Hospitals are complex systems, and the flow of patients is dynamic and nonlinear in such systems. Network representation allows flow algorithms to observe bottlenecks as candidates for optimisation. To model the dynamic behaviour of the patient flow, we need to consider the variability in arrival rates and service times (length of stay). Previously proposed dynamic flow algorithms mainly focused on arrival and departure rates, inflow and outflow, edges' and vertices' capacity, and routing, with applications mainly in transportation and telecommunication. In hospitals, bottlenecks that emerge from the patients' flow are a result of the vertices (wards) behaviour defined by capacity (beds), number of servers (staff), service time variability, and edges (care pathways) distribution probability. We offer a modified flow algorithm that takes a hospital network, iterates over the patients' arrival rates, and measures the flow with respect to vertices' capacities, servers, service time variability, edge capacity, and distribution probability. The result is a dynamic residual graph to measure the bottlenecks' persistency and severity, identify the root causes of bottlenecks, and wards' dynamic nonlinear behaviour. The algorithm provides a quick holistic view of hospital performance and the analysis of the edges and vertices' behaviour over time.

The degree of connectivity among hospital wards and the dynamic nonlinear flow of patients cause bottlenecks to begin in non-priority wards, accumulate within the paths, distribute throughout the hospital, and emerge as overflow in crucial wards. This requires a network-based modeling approach to address the bottlenecks caused by second- and third-order wards and to significantly influence the overall and emergent performance of multiple wards. Understanding the relative merits of different network modeling and analysis approaches in this complex environment is often challenging and requires a holistic strategy to identify persistent bottlenecks and provide evidence-based scenarios. This article introduces a novel hybrid modeling approach that integrates network analysis algorithms and agent-based network simulation of patient flow over a complete hospital network. Through network analysis, such as structural hole and flow algorithms, the approach identifies common persistent bottlenecks from the flow and structural perspectives, while percolation and perturbation analyses measure the performance improvement of wards based on variations in patient flow, and the simulations enable the investigation of scenarios. The results indicate the wards and patient types that can contribute to improving the hospital’s performance. The proposed approach facilitates holistic, dynamic modeling of hospitals, irrespective of their network scale, and enables the identification of bottleneck sources and their associated paths, contributing to a comprehensive assessment of the system’s performance.

The dynamic and evolving nature of complex systems influences the behaviour of individual parts and the performance of the whole system, which hinders the flexibility in modelling and applicability of the modelling approaches for various systems. Modelling approaches which are developed for other types of systems have limitations in capturing the behaviour of health systems. This can stem from the dependencies of models on the system structure, type and data structure. From the network perspective, health systems can have various representations, which are defined by each network topology, type and parameters. This makes it challenging to utilize an approach developed to analyse and model systems of other aspects and domains.    

The degree of flexibility of an approach depends on its scalability to be able to model a system that grows, its generality to model systems of various types, its adaptability to internal changes, and its flexibility to topology without the need for change. Additionally, flexibility should enable the approach adjustment with new functions and features to facilitate and analyse other aspects of a system easily. Network representation of complex health systems facilitates the application of network algorithms and network simulation methods to enhance the modelling approaches. This requires the adjustment of these algorithms and methods, which can be achieved by tuning, merging, modifying, and gaming procedures. Such adjustments increase the efficiency of a model to analyse different aspects of a system and overcome limitations.      

This thesis offers various network-agnostic computational approaches for modelling and validating complex health systems. For this, three different case studies are provided to explore which represent the complex societal, hospital and organisational systems, respectively. The proposed modelling approaches for these systems aim to facilitate the quantification of vertices and edges, classify the vertices’ behaviours, promote verification and validation, evaluate the systems' performances, and enhance the link prediction for a more accurate representation of the systems. 

The key contribution of this thesis is to offer approaches which can facilitate scalability, generality, adaptability, topological flexibility, and adjustability. This is achieved by adjusting the network algorithms and simulation methods based on the purpose of the modelling. Hence, 1) a gaming simulation approach is proposed to facilitate the quantification of the edges in a complex societal system, 2) ranking algorithm is merged with path analysis to quantify the vertices and identify the vertices persistency in a complex societal system, 3) ranking algorithm is merged with system dynamic simulation to facilitate the quantification of the vertices as the complex societal system evolve and change, 4) an agent-based network simulation is implemented along with network algorithms to identify the bottlenecks using flow and structural hole algorithms and evaluation the performances of the wards using percolation and perturbation algorithm in a complex hospital system, 5) a modification of flow algorithm is proposed to model the dynamic nonlinear flow of the patients in a complex hospital system, 6) a link prediction approach which merges the path analysis and non\_randomness algorithm to identify the missing links in a complex organizational system, and finally 7) a multi-network simulation to evaluate the performances of the organizations in parallel. 

The thesis provides two different classifications of the proposed approaches. The first classification indicates how each approach contributes to modelling the system based on the underlying system scale, type, dynamic, topology and model adjustability, and the second classification indicates the proper application of network algorithms and network simulation methods based on the underlying health system type and the purpose of the analysis.  

Each approach provides a holistic view of the systems through matrix or network representation to inform about their states and a view of the vertices’ dynamic behaviours to evaluate their performances.  

Den dynamiska och utvecklande karaktären hos komplexa system påverkar beteendet hos enskilda delar och hela systemets prestanda, vilket hindrar flexibiliteten i modellering och tillämpbarheten av modelleringsmetoderna för olika system. Modelleringsmetoder som utvecklats för andra typer av system har begränsningar för att fånga hälsosystemens beteende. Detta kan härröra från modellers beroende av systemstruktur, typ och datastruktur. Ur ett nätverksperspektiv kan hälsosystem ha olika representationer som definieras av varje nätverkstopologi, typ och parametrar. Detta gör det utmanande att använda ett tillvägagångssätt utvecklat för att analysera och modellera system av andra aspekter och domäner.

Graden av flexibilitet för ett tillvägagångssätt beror på dess skalbarhet för att kunna modellera ett system som växer, generalitet till modellsystem av olika typer, anpassningsförmåga till de interna förändringarna och flexibilitet till topologi utan behov av förändring. Dessutom bör flexibilitet möjliggöra tillvägagångssättjustering med nya funktioner och funktioner för att enkelt underlätta och analysera andra aspekter av ett system. Nätverksrepresentation av komplexa hälsosystem underlättar tillämpningen av nätverksalgoritmer och nätverkssimuleringsmetoder för att förbättra modelleringsmetoderna. Detta kräver justering av dessa algoritmer och metoder, vilket kan uppnås genom justering, sammanslagning, modifiering och spelprocedurer. Sådana justeringar ökar effektiviteten hos en modell för att analysera olika aspekter av ett system och övervinna begränsningar.

Denna avhandling erbjuder olika nätverks-agnostiska beräkningsmetoder för modellering och validering av komplexa hälsosystem. För detta tillhandahålls tre olika fallstudier för att utforska vilka som representerar de komplexa samhälleliga, sjukhus- respektive organisationssystemen. De föreslagna modelleringsmetoderna för dessa system syftar till att underlätta kvantifieringen av hörn och kanter, klassificera hörnens beteenden, främja verifieringen och valideringen, utvärdera systemens prestanda och förbättra länkförutsägelsen för mer exakt representation av systemen.

Det viktigaste bidraget för denna avhandling är att erbjuda tillvägagångssätt som kan underlätta skalbarhet, generalitet, anpassningsförmåga, topologisk flexibilitet och justerbarhet. Detta uppnås genom att justera nätverksalgoritmerna och simuleringsmetoderna utifrån syftet med modelleringen. Därför föreslås 1) en spelsimuleringsmetod för att underlätta kvantifieringen av kanterna i ett komplext samhälleligt system, 2) rankningsalgoritmen slås samman med väganalys för att kvantifiera hörnen och identifiera grenarnas beständighet i ett komplext samhälleligt system, 3) rankning Algoritmen slås samman med systemdynamisk simulering för att underlätta kvantifieringen av hörnen som komplexet samhälleliga system utvecklas och förändras, 4) en agentbaserad nätverkssimulering implementeras tillsammans med nätverksalgoritmer för att identifiera flaskhalsar med hjälp av flödes- och strukturella hålalgoritmer och utvärdering av avdelningarnas prestanda med hjälp av perkolations- och störningsalgoritmer i ett komplext sjukhussystem, 5) en modifiering av flödesalgoritmen föreslås för att modellera det dynamiska olinjära flödet av patienter i ett komplext sjukhussystem, 6) en länkförutsägelsemetod som kombinerar väganalysen och algoritmen för icke-slumpmässighet för att identifiera de saknade länkarna i ett komplext organisationssystem, och slutligen 7) en simulering av flera nätverk för att parallellt utvärdera organisationernas prestationer.

Avhandlingen ger två olika klassificeringar av de föreslagna tillvägagångssätten. Den första klassificeringen anger hur varje tillvägagångssätt bidrar till att modellera systemet baserat på den underliggande systemets skala, typ, dynamik, topologi och modellens justerbarhet; och den andra klassificeringen indikerar korrekt tillämpning av nätverksalgoritmer och nätverkssimuleringsmetoder baserat på den underliggande typen av hälsosystem och syftet med analysen.

Varje tillvägagångssätt ger en holistisk bild av systemen genom matris- eller nätverksrepresentation för att informera om dess tillstånd, och en bild av hörnens dynamiska beteenden för att utvärdera deras prestationer.

Many important systems, both natural and artificial, are complex in nature, and models and simulations are one of the main instruments to study them. In this paper, we present an approach where a complex social system is represented at a high level of abstraction as a network, thereby addressing several challenges such as quantification, intervention, adaptation and validation. The network represents the factors that influence the mental health and wellbeing in children and young people. In this article, we present an approach that links a system dynamics simulation to simulate the network and ranking algorithms to measure the vertices' behaviors. The network is enhanced by adding edge strengths in the form of correlations between vertices (established through literature). Such an approach allows us to exploit the network structure to qualify and quantify the vertices of the network, to overlay different processes over the network topology, to add and remove new vertices, and therefore interact dynamically. This in turn allows for the qualification of vertices' importance and network resilience. System dynamics simulation allows for policy analysis, where different scenarios are analyzed by stimulating a set of vertices and the effect over the network is observed. This approach allows for an abstract, flexible, yet comprehensive way of analyzing a complex social network at any scale.

In the realm of cloud native environments, Ku-bernetes has emerged as the de facto orchestration system for containers, and the service mesh architecture, with its interconnected microservices, has become increasingly prominent. Efficient scheduling and resource allocation for these microservices play a pivotal role in achieving high performance and maintaining system reliability. In this paper, we introduce a novel approach for container scheduling within Kubernetes clusters, leveraging Graph Attention Networks (GATs) for representation learning. Our proposed method captures the intricate dependencies among containers and services by constructing a representation graph. The deep Q-learning algorithm is then employed to optimize scheduling decisions, focusing on container-to-node placements, CPU request-response allocation, and adherence to node affinity and anti-affinity rules. Our experiments demonstrate that our GATs-based method outperforms traditional scheduling strategies, leading to enhanced resource utilization, reduced service latency, and improved overall system throughput. The insights gleaned from this study pave the way for a new frontier in cloud native performance optimization and offer tangible benefits to industries adopting microservice-based architectures.

Demands for health care are becoming overwhelming for healthcare systems around the world regarding theavailability of resources, particularly, in emergency departments (EDs) that are continuously open and mustserve immediately any patient who comes in. Efficient management of EDs and their resources is requiredmore than ever. This could be achieved either by optimizing resource utilization or by the improvement ofhospital layout. This paper investigates, through data-driven simulation alternative designs of workflowsand layouts to operate the ED of the Uppsala University Hospital in Sweden. Results are analyzed tounderstand the requirements across the hospital for reduced waiting times in the ED. The main observationrevealed that introducing a new ward dedicated to patients having complex diagnoses with a capacity ofless than 20 beds leads to lower waiting times. Furthermore, the use of data-mining was of great help inreducing the efforts of building the simulation model.

To promote policy analysis and decision-making in mental health and well-being, simulations are used to scrutinize causal maps and provide policymakers reasonable evidence. This paper proposes and illustrates a multi-methodology hybrid approach by building a hierarchy of models, moving from a systems dynamics model to a simulation based on PageRank to quantify and assess a complex mental health map. The motives are: (1) to aid scenario analysis and comparison for possible policy interventions, (2) to quantify and validate mental health factors, and (3) to gain new insights into the core and confounding factors that affect mental health. The results indicate that the approach identifies factors that cause significant and frequent variation on mental health. Furthermore, validation confirms PageRank accuracy and detects minor fluctuations and variation in model's output behavior.

Various factors influence mental well-being, and span individual, social and familial levels. These factors are connected in many ways, forming a complex web of factors and providing pathways for developing programs to improve well-being and for further research. These factors can be studied individually using traditional methods and mapped together to be analyzed holistically from a complex system perspective. This study provides a novel approach using PageRank and social network analysis to understand such maps. The motives are: (1) to realize the most influential factors in such complex networks, (2) to understand factors that influence variations from different network aspects. A previously developed map for children's mental well-being was adopted to evaluate the approach. To achieve our motives, we have developed an approach using PageRank and Social Network Analysis. The results indicate that regardless of the network scale, two key factors called "Quantity and Quality of Relationships" and "Advocacy" can influence children's mental well-being significantly. Moreover, the divergence analysis reveals that one factor, "Recognition/Value Placed on well-being at School" causes a wide range of diffusion throughout the system.

Hospitals are complex systems, and the flow of patients is dynamic and nonlinear in such systems. Network representation allows flow algorithms to observe bottlenecks as candidates for optimisation. To model the dynamic behaviour of the patient flow, we need to consider the variability in arrival rates and service times (length of stay). Previously proposed dynamic flow algorithms mainly focused on arrival and departure rates, inflow and outflow, edges’ and vertices’ capacity, and routing, with applications mainly in transportation and telecommunication. In hospitals, bottlenecks that emerge from the patients’ flow are a result of the vertices (wards) behaviour defined by capacity (beds), number of servers (staff), service time variability, and edges (care pathways) distribution probability. We offer a modified flow algorithm that takes a hospital network, iterates over the patients’ arrival rates, and measures the flow with respect to vertices’ capacities, servers, service time variability, edge capacity, and distribution probability. The result is a dynamic residual graph to measure the bottlenecks’ persistency and severity, identify the root causes of bottlenecks, and wards’ dynamic nonlinear behaviour. The algorithm provides a quick holistic view of hospital performance and the analysis of the edges and vertices’ behaviour over time.

The degree of connectivity among hospital wards and the dynamic nonlinear flow of patients cause bottlenecks to begin in non-priority wards, accumulate within the paths, distribute throughout the hospital, and emerge as overflow in crucial wards. This requires a network-based modeling approach to address the bottlenecks caused by second- and third-order wards and to significantly influence the overall and emergent performance of multiple wards. Understanding the relative merits of different network modeling and analysis approaches in this complex environment is often challenging and requires a holistic strategy to identify persistent bottlenecks and provide evidence-based scenarios. This article introduces a novel hybrid modeling approach that integrates network analysis algorithms and agent-based network simulation of patient flow over a complete hospital network. Through network analysis, such as structural hole and flow algorithms, the approach identifies common persistent bottlenecks from the flow and structural perspectives, while percolation and perturbation analyses measure the performance improvement of wards based on variations in patient flow, and the simulations enable the investigation of scenarios. The results indicate the wards and patient types that can contribute to improving the hospital's performance. The proposed approach facilitates holistic, dynamic modeling of hospitals, irrespective of their network scale, and enables the identification of bottleneck sources and their associated paths, contributing to a comprehensive assessment of the system's performance.