This paper builds upon previous research into training Artificial Neural Network (ANN)-based Proportional-Integral-Derivative (PID) controllers using the Scheduled Sampling (SS) approach. While SS was competitive for First-Order Plus Dead Time systems, its application to more challenging situations was to be studied. To address this issue, we introduce an Enhanced Scheduled Sampling (ESS) and apply it to a non-linear Continuous Stirred-Tank Reactor. The presented ESS methodology incorporates key enhancements such as weighted ANN actuation to blend controller outputs, including a sequence-based control error term and a controlled dynamic learning rate adjustment strategy. Preliminary results show that ESS models substantially outperform those trained with conventional/offline training, achieving control performance closer to the PID benchmark. The ESS framework robustly manages the challenges posed by complex systems, thus laying the foundation for developing effective ANN controllers for advancing future transfer learning research in control.

The CEC-UAB simulator models energy dynamics in citizen energy communities, simulating household consumption, photovoltaic generation, battery storage, and user behavior. This study leverages the simulator to evaluate dynamic energy allocation through predicting distribution coefficients. We compare the Holt-Winters Seasonal Forecasting Approach with the machine learning-based XGBoostLSS method. Using realistic CEC-UAB data, XGBoostLSS outperforms Holt-Winters, achieving a Mean Absolute Error (MAE) of 0.016 versus 0.023, Root Mean Squared Error (RMSE) of 0.022 versus 0.031, and Mean Absolute Scaled Error (MASE) of 0.167 versus 0.240. These results highlight the potential of combining advanced forecasting with realistic simulation tools to enhance fairness and efficiency in community energy systems.

In this paper, we present the implementation of the Benchmark Simulation Model No.1 (BSM1) on a Speedgoat Performance real-time target machine, with the aim of enabling hardware-in-the-loop (HIL) testing of advanced control strategies for wastewater treatment plants (WWTPs). Our main contribution lies in adapting the BSM1 Simulink model for execution in real-time environments. We focus on the dissolved oxygen (DO) control loop and integrate an artificial neural network (ANN)-based controller previously proposed by the authors. The required adjustments include resolving algebraic loops, handling fixed-step time constraints, and enabling real-time signal visualization through interpolation. Preliminary results confirm that the adapted BSM1 model runs reliably on the Speedgoat platform, preserving the dynamics of the original simulation and enabling future real-time control experimentation.

Collective Self-Consumption (CSC) is among the most widely adopted models for energy communities in countries like Spain and France. Despite its growth, challenges remain in optimizing photovoltaic energy distribution, improving short- to medium-term investment returns, and advancing toward smarter, self-sustaining communities. This study examines the Spain regulatory framework to identify key opportunities for enhancing CSC performance. A real-world case study of a Municipal Energy Community (MEC) in Barcelona is analyzed employing historical consumption and generation data. Simulations across two time-interval scenarios are presented, with the objective of evaluating current energy management strategies. The results highlight critical areas where optimization algorithms or machine learning approaches could substantially improve energy distribution and overall community performance.

Accurate and interpretable forecasting of photo-voltaic (PV) output is critical for grid integration and day-ahead market participation. Traditional black-box models often neglect the evolving internal dynamics of solar panels, particularly changes in efficiency due to aging and environmental conditions. This work introduces a novel framework that combines online machine learning with Bayesian inference to simultaneously predict solar power output and infer real-time panel efficiency. The model incrementally updates its understanding of efficiency based on observed data, providing continuous adaptation to changing conditions. By modeling efficiency as a probabilistic parameter, we quantify uncertainty in both predictions and inferences. Our method provides a transparent, adaptive, and uncertainty-aware solution.

Proportional-Integral-Derivative (PID) controllers are extensively used in industrial control applications due to their simplicity and effectiveness in various control tasks. In recent years, there has been a growing emphasis on the integration of Artificial Neural Networks (ANNs) with control theory. This integration aims to harness the versatility of ANNs to facilitate controller design in dynamic environments. Additionally, it opens the possibility of transfer learning for these models, allowing knowledge gained from one control scenario to be applied to others' thereby enhancing adaptability and efficiency in control applications. In this work-in-progress paper, we propose a training framework that addresses the key challenges of modeling PIDs as ANNs, specifically the discrepancy between training and inference behaviors, known as exposure bias, commonly encountered in text summarization models. To tackle this, we integrate scheduled sampling, a technique devised for text sequence generation tasks, with an online control simulation environment.

In this paper, we focus on the design and implementation of a deep learning based model for the identification and control of stable second order mechanical systems. To do so, we propose a model composed of two neural networks. A first neural network performs the identification of the mass, the elastic and damping constants of the system from its open-loop response. After that, a second network predicts the PID controller parameters which are necessary for the correct operation of the system. The proposed system is able to estimate process parameters with a reduced error and provide a resulting PID controller offering a satisfactory system response.

In this paper, we address the design of data-based Artificial Neural Networks (ANN) controllers. More specifically, we consider a scalable design based on a Transfer Learning approach where an ANN controller trained at a given source scenario is transferred to other target domains. In order to properly assess the transfer suitability of the controller, the adoption of a Transfer Suitability Metric (TSM) is required. And here resides the main goal of this paper: to develop a TSM able to measure the amount of information captured by a neural network to estimate a desired output from input data. To do so, we resort to Mutual Information (MI) studies addressing the learning process in a neural network. As shown in the paper, we propose a MI-based metric able to assess the transfer suitability while reducing metric computation complexity.

In the last years, the industrial digitalisation and the Industry 4.0 paradigm is no longer a fairy-tale but a reality. It is becoming more common to find industrial environments relying and adopting data-based approaches to perform some sorts of processes. Some of them are related to the industrial control, where the incursion of Artificial Neural Networks (ANNs) is promoting the usage of data-based solutions to substitute conventional control structures. Besides, one of the greatest issues related to the ANN time-consuming training process has been alleviated by means of Transfer Learning (TL) methods. However, in the industrial control domain TL cannot be freely adopted since the final performance of the transferred control structure cannot be known before substituting the conventional structure. This is an issue that needs to be tackled, especially in critical industrial scenarios where an incorrect control can produce huge disasters. For that reason we present here the Transfer Suitability Metric (TSM). Based on the environments similarities, its main aim is to compute the transference suitability of ANN-based controllers in order to transfer the ANN to the target domain without resorting to new control design and optimization. It provides the plant operators with an insight of the controller behaviour before it is finally substituting the conventional control structure. Results have shown that the metric is highly correlated with the final control behaviour in the sense that the higher the metric, the better the final ANN-based controller performance.

The incursion of the Industry 4.0 paradigm and the Artificial Neural Networks (ANNs) is changing the way as the industrial systems are conceived and controlled. Now, it is more common to talk about data-driven methods either supporting conventional industrial control strategies, or acting as the control itself. Thus, one can find that in the last years it is more common to find control systems which are purely based on data leaving aside the highly complex mathematical models. However, data-driven models and ANNs have to be correctly trained in order to offer a good performance and therefore, be contemplated as the core part of a control strategy. This can become a time-demanding and tedious process. For that reason, Transfer Learning (TL) techniques can be adopted to ease the conception, design and training processes of the data-based and ANNs methods, since the efforts have to be mainly focused on training a unique net which will be then transferred into the other scenarios. In that sense, we present here a TL approach to design and implement the whole control of a Wastewater Treatment Plant (WWTP). First, the control of the quickest dynamics under control is performed by means of a Long Short-Term Memory cell (LSTM) based Proportional Integral (PI) controller (LSTM-based PI). Once the LSTM is trained and tested, its knowledge will be transferred into the remaining WWTP control loops. In that way, an ease and reduction in the time involved in the design and training of the control as well as in its complexity is achieved. Results have shown a twofold achievement: (i) the LSTM-based PI achieves an improvement of the control performance with respect to a conventional PI controller around a 93.56% and a 99.07% in terms of the Integrated Absolute (IAE) and Integrated Squared (ISE) errors between the desired measurement and the obtained one, respectively, and (ii) the LSTM-based PI controller achieves an average improvement in the IAE and ISE around a 9.55% and 15.25%, respectively, when it is transferred into a different WWTP control loop.

Wastewater Treatment Plants (WWTPs) are industries where highly complex and non-linear processes are performed to reduce the pollutant concentrations of residual waters. However, some nitrogen and phosphorus derived pollutants are generated in these processes. As a consequence, certain control strategies have been developed to maintain these pollutants under certain limits. Benchmark Simulation Model No.1 (BSM1), a framework emulating the behaviour of a general purpose WWTP, considers a default controller strategy based on Proportional Integral (PI) controllers. Nevertheless, these controllers are based on linearised models of the WWTP behaviour. For that reason, this work proposes a new control approach based on Internal Model Controllers (IMC) adopting Artificial Neural Networks (ANNs), which are able to model the real plant behaviour without performing linearisation. Results show that the proposed IMC is improving the default controller performance around a 16% and a 53% in terms of the Integral Absolute Error (IAE) and the Integral Square Error (ISE), respectively.

Road traffic forecasting systems are in scenarios where sensor or system failure occur. In those scenarios, it is known that missing values negatively affect estimation accuracy although it is being often underestimate in current deep neural network approaches. Our assumption is that traffic data can be generated from a latent space. Thus, we propose an online unsupervised data imputation method based on learning the data distribution using a variational autoencoder (VAE). This is used as an independent pre-processing step prior to traffic forecasting which is then evaluated against missing data of a real-world dataset. Compared to other methods, we show that VAE improves post-imputation traffic forecasting performance while allowing for data augmentation, data compression and traffic classification at the same time.

In the new envisaged paradigm of vehicular communications, critical safety applications have strict requirements in terms of latency and robustness due to the critical nature of their mission that require periodic status exchange and asynchronous event notifications for a reliable cooperative awareness. Current technologies like IEEE 802.11p and recent solutions like fixed period beaconing or moderately reactive adaptive approaches do not cope with these requirements and lead to scalability problems in high density scenarios. With the aim of avoiding channel congestion in those scenarios we make use of trajectory prediction to reduce the number of transmissions required for a full awareness of the vehicle's position and speed. To do so, only a data prediction model of the vehicle's trajectory is sent over the channel. This allows to meet the latency requirements of safety applications while not relying exclusively on MAC congestion control protocols nor modifying the current standard MAC layer. In order to evaluate the proposed approach, we simulate a V2I network in a road intersection under high density traffic taking into account the packet delivery ratio and the predicted position error metrics. Finally, the simulation results show a better position awareness with a reduced channel load compared to the fixed periodic beaconing approach under high density traffic.

Ultra wide band (UWB) wireless transmission has received notable and considerable attention in the field of next generation location-aware wireless sensor networks (WSNs). This trend is due to the large bandwidth of UWB signals contributing many advantages for positioning, communication, and radar applications: penetration through obstacles, accurate position estimation, high-speed data transmission, and a low-cost, low power transceiver. Commercially available UWB radio modules were evaluated. Such modules have the ability to very precisely measure time of arrival of RF signals, range, or localization. The physical layers specify the received signal strength indicator utilized in the localization technique. We estimated and compared the distance of a walking human with the reference distance in different environments, indoor LOS and hard-NLOS utilizing one of these commercial modules. This report also introduces the identification and mitigation of NLOS channels. The results were highly acceptable for indoor localization because the module attained ranging accuracy in a hard-NLOS environment below one meter.

The impact of the Internet of Things (IoT) on the evolution toward next generation smart environments (e.g., smart homes, buildings, and cities) will largely depend on the efficient integration of IoT and cloud computing technologies. With the predicted explosion in the number of connected devices and IoT services, current centralized cloud architectures, which tend to consolidate computing and storage resources into a few large data centers, will inevitably lead to excessive network load, end-to-end service latencies, and overall power consumption. Thanks to recent advances in network virtualization and programmability, highly distributed cloud networking architectures are a promising solution to efficiently host, manage, and optimize next generation IoT services in smart environments. In this paper, we mathematically formulate the service distribution problem (SDP) in IoT-Cloud networks, referred to as the IoT-CSDP, as a minimum cost mixed-cast flow problem that can be efficiently solved via linear programming. We focus on energy consumption as the major driver of today's network and cloud operational costs and characterize the heterogeneous set of IoT-Cloud network resources according to their associated sensing, computing, and transport capacity and energy efficiency. Our results show that, when properly optimized, the flexibility of IoT-Cloud networks can be efficiently exploited to deliver a wide range of IoT services in the context of next generation smart environments, while significantly reducing overall power consumption.

Data aggregation plays an important role in wireless sensor networks (WSNs) as far as it reduces power consumption and boosts the scalability of the network, especially in topologies that are prone to bottlenecks (e.g. cluster-trees). Existing works in the literature use clustering approaches, principal component analysis (PCA) and/or compressed sensing (CS) strategies. Our contribution is aligned with PCA and explores whether a projection basis that is not the eigenvectors basis may be valid to sustain a normalized mean squared error (NMSE) threshold in signal reconstruction and reduce the energy consumption. We derivate first the NSME achieved with the new basis and elaborate then on the Jacobi eigenvalue decomposition ideas to propose a new subspace-based data aggregation method. The proposed solution reduces transmissions among the sink and one or more data aggregation nodes (DANs) in the network. In our simulations, we consider without loss of generality a single cluster network and results show that the new technique succeeds in satisfying the NMSE requirement and gets close in terms of energy consumption to the best possible solution employing subspace representations. Additionally, the proposed method alleviates the computational load with respect to an eigenvector-based strategy (by a factor of six in our simulations).

During the past years, the development of indoor localization systems has been a hot topic in research because the Global Navigation Satellite Systems (GNSS) suffer from a significant performance degradation as far as line of sight to the satellites is not available. The proposed system employs the Received Signal Strength Indicator (RSSI) from multiple anchor nodes from a operating Wireless Sensor Network (WSN). Additionally, we place multiple receivers around the body of the user and thanks to machine learning techniques, we are able to estimate the distance and angle between the user and any of the anchor nodes of the WSN. This allows us to estimate the heading of the user without the use of inertial sensors or magnetometers. Finally the position estimate of the user is refined using an Extended Kalman Filter (EKF) with the constant velocity kinematic model. The system has been validated in real scenarios obtaining a Root Mean Square Error (RMSE) below the meter for the different tests performed, which is similar to the accuracies achieved by inertial-sensors-based systems.

Wireless Sensor Networks (WSNs) are planned to support a wide range of industrial applications in the near future. The Timeslotted Channel Hopping (TSCH) mode of the IEEE 802.15.4e protocol has been specially designed for harsh industrial environments. In this context, the IETF 6TiSCH working group is currently defining how this standard must be adapted to Low-power and Lossy Networks (LLNs), such as WSNs. The uncertainty and dynamics of industrial environments, combined with the mobility of certain nodes complicates routing. In this paper, we present an extension of the 6TiSCH routing approach to handle the mobility of certain nodes in industrial scenarios. Routing among static nodes is managed using the same approach as 6TiSCH (RPL - IPv6 Routing Protocol for Low- Power and Lossy Networks). Then, we apply a novel position based approach to enhance the communications among mobile and static nodes. This combines end-to-end reliability estimations with a blacklisting process based on the node location. As a result, we can take advantage of the high reliability achieved by gradient-based routing techniques, and also handle the node mobility of non-static nodes. The simulation results indicate that the reliability of the communications among mobile and static nodes is increased, even with high positioning errors, compared to existent geographical routing approaches. As a result, the reliability and the robustness of the IEEE 802.15.4e WSNs with mobile nodes is enhanced even in harsh conditions.

Nowadays, wireless sensor networks (WSN) are used in many different areas. Their capabilities have been increased in the recent years due to the recent advances in electronics. As a result, a single WSN can simultaneously manage multiple applications, generating heterogeneous traffic. Since each application has a different set of requirements, in terms of latency, reliability or energy consumption, single-tree routing schemes cannot efficiently work in this scenario. In order to deal with this situation, this work proposes a multi-tree routing solution based on a gradient routing approach. The proposed scheme constructs, in the same routing process, a different tree for each specific traffic, adapted to its particular requirements. Therefore, multiple and maybe opposite requirements can be fulfilled in the same WSN. Moreover, 3 different trees are proposed for the major data traffic groups in WSN (event detection, non-critical monitoring and critical monitoring). Finally, the proposed solution has been applied in a real scenario for an habitat monitoring application, including alarm messages, ambient conditions measurements and an indoor positioning system. This has validated the implementability of the proposed solution and its capability to efficiently manage heterogeneous traffic in a single WSN.

Wireless sensor networks (WSNs) have strict energy consumption requirements. Moreover, the complexity constraints of the nodes and the wireless dynamics must be considered in real life implementations. CTP (Collection Tree Protocol) is a state-of-the-art routing protocol that considers the main issues that arise in practical WSN applications. Nowadays, commercial wireless sensors can adjust their transmission power to reduce the energy consumption and the collision probability of the network. Since nodes in CTP transmit at a predefined power, the reliability and the lifetime of the network may be reduced. To solve this, this paper proposes an alternative routing metric for CTP, referred to as MaxPDR, that includes a transmission power control in the routing process. With this strategy, the incompatibility issues and the additional signaling that may arise with the combination of individual techniques are avoided. MaxPDR has been implemented in commercial motes to evaluate its performance and compare it with the routing metrics used by the original CTP and ZigBee.

Relaying is a promising technique for the next generation cellular networks. It is highly recommended in the 3GPP LTE-Advanced because it is expected to satisfy the ever growing capacity and coverage demands in a cost-efficient way. Yet, in order to fully exploit the benefits of relaying, we should examine the radio resource allocation between the eNB and the relay nodes. In this paper, we propose a dynamic Physical Resource Blocks (PRBs) allocation scheme in a dual-hop LTE-advanced by using game theory. We define a new repeated game in which a selfish node can achieve cooperative spectrum opportunities sharing under the threat of punishment. Simulation results show that the proposed scheme significantly improves the spectrum utilization and total achieved throughput in the system. We also demonstrate that the game rapidly attain Pareto-efficiency.

In this paper, we consider a cooperative system based on relay selection in a scenario where the available channel state information (CSI) is subject to delays. In order to exploit the selection diversity gains of the system while providing robustness against CSI inaccuracy, we propose a robust relay selection strategy based on a minimum mean square error (MMSE) Bayesian estimator. As shown in the paper, the proposed robust strategy provides significant gains in scenarios with different levels of CSI inaccuracy.

In this paper, we analyze the outage probability and diversity order of opportunistic relay selection in a scenario based on decode and forward and where the available channel state information (CSI) is outdated. The study is conducted analytically by obtaining a closed-form expression for the outage probability, which is defined as the probability that the instantaneous capacity is below a target value. We derive high-SNR approximations for the outage probability. By doing so, we demonstrate that the diversity order of the system is reduced to 1 when CSI is outdated, being this behavior independent of the level of CSI accuracy. A physical explanation for this extreme loss of diversity is provided along with numerical results to support the analytical study.

This work proposes an algorithm to perform the resource allocation in the uplink of an IEEE802.16 standard-based system. The approach is valid for point to multi-point (PMP) and also for tree-deployed mesh networks, already defined for the Worldwide Interoperability for Microwave Access (WiMax). Our solution is based on a proportionally fair distribution of resources and it is formulated using the network utility maximization (NUM) framework. Thanks to convex decomposition techniques, we derive a novel way of solving the NUM problem in a distributed manner. The goal is to attain the global optimal scheduling at the subscriber stations (SS) without the need of gathering information at a central node in the network. The results show significant gains in the time required to reach the optimal resource allocation for a given set of demands.

Orthogonal random beamforming (ORB) constitutes a mean to exploit spatial multiplexing and multi-user diversity (MUD) gains in multi-antenna broadcast channels. To do so, as many random beamformers as transmit antennas (M) are generated and on each beam the user experiencing the most favorable channel conditions is scheduled. Whereas for a large number of users the sum-rate of ORB exhibits an identical growth rate as that of dirty paper coding, performance in sparse networks (or in networks with an uneven spatial distribution of users) is known to be severely impaired. To circumvent that, in this paper we modify the scheduling process in ORB in order to select a subset out of the M available beams. We propose several beam selection algorithms and assess their performance in terms of sum-rate and aggregated throughput (i.e., rate achieved with practical modulation and coding schemes), along with an analysis of their computational complexity. Since ORB schemes require partial channel state information (CSI) to be fed back to the transmitter, we finally investigate the impact of CSI quantization on system performance. More specifically, we prove that most of the MUD can be still exploited with very few quantization bits and we derive a beam selection approach trading-off system performance vs. feedback channel requirements.

In this paper, we explore spatial vs. multi-user diversity tradeoffs in a cellular system with selective feedback. We first derive closed-form expressions of the average system capacity for both SISO and STBC transmission schemes in order to analytically assess the impact of the number of terminals and bandwidth restrictions in the feedback channel. Next, we analyze several design trade-offs in terms of increased average (long term) system capacity vs. robustness to short-term SNR fluctuations for both transmission schemes under consideration

In this paper, we explore spatial vs. multi-user diversity tradeoffs in terms of outage capacity for a non-homogeneous cellular system with selective feedback. More precisely, we analytically derive an upper bound of the outage capacity of both a SISO and an OSTBC transmission scheme and, further, analyze some interesting trade-offs concerning the impact of terminal count and bandwidth restrictions. Such outage capacity analysis is particulary suited for the study of delay-constrained services. Numerical examples reveal that in many scenarios OSTBC is far less sensitive to impairments in the feedback channel.

In multi-antenna downlink systems the optimization of linear preceding is severely hampered by the amount of feedback. An efficient solution consists in opportunistic schemes, which generate M random beams and schedule the users with the highest signal-to-noise-plus-interference ratios (SINRs), which can be made available to the transmitter with very little feedback. Although this technique has been shown to be optimal for asymptotically large number of users, severe performance degradation occurs in practical system where the number of users is limited. In this paper we propose an enhancement of this strategy based on an adaptive beam selection procedure. Instead of transmitting all the generated beams, the scheduler picks the optimum subset of beams that maximizes the system sum-rate according to the feedback information. We propose and compare several beam selection algorithms according to different complexity requirements. In particular, we show that the proposed approaches give substantial gains with respect to conventional opportunistic schemes

Opportunistic schemes employing multiple beams have recently attracted significant interest due to the capability to achieve both multiuser diversity and spatial multiplexing gain at limited feedback load. In this paper we explore the effect of the feedback quantization on the performance of these schemes. We derive a closed-form expression of the system throughput with and without feedback quantization. By doing so, we analytically assess the impact of the number of terminals and the restriction in the feedback bandwidth. It is shown that most of the throughput is preserved by using a few quantization bits

In this paper, we investigate a cross-layer approach to transmit antenna selection capable of adapting the number of active antennas to varying channel conditions. We address a cross-layer methodology in the sense that the criterion for the selection of antenna subsets is the maximization of link layer throughput which takes into account characteristics both at the physical and link layers. In order to enhance system performance, adaptive modulation is included to jointly perform antenna selection and rate adaptation. Performance assessment is conducted in terms of link layer throughput and transmission delay

We explore spatial vs. multi-user diversity tradeoffs in a cellular system with limited feedback. When the average feedback per individual user must be kept low, we show that spatial diversity gains, provided by antenna selection mechanisms and space-time block coding, clearly exceed those of multi-user diversity. Performance assessment is conducted, both analytically and by means of computer simulations, in terms of average system capacity and throughput. Closed-form expressions are derived for the SNR densities associated with the different transmission configurations, along with an approximate lower bound for system throughput.

The paper shows how both spatial and multi-user (MU) diversity can be jointly exploited in a cellular system. By combining space-time block-coding with transmit antenna selection (AS), system performance in terms of channel capacity and for a low to moderate number of users can be substantially improved with respect to the single-input single-output (SISO) case. However, a SISO configuration with AS outperforms both configurations for the whole range of active users. In terms of throughput, however, part or all of the advantage exhibited by the SISO and SISO-AS configurations is lost in favor of those featuring STBC schemes. Closed-form expressions are derived analytically for the SNR densities along with an approximate lower bound for system throughput.

In this paper, we address the problem of transmit beamforming, power allocation, bit loading, and admission control in a multi-user scenario, where several single antenna mobile terminals are served by one base station equipped with an antenna array. In particular, we explore the impact of using either optimal or zero-forcing transmit beamforming schemes in combination with different bit allocation strategies, namely the maximization of the sum rate (MSR), the maximization of the minimum rate (MMR) and a modified version of the latter, for a finite set of modulation schemes. The performance evaluation is conducted by means of system-level simulations, using a realistic channel model for urban micro cells, with an emphasis not only on the aggregated cell throughput but also on the associated fairness issues.

This paper focuses on how computational complexity associated to an algorithm for the maximisation of throughput in a multiple-input multiple-output system can be reduced. Throughput optimisation is achieved by selecting the appropriate subset of antennas on the transmit side. Given the highly non-linear nature of the throughput expression and the finite set of combinations, a straightforward approach consists in checking every single subset. However, this results in a prohibitive complexity. This paper presents two methods, named top-down and bottom-up approaches, that lower computational burden by recursively obtaining throughput expressions and, thus, avoiding unnecessary re-computations. The resulting schemes are compared in terms of number of required floating-point operations.