Real-time scheduling of parallel tasks in the Linux Kernel

This paper proposes a global multiprocessor scheduling algorithm for the Linux kernel that combines the global EDF scheduler with a priority-aware work-stealing load balancing scheme, enabling parallel real-time tasks to be executed on more than one processor at a given time instant. We state that some priority inversion may actually be acceptable, provided it helps reduce contention, communication, synchronisation and coordination between parallel threads, while still guaranteeing the expected system’s predictability. Experimental results demonstrate the low scheduling overhead of the proposed approach comparatively to an existing real-time deadline-oriented scheduling class for the Linux kernel.

Supporting real-time parallel task models with work-stealing

Dynamic parallel scheduling using work-stealing has gained popularity in academia and industry for its good performance, ease of implementation and theoretical bounds on space and time. Cores treat their own double-ended queues (deques) as a stack, pushing and popping threads from the bottom, but treat the deque of another randomly selected busy core as a queue, stealing threads only from the top, whenever they are idle. However, this standard approach cannot be directly applied to real-time systems, where the importance of parallelising tasks is increasing due to the limitations of multiprocessor scheduling theory regarding parallelism. Using one deque per core is obviously a source of priority inversion since high priority tasks may eventually be enqueued after lower priority tasks, possibly leading to deadline misses as in this case the lower priority tasks are the candidates when a stealing operation occurs. Our proposal is to replace the single non-priority deque of work-stealing with ordered per-processor priority deques of ready threads. The scheduling algorithm starts with a single deque per-core, but unlike traditional work-stealing, the total number of deques in the system may now exceed the number of processors. Instead of stealing randomly, cores steal from the highest priority deque.

Implementing multicore real-time scheduling algorithms based on task splitting using ada 2012

Multiprocessors, particularly in the form of multicores, are becoming standard building blocks for executing reliable software. But their use for applications with hard real-time requirements is non-trivial. Well-known realtime scheduling algorithms in the uniprocessor context (Rate-Monotonic [1] or Earliest-Deadline-First [1]) do not perform well on multiprocessors. For this reason the scientific community in the area of real-time systems has produced new algorithms specifically for multiprocessors. In the meanwhile, a proposal [2] exists for extending the Ada language with new basic constructs which can be used for implementing new algorithms for real-time scheduling; the family of task splitting algorithms is one of them which was emphasized in the proposal [2]. Consequently, assessing whether existing task splitting multiprocessor scheduling algorithms can be implemented with these constructs is paramount. In this paper we present a list of state-of-art task-splitting multiprocessor scheduling algorithms and, for each of them, we present detailed Ada code that uses the new constructs.

LLF schedulability analysis on multiprocessor platforms

LLF (Least Laxity First) scheduling, which assigns a higher priority to a task with smaller laxity, has been known as an optimal preemptive scheduling algorithm on a single processor platform. However, its characteristics upon multiprocessor platforms have been little studied until now. Orthogonally, it has remained open how to efficiently schedule general task systems, including constrained deadline task systems, upon multiprocessors. Recent studies have introduced zero laxity (ZL) policy, which assigns a higher priority to a task with zero laxity, as a promising scheduling approach for such systems (e.g., EDZL). Towards understanding the importance of laxity in multiprocessor scheduling, this paper investigates the characteristics of ZL policy and presents the first ZL schedulability test for any work-conserving scheduling algorithm that employs this policy. It then investigates the characteristics of LLF scheduling, which also employs the ZL policy, and derives the first LLF-specific schedulability test on multiprocessors. It is shown that the proposed LLF test dominates the ZL test as well as the state-of-art EDZL test.

Scheduling arbitrary-deadline sporadic task systems on multiprocessors

A new algorithm is proposed for scheduling preemptible arbitrary-deadline sporadic task systems upon multiprocessor platforms, with interprocessor migration permitted. This algorithm is based on a task-splitting approach - while most tasks are entirely assigned to specific processors, a few tasks (fewer than the number of processors) may be split across two processors. This algorithm can be used for two distinct purposes: for actually scheduling specific sporadic task systems, and for feasibility analysis. Simulation- based evaluation indicates that this algorithm offers a significant improvement on the ability to schedule arbitrary- deadline sporadic task systems as compared to the contemporary state-of-art. With regard to feasibility analysis, the new algorithm is proved to offer superior performance guarantees in comparison to prior feasibility tests.

Energy Resource Management under the Influence of the Weekend Transition Considering an Intensive use of Electric Vehicles

Energy resource scheduling is becoming increasingly important, as the use of distributed resources is intensified and of massive electric vehicle is envisaged. The present paper proposes a methodology for day-ahead energy resource scheduling for smart grids considering the intensive use of distributed generation and Vehicle-to-Grid (V2G). This method considers that the energy resources are managed by a Virtual Power Player (VPP) which established contracts with their owners. It takes into account these contracts, the users' requirements subjected to the VPP, and several discharge price steps. The full AC power flow calculation included in the model takes into account network constraints. The influence of the successive day requirements on the day-ahead optimal solution is discussed and considered in the proposed model. A case study with a 33-bus distribution network and V2G is used to illustrate the good performance of the proposed method.

Real-time Task-Splitting scheduling algorithms framework

Nos dias de hoje, os sistemas de tempo real crescem em importância e complexidade. Mediante a passagem do ambiente uniprocessador para multiprocessador, o trabalho realizado no primeiro não é completamente aplicável no segundo, dado que o nível de complexidade difere, principalmente devido à existência de múltiplos processadores no sistema. Cedo percebeu-se, que a complexidade do problema não cresce linearmente com a adição destes. Na verdade, esta complexidade apresenta-se como uma barreira ao avanço científico nesta área que, para já, se mantém desconhecida, e isto testemunha-se, essencialmente no caso de escalonamento de tarefas. A passagem para este novo ambiente, quer se trate de sistemas de tempo real ou não, promete gerar a oportunidade de realizar trabalho que no primeiro caso nunca seria possível, criando assim, novas garantias de desempenho, menos gastos monetários e menores consumos de energia. Este último fator, apresentou-se desde cedo, como, talvez, a maior barreira de desenvolvimento de novos processadores na área uniprocessador, dado que, à medida que novos eram lançados para o mercado, ao mesmo tempo que ofereciam maior performance, foram levando ao conhecimento de um limite de geração de calor que obrigou ao surgimento da área multiprocessador. No futuro, espera-se que o número de processadores num determinado chip venha a aumentar, e como é óbvio, novas técnicas de exploração das suas inerentes vantagens têm de ser desenvolvidas, e a área relacionada com os algoritmos de escalonamento não é exceção. Ao longo dos anos, diferentes categorias de algoritmos multiprocessador para dar resposta a este problema têm vindo a ser desenvolvidos, destacando-se principalmente estes: globais, particionados e semi-particionados. A perspectiva global, supõe a existência de uma fila global que é acessível por todos os processadores disponíveis. Este fato torna disponível a migração de tarefas, isto é, é possível parar a execução de uma tarefa e resumir a sua execução num processador distinto. Num dado instante, num grupo de tarefas, m, as tarefas de maior prioridade são selecionadas para execução. Este tipo promete limites de utilização altos, a custo elevado de preempções/migrações de tarefas. Em contraste, os algoritmos particionados, colocam as tarefas em partições, e estas, são atribuídas a um dos processadores disponíveis, isto é, para cada processador, é atribuída uma partição. Por essa razão, a migração de tarefas não é possível, acabando por fazer com que o limite de utilização não seja tão alto quando comparado com o caso anterior, mas o número de preempções de tarefas decresce significativamente. O esquema semi-particionado, é uma resposta de caráter hibrido entre os casos anteriores, pois existem tarefas que são particionadas, para serem executadas exclusivamente por um grupo de processadores, e outras que são atribuídas a apenas um processador. Com isto, resulta uma solução que é capaz de distribuir o trabalho a ser realizado de uma forma mais eficiente e balanceada. Infelizmente, para todos estes casos, existe uma discrepância entre a teoria e a prática, pois acaba-se por se assumir conceitos que não são aplicáveis na vida real. Para dar resposta a este problema, é necessário implementar estes algoritmos de escalonamento em sistemas operativos reais e averiguar a sua aplicabilidade, para caso isso não aconteça, as alterações necessárias sejam feitas, quer a nível teórico quer a nível prá

Building object-oriented software with the D-Bus messaging system

Object-oriented programming is a widely adopted paradigm for desktop software development. This paradigm partitions software into separate entities, objects, which consist of data and related procedures used to modify and inspect it. The paradigm has evolved during the last few decades to emphasize decoupling between object implementations, via means such as explicit interface inheritance and event-based implicit invocation. Inter-process communication (IPC) technologies allow applications to interact with each other. This enables making software distributed across multiple processes, resulting in a modular architecture with benefits in resource sharing, robustness, code reuse and security. The support for object-oriented programming concepts varies between IPC systems. This thesis is focused on the D-Bus system, which has recently gained a lot of users, but is still scantily researched. D-Bus has support for asynchronous remote procedure calls with return values and a content-based publish/subscribe event delivery mechanism. In this thesis, several patterns for method invocation in D-Bus and similar systems are compared. The patterns that simulate synchronous local calls are shown to be dangerous. Later, we present a state-caching proxy construct, which avoids the complexity of properly asynchronous calls for object inspection. The proxy and certain supplementary constructs are presented conceptually as generic object-oriented design patterns. The e ect of these patterns on non-functional qualities of software, such as complexity, performance and power consumption, is reasoned about based on the properties of the D-Bus system. The use of the patterns reduces complexity, but maintains the other qualities at a good level. Finally, we present currently existing means of specifying D-Bus object interfaces for the purposes of code and documentation generation. The interface description language used by the Telepathy modular IM/VoIP framework is found to be an useful extension of the basic D-Bus introspection format.

Design Space Exploration for MPSoC Architectures

Multiprocessor system-on-chip (MPSoC) designs utilize the available technology and communication architectures to meet the requirements of the upcoming applications. In MPSoC, the communication platform is both the key enabler, as well as the key differentiator for realizing efficient MPSoCs. It provides product differentiation to meet a diverse, multi-dimensional set of design constraints, including performance, power, energy, reconfigurability, scalability, cost, reliability and time-to-market. The communication resources of a single interconnection platform cannot be fully utilized by all kind of applications, such as the availability of higher communication bandwidth for computation but not data intensive applications is often unfeasible in the practical implementation. This thesis aims to perform the architecture-level design space exploration towards efficient and scalable resource utilization for MPSoC communication architecture. In order to meet the performance requirements within the design constraints, careful selection of MPSoC communication platform, resource aware partitioning and mapping of the application play important role. To enhance the utilization of communication resources, variety of techniques such as resource sharing, multicast to avoid re-transmission of identical data, and adaptive routing can be used. For implementation, these techniques should be customized according to the platform architecture. To address the resource utilization of MPSoC communication platforms, variety of architectures with different design parameters and performance levels, namely Segmented bus (SegBus), Network-on-Chip (NoC) and Three-Dimensional NoC (3D-NoC), are selected. Average packet latency and power consumption are the evaluation parameters for the proposed techniques. In conventional computing architectures, fault on a component makes the connected fault-free components inoperative. Resource sharing approach can utilize the fault-free components to retain the system performance by reducing the impact of faults. Design space exploration also guides to narrow down the selection of MPSoC architecture, which can meet the performance requirements with design constraints.

Multilayer optimization in radio resource allocation for the packet transmission in wireless networks

In the last decade mobile wireless communications have witnessed an explosive growth in the user’s penetration rate and their widespread deployment around the globe. It is expected that this tendency will continue to increase with the convergence of fixed Internet wired networks with mobile ones and with the evolution to the full IP architecture paradigm. Therefore mobile wireless communications will be of paramount importance on the development of the information society of the near future. In particular a research topic of particular relevance in telecommunications nowadays is related to the design and implementation of mobile communication systems of 4th generation. 4G networks will be characterized by the support of multiple radio access technologies in a core network fully compliant with the Internet Protocol (all IP paradigm). Such networks will sustain the stringent quality of service (QoS) requirements and the expected high data rates from the type of multimedia applications to be available in the near future. The approach followed in the design and implementation of the mobile wireless networks of current generation (2G and 3G) has been the stratification of the architecture into a communication protocol model composed by a set of layers, in which each one encompasses some set of functionalities. In such protocol layered model, communications is only allowed between adjacent layers and through specific interface service points. This modular concept eases the implementation of new functionalities as the behaviour of each layer in the protocol stack is not affected by the others. However, the fact that lower layers in the protocol stack model do not utilize information available from upper layers, and vice versa, downgrades the performance achieved. This is particularly relevant if multiple antenna systems, in a MIMO (Multiple Input Multiple Output) configuration, are implemented. MIMO schemes introduce another degree of freedom for radio resource allocation: the space domain. Contrary to the time and frequency domains, radio resources mapped into the spatial domain cannot be assumed as completely orthogonal, due to the amount of interference resulting from users transmitting in the same frequency sub-channel and/or time slots but in different spatial beams. Therefore, the availability of information regarding the state of radio resources, from lower to upper layers, is of fundamental importance in the prosecution of the levels of QoS expected from those multimedia applications. In order to match applications requirements and the constraints of the mobile radio channel, in the last few years researches have proposed a new paradigm for the layered architecture for communications: the cross-layer design framework. In a general way, the cross-layer design paradigm refers to a protocol design in which the dependence between protocol layers is actively exploited, by breaking out the stringent rules which restrict the communication only between adjacent layers in the original reference model, and allowing direct interaction among different layers of the stack. An efficient management of the set of available radio resources demand for the implementation of efficient and low complexity packet schedulers which prioritize user’s transmissions according to inputs provided from lower as well as upper layers in the protocol stack, fully compliant with the cross-layer design paradigm. Specifically, efficiently designed packet schedulers for 4G networks should result in the maximization of the capacity available, through the consideration of the limitations imposed by the mobile radio channel and comply with the set of QoS requirements from the application layer. IEEE 802.16e standard, also named as Mobile WiMAX, seems to comply with the specifications of 4G mobile networks. The scalable architecture, low cost implementation and high data throughput, enable efficient data multiplexing and low data latency, which are attributes essential to enable broadband data services. Also, the connection oriented approach of Its medium access layer is fully compliant with the quality of service demands from such applications. Therefore, Mobile WiMAX seems to be a promising 4G mobile wireless networks candidate. In this thesis it is proposed the investigation, design and implementation of packet scheduling algorithms for the efficient management of the set of available radio resources, in time, frequency and spatial domains of the Mobile WiMAX networks. The proposed algorithms combine input metrics from physical layer and QoS requirements from upper layers, according to the crosslayer design paradigm. Proposed schedulers are evaluated by means of system level simulations, conducted in a system level simulation platform implementing the physical and medium access control layers of the IEEE802.16e standard.

Least-cost Disjoint Paths with Dependent Cost Structure in Wavelength Continuous Optical WDM Networks

One of the important issues in establishing a fault tolerant connection in a wavelength division multiplexing optical network is computing a pair of disjoint working and protection paths and a free wavelength along the paths. While most of the earlier research focused only on computing disjoint paths, in this work we consider computing both disjoint paths and a free wavelength along the paths. The concept of dependent cost structure (DCS) of protection paths to enhance their resource sharing ability was proposed in our earlier work. In this work we extend the concept of DCS of protection paths to wavelength continuous networks. We formalize the problem of computing disjoint paths with DCS in wavelength continuous networks and prove that it is NP-complete. We present an iterative heuristic that uses a layered graph model to compute disjoint paths with DCS and identify a free wavelength.

Hardware/Software Design of Dynamic Real-Time Schedulers for Embedded Multiprocessor Systems

The new generation of multicore processors opens new perspectives for the design of embedded systems. Multiprocessing, however, poses new challenges to the scheduling of real-time applications, in which the ever-increasing computational demands are constantly flanked by the need of meeting critical time constraints. Many research works have contributed to this field introducing new advanced scheduling algorithms. However, despite many of these works have solidly demonstrated their effectiveness, the actual support for multiprocessor real-time scheduling offered by current operating systems is still very limited. This dissertation deals with implementative aspects of real-time schedulers in modern embedded multiprocessor systems. The first contribution is represented by an open-source scheduling framework, which is capable of realizing complex multiprocessor scheduling policies, such as G-EDF, on conventional operating systems exploiting only their native scheduler from user-space. A set of experimental evaluations compare the proposed solution to other research projects that pursue the same goals by means of kernel modifications, highlighting comparable scheduling performances. The principles that underpin the operation of the framework, originally designed for symmetric multiprocessors, have been further extended first to asymmetric ones, which are subjected to major restrictions such as the lack of support for task migrations, and later to re-programmable hardware architectures (FPGAs). In the latter case, this work introduces a scheduling accelerator, which offloads most of the scheduling operations to the hardware and exhibits extremely low scheduling jitter. The realization of a portable scheduling framework presented many interesting software challenges. One of these has been represented by timekeeping. In this regard, a further contribution is represented by a novel data structure, called addressable binary heap (ABH). Such ABH, which is conceptually a pointer-based implementation of a binary heap, shows very interesting average and worst-case performances when addressing the problem of tick-less timekeeping of high-resolution timers.

Operating System Contribution to Composable Timing Behaviour in High-Integrity Real-Time Systems

The development of High-Integrity Real-Time Systems has a high footprint in terms of human, material and schedule costs. Factoring functional, reusable logic in the application favors incremental development and contains costs. Yet, achieving incrementality in the timing behavior is a much harder problem. Complex features at all levels of the execution stack, aimed to boost average-case performance, exhibit timing behavior highly dependent on execution history, which wrecks time composability and incrementaility with it. Our goal here is to restitute time composability to the execution stack, working bottom up across it. We first characterize time composability without making assumptions on the system architecture or the software deployment to it. Later, we focus on the role played by the real-time operating system in our pursuit. Initially we consider single-core processors and, becoming less permissive on the admissible hardware features, we devise solutions that restore a convincing degree of time composability. To show what can be done for real, we developed TiCOS, an ARINC-compliant kernel, and re-designed ORK+, a kernel for Ada Ravenscar runtimes. In that work, we added support for limited-preemption to ORK+, an absolute premiere in the landscape of real-word kernels. Our implementation allows resource sharing to co-exist with limited-preemptive scheduling, which extends state of the art. We then turn our attention to multicore architectures, first considering partitioned systems, for which we achieve results close to those obtained for single-core processors. Subsequently, we shy away from the over-provision of those systems and consider less restrictive uses of homogeneous multiprocessors, where the scheduling algorithm is key to high schedulable utilization. To that end we single out RUN, a promising baseline, and extend it to SPRINT, which supports sporadic task sets, hence matches real-world industrial needs better. To corroborate our results we present findings from real-world case studies from avionic industry.

A serial scheme for minimizing the duration of resource-constrained projects within Microsoft Project

Microsoft Project is one of the most-widely used software packages for project management. For the scheduling of resource-constrained projects, the package applies a priority-based procedure using a specific schedule-generation scheme. This procedure performs relatively poorly when compared against other software packages or state-of-the-art methods for resource-constrained project scheduling. In Microsoft Project 2010, it is possible to work with schedules that are infeasible with respect to the precedence or the resource constraints. We propose a novel schedule-generation scheme that makes use of this possibility. Under this scheme, the project tasks are scheduled sequentially while taking into account all temporal and resource constraints that a user can define within Microsoft Project. The scheme can be implemented as a priority-rule based heuristic procedure. Our computational results for two real-world construction projects indicate that this procedure outperforms the built-in procedure of Microsoft Project

Risk sharing with Multilateral Financial Institutions in infrastructure and energy project financing : effect on capital relief for commercial banks

(Matsukawa and Habeck, 2007) analyse the main instruments for risk mitigation in infrastructure financing with Multilateral Financial Institutions (MFIs). Their review coincided with the global financial crisis of 2007-08, and is highly relevant in current times considering the sovereign debt crisis, the lack of available capital and the increases in bank regulation in Western economies. The current macroeconomic environment has seen a slowdown in the level of finance for infrastructure projects, as they pose a higher credit risk given their requirements for long term investments. The rationale for this work is to look for innovative solutions that are focused on the credit risk mitigation of infrastructure and energy projects whilst optimizing the economic capital allocation for commercial banks. This objective is achieved through risk-sharing with MFIs and looking for capital relief in project finance transactions. This research finds out the answer to the main question: "What is the impact of risk-sharing with MFIs on project finance transactions to increase their efficiency and viability?", and is developed from the perspective of a commercial bank assessing the economic capital used and analysing the relevant variables for it: Probability of Default, Loss Given Default and Recovery Rates, (Altman, 2010). An overview of project finance for the infrastructure and energy sectors in terms of the volume of transactions worldwide is outlined, along with a summary of risk-sharing financing with MFIs. A review of the current regulatory framework beneath risk-sharing in structured finance with MFIs is also analysed. From here, the impact of risk-sharing and the diversification effect in infrastructure and energy projects is assessed, from the perspective of economic capital allocation for a commercial bank. CreditMetrics (J. P. Morgan, 1997) is applied over an existing well diversified portfolio of project finance infrastructure and energy investments, working with the main risk capital measures: economic capital, RAROC, and EVA. The conclusions of this research show that economic capital allocation on a portfolio of project finance along with risk-sharing with MFIs have a huge impact on capital relief whilst increasing performance profitability for commercial banks. There is an outstanding diversification effect due to the portfolio, which is combined with risk mitigation and an improvement in recovery rates through Partial Credit Guarantees issued by MFIs. A stress test scenario analysis is applied to the current assumptions and credit risk model, considering a downgrade in the rating for the commercial bank (lender) and an increase of default in emerging countries, presenting a direct impact on economic capital, through an increase in expected loss and a decrease in performance profitability. Getting capital relief through risk-sharing makes it more viable for commercial banks to finance infrastructure and energy projects, with the beneficial effect of a direct impact of these investments on GDP growth and employment. The main contribution of this work is to promote a strategic economic capital allocation in infrastructure and energy financing through innovative risk-sharing with MFIs and economic pricing to create economic value added for banks, and to allow the financing of more infrastructure and energy projects. This work suggests several topics for further research in relation to issues analysed. (Matsukawa and Habeck, 2007) analizan los principales instrumentos de mitigación de riesgos en las Instituciones Financieras Multilaterales (IFMs) para la financiación de infraestructuras. Su presentación coincidió con el inicio de la crisis financiera en Agosto de 2007, y sus consecuencias persisten en la actualidad, destacando la deuda soberana en economías desarrolladas y los problemas capitalización de los bancos. Este entorno macroeconómico ha ralentizado la financiación de proyectos de infraestructuras. El actual trabajo de investigación tiene su motivación en la búsqueda de soluciones para la financiación de proyectos de infraestructuras y de energía, mitigando los riesgos inherentes, con el objeto de reducir el consumo de capital económico en los bancos financiadores. Este objetivo se alcanza compartiendo el riesgo de la financiación con IFMs, a través de estructuras de risk-sharing. La investigación responde la pregunta: "Cuál es el impacto de risk-sharing con IFMs, en la financiación de proyectos para aumentar su eficiencia y viabilidad?". El trabajo se desarrolla desde el enfoque de un banco comercial, estimando el consumo de capital económico en la financiación de proyectos y analizando las principales variables del riesgo de crédito, Probability of Default, Loss Given Default and Recovery Rates, (Altman, 2010). La investigación presenta las cifras globales de Project Finance en los sectores de infraestructuras y de energía, y analiza el marco regulatorio internacional en relación al consumo de capital económico en la financiación de proyectos en los que participan IFMs. A continuación, el trabajo modeliza una cartera real, bien diversificada, de Project Finance de infraestructuras y de energía, aplicando la metodología CreditMet- rics (J. P. Morgan, 1997). Su objeto es estimar el consumo de capital económico y la rentabilidad de la cartera de proyectos a través del RAROC y EVA. La modelización permite estimar el efecto diversificación y la liberación de capital económico consecuencia del risk-sharing. Los resultados muestran el enorme impacto del efecto diversificación de la cartera, así como de las garantías parciales de las IFMs que mitigan riesgos, mejoran el recovery rate de los proyectos y reducen el consumo de capital económico para el banco comercial, mientras aumentan la rentabilidad, RAROC, y crean valor económico, EVA. En escenarios económicos de inestabilidad, empeoramiento del rating de los bancos, aumentos de default en los proyectos y de correlación en las carteras, hay un impacto directo en el capital económico y en la pérdida de rentabilidad. La liberación de capital económico, como se plantea en la presente investigación, permitirá financiar más proyectos de infraestructuras y de energía, lo que repercutirá en un mayor crecimiento económico y creación de empleo. La principal contribución de este trabajo es promover la gestión activa del capital económico en la financiación de infraestructuras y de proyectos energéticos, a través de estructuras innovadoras de risk-sharing con IFMs y de creación de valor económico en los bancos comerciales, lo que mejoraría su eficiencia y capitalización. La aportación metodológica del trabajo se convierte por su originalidad en una contribución, que sugiere y facilita nuevas líneas de investigación académica en las principales variables del riesgo de crédito que afectan al capital económico en la financiación de proyectos.