An urban emergency medical service is defined as a service that responds to 'habitual emergencies' thus can be solved by a single organisation. Hence, disaster services and specific hazard emergencies are out of this work scope (Simpson and Hancock, 2009). Further, the work focuses on medical emergencies that take place in high-density urban areas; therefore, the service is subject to city dynamics. City dynamics is defined as an urban area where dynamism exists, and dynamism is described as a force that stimulates changes in short periods of time, such as hours or days (Silva et al., 2014). In sum, this work studies how daily traffic and population changes affect the uEMS strategic planning.
More specifically, we claim that the location of people and traffic, through the day, is not static in an urban environment (Lam et al., 2015; Vasić et al., 2014), and these two variables (people and traffic) are the most relevant ones when designing an urban EMS strategic plan - i.e. people in constant movement represent a possible dynamic demand (Krishnan et al., 2016; Wang et al., 2015), whereas traffic represents the network load because it constrains how quickly an emergency vehicle can reach a medical emergency (Erkut et al., 2009; Kim, 2016; Ingolfsson et al., 2008; Budge et al., 2010; Westgate et al., 2013) and, it correlates with road crashes and injuries (Ferreira and Couto, 2013; Amorim et al., 2017).
To assess how the urban behaviour interferes with uEMS, we propose a scenario-based optimisation model to locate uEMS vehicle stations according to victims' heterogeneity and city dynamics. Subsequently, we compare it with less robust solutions using numerical simulation and different performance metrics. In short, this framework analyses the performance of the uEMS response under different station configurations and contributes to the literature in the following ways:
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Formalizes a methodology to plan a strategic EMS response solution prepared for a dynamic environment;
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Uses the concept of urban dynamics and victims' survival, thereby implementing a scenario-based survival optimisation model;
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Uses a numerical application of the proposed methodology and models;
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Assesses the impact of city dynamics using several performance metrics calculated through simulation.
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Compare the proposed solution with static or non-survival models, showing the importance of these two concepts and their applicability.
1.2. EMS response models
The first emergency service location models date back to the year 1955 with the fire station location problem by Valinsky (1955) and Hogg (1968), and with the EMS station location problem by Savas (1969). Nevertheless, it was the work of Toregas et al. (1971) and Church and Velle (1974) that brought the emergency station location problem to the operation research community.
Toregas et al. (1971) present a solution that ensures all demand is covered by a maximum time or distance threshold which was named Location Set Covering Problem (LSCP). Church and Velle (1974) improve Toregas et al. (1971) work by using the concept of maximal coverage to implement the resources limitation neglected by Toregas et al. (1971). The addition of resources limitation resulted in the Maximal Coverage Location Problem (MCLP). These classic location problems were soon surpassed by stochastic models that try to deal with uncertainty in an attempt to come closer to the practitioners' needs. The most important ones are the Maximum Expected Covering Location Problem (MEXCLP) by Daskin and Stern (1981), Daskin (1983) and the Maximum Availability Location Problem (MALP) by Hogan and Revelle (1986), Revelle and Hogan (1989). The authors implement facility reliability and busyness probability to solve the fact that once a facility is called for service the demand under its coverage is no longer covered.
More recently, Maxwell et al. (2009) classified research on dynamic allocation problems into three categories depending on the following: when real-time solution is required to make redeployment decisions (Brotcorne et al., 2003; Kolesar and Walker, 1974; Gendreau et al., 2001; Nair and Miller-Hooks, 2006); when solving the model involves computing optimal vehicle positions for every number of available vehicles via an integer programming formulation in an offline preparatory phase (Ingolfsson, 2006; Gendreau et al., 2005); or when one intends to incorporate system randomness into the model by using Markov decision processes (Berman, 1981a, 1981b, 1981c; Zhang et al., 2008; Alanis et al., 2013; Berman and Odoni, 1982; Jarvis, 1981) or make decisions under particular system configurations (Andersson and Varbrand, 2006; Andersson, 2005).
The bibliography shows that multi-period location models, where time is discrete, are a better practical solution for dynamic location problem than average-period models because in the latter time is continuous. This is proven by Miller et al. (2007) and supported by Boloori Arabani and Farahani, (2012).
The concept of scenario-based approaches is also used when uncertainty is present. Serra and Marianov (1998) solved the p-median problem (PMP) under scenario-based demand uncertainty. When the number of facilities, or vehicles, is uncertain, Current et al. (1998) propose a scenario-based approach and solve the problem with a general-purpose mixed integer programming (MIP) solver. A detailed literature review focusing on the different EMS logistical problems can be read in the work of Reuter-Oppermann et al. (2017).
Moreover, with the advance of computer power and the availability of powerful personal computers, simulation models have become a useful tool for researchers wanting to formulate more realistic and complex problems, be it to assess solutions or to support optimised solutions (Restrepo et al., 2008; Maxwell et al., 2010; Yue et al., 2012; Mccormack and Coates, 2015; Iannoni et al., 2009; Su and Shih, 2003).
Nevertheless, in urban Emergency Medical Services (uEMS), contrary to non-emergency facility location problems, underestimated or overestimated solutions have not only a monetary impact but carry a social impact. A wrong decision leads to higher response times to life-threatening medical emergencies, which impacts victims' survivability. To better understand the full range of the EMS system and how to plan it, the reader is pointed to the literature review made by Aringhieri et al. (2017) where the authors made a detailed analysis of the vehicle location, and relocation problem, and described dispatching and routing policies. The authors also study the interplay between the EMS system and other health services, forecast techniques and resource management.
When talking about victims' survivability, Sánchez-Mangas et al. (2010) studied the impact of medical response in road crashes and concluded that reducing the EMS response by 10 minutes may reduce road crash fatalities by 30%. Although this number can vary depending on many factors, it is obvious that a quicker medical response will result in improved medical assistance (Blackwell and Kaufman, 2002; Pons et al., 2005). In conformity, Erkut et al. (2008) note that survival probability and victims' heterogeneity models should prevail over coverage concepts when dealing with medical emergencies. These types of models have already been used in recent works (Knight et al., 2012, Mccormack and Coates, 2015).
Mccormack and Coates (2015) showed that without additional resources it is possible to increase cardiac arrest victims' survival; however, the proposed model only divides medical emergencies into two types: cardiac arrests and non-cardiac arrests. Another drawback in comparison to what we propose is the fact that the authors simplify the simulation by using approximated distances and average speeds when calculating travel times; adopting the same traffic conditions for inbound and outbound directions. This not only leads to synthetic travel conditions but also eliminates the possibility to account for the commuting impact in the network - i.e. higher travel times for inbound routes during the morning versus higher travel times for outbound routes during the afternoon. With cities becoming smart due to the introduction of intelligent systems and easy access to real-time information, such as Urban Traffic Control systems, access to traffic information can be a reality to uEMS and was proven to be beneficial on the tactical level (Amorim et al., 2018).
In a different approach, Kepaptsoglou et al. (2012) assume a uEMS model to solely respond to road crashes, disregarding other types of medical emergencies. Knight et al., (2012) address the heterogeneity of medical emergencies more directly. They propose a Maximal Expected Survival Location Model for Heterogeneous Patients using an exponential survival function for cardiac arrests, step functions for other types of medical emergencies, and a weight variable to prioritise emergencies.
Amorim et al. (2017) investigate uEMS station location for long-term planning periods and identify differences in the station configurations depending on how they assess victims' heterogeneity. However, by using an average-period approach, they are unable to detect the influence of city dynamics in the system response, and the solution might fail for specific periods of time according to the different traffic and demand characteristics. In the other hand, Dibene et al. (2017) implement robust scenario-based solutions for the classic Location Set Covering Model (LSCM), the Maximal Covering Location Problem (MCLP) and the Double Standard Model (DSM). They consider several factors such as if it is a work or off-day, the time of the day, geographical organisation and call priority, but not directly applying survival functions when measuring the system performance. They prove that the current solution in Tijuana, Mexico, could be improved regarding response time and demand coverage but could not show evidence regarding victims' survival.
Moreover, they only account for dynamics related to demand, thus not accounting for traffic changes. Krishnan et al. (2016) apply risk-based metrics to the vehicle location problem using Conditional-Value-at-Risk (CVaR). However, they tackle the problem under the view of system failure which assesses the number of calls not served; thus, they do not consider the victims' heterogeneity or victims' survival.
Recent work by Zaffar et al. (2016) compares performance metrics used in emergency vehicle location models with a focus on coverage, response time and survivability, and conclude that survivability models perform better in both survival and coverage metrics using a simulation-optimisation model. The authors show that demand varies in time and space along the day and week. Nevertheless, the proposed model disregards traffic changes and simplifies the travel time factor by assuming Manhattan distances and using an average speed for the emergency vehicles. Moreover, the study does not account for victims' heterogeneity, and victims' survivability is assessed by a linear function simplified from Mclay and Mayorga (2010) which focuses on cardiac arrest.
There is a gap in the study and performance assessment of EMS strategic decisions such as vehicle or station locations. The literature review shows the progress made in performance metrics and robust solutions, but there is yet no significant scientific input in the use of multi-period survival-based solutions to assess the impact of dynamic urban factors such as traffic and demand. Our work tries to fill this gap by providing a data-driven scenario optimisation solution that accounts for demand and traffic fluctuations and presents a performance comparison between the multi-period approach and average-periods solutions by analysing, through simulation, different performance metrics and using real data.
This work will not focus on the problem of the number and allocation of vehicles to stations at the tactical level (planning for short periods). However, it is essential to provide the reader with literature that can sufficiently fill this gap. van Essen et al. (2013) study EMS planning at both strategic and tactical level, discussing the problem of sub-optimal solutions when tackling the two problems separated. They propose a combined solution for the two problems. Another critical tactical decision in EMS, particularly in urban environments, is the dispatching and possible reallocation of the vehicles. Schmid (2012) studies EMS at this level and formulates the allocation and relocation problem for the medical emergency. The formulation presented can also be adapted to determinate the adequate number of vehicles at each station...
Language: en |