Scheduling Configuration Research Articles

RouteNet-Fermi: Network Modeling With Graph Neural Networks

Network models are an essential block of modern networks. For example, they are widely used in network planning and optimization. However, as networks increase in scale and complexity, some models present limitations, such as the assumption of Markovian traffic in queuing theory models, or the high computational cost of network simulators. Recent advances in machine learning, such as Graph Neural Networks (GNN), are enabling a new generation of network models that are data-driven and can learn complex non-linear behaviors. In this paper, we present RouteNet-Fermi, a custom GNN model that shares the same goals as Queuing Theory, while being considerably more accurate in the presence of realistic traffic models. The proposed model predicts accurately the delay, jitter, and packet loss of a network. We have tested RouteNet-Fermi in networks of increasing size (up to 300 nodes), including samples with mixed traffic profiles — e.g., with complex non-Markovian models — and arbitrary routing and queue scheduling configurations. Our experimental results show that RouteNet-Fermi achieves similar accuracy as computationally-expensive packet-level simulators and scales accurately to larger networks. Our model produces delay estimates with a mean relative error of 6.24% when applied to a test dataset of 1,000 samples, including network topologies one order of magnitude larger than those seen during training. Finally, we have also evaluated RouteNet-Fermi with measurements from a physical testbed and packet traces from a real-life network.

Fast DRL-based scheduler configuration tuning for reducing tail latency in edge-cloud jobs

Edge-cloud applications are rapidly prevailing in recent years and pose the challenge of using both resource-strenuous edge devices and elastic cloud resources under dynamic workloads. Efficient resource allocation on edge-cloud jobs via cluster schedulers (e.g. Kubernetes/Volcano scheduler) is essential to guarantee their performance, e.g. tail latency, and such allocation is sensitive to scheduler configurations such as applied scheduling algorithms and task restart/discard policy. Deep reinforcement learning (DRL) is increasingly applied to optimize scheduling decisions. However, DRL faces the conundrum of achieving high rewards at a dauntingly long training time (e.g. hours or days), making it difficult to tune the scheduler configurations online in accordance to dynamically changing edge-cloud workloads and resources. For such an issue, this paper proposes EdgeTuner, a fast scheduler configuration tuning approach that efficiently leverages DRL to reduce tail latency of edge-cloud jobs. The enabling feature of EdgeTuner is to effectively simulate the execution of edge-cloud jobs under different scheduler configurations and thus quickly estimate these configurations’ influence on job performance. The simulation results allow EdgeTuner to timely train a DRL agent in order to properly tune scheduler configurations in dynamic edge-cloud environment. We implement EdgeTuner in both Kubernetes and Volcano schedulers and extensively evaluate it on real workloads driven by Alibaba production traces. Our results show that EdgeTuner outperforms prevailing scheduling algorithms by achieving much lower tail latency while accelerating DRL training speed by an average of 151.63x.

K8sSim: A Simulation Tool for Kubernetes Schedulers and Its Applications in Scheduling Algorithm Optimization

In recent years, Kubernetes (K8s) has become a dominant resource management and scheduling system in the cloud. In practical scenarios, short-running cloud workloads are usually scheduled through different scheduling algorithms provided by Kubernetes. For example, artificial intelligence (AI) workloads are scheduled through different Volcano scheduling algorithms, such as GANG_MRP, GANG_LRP, and GANG_BRA. One key challenge is that the selection of scheduling algorithms has considerable impacts on job performance results. However, it takes a prohibitively long time to select the optimal algorithm because applying one algorithm in one single job may take a few minutes to complete. This poses the urgent requirement of a simulator that can quickly evaluate the performance impacts of different algorithms, while also considering scheduling-related factors, such as cluster resources, job structures and scheduler configurations. In this paper, we design and implement a Kubernetes simulator called K8sSim, which incorporates typical Kubernetes and Volcano scheduling algorithms for both generic and AI workloads, and provides an accurate simulation of their scheduling process in real clusters. We use real cluster traces from Alibaba to evaluate the effectiveness of K8sSim, and the evaluation results show that (i) compared to the real cluster, K8sSim can accurately evaluate the performance of different scheduling algorithms with similar CloseRate (a novel metric we define to intuitively show the simulation accuracy), and (ii) it can also quickly obtain the scheduling results of different scheduling algorithms by accelerating the scheduling time by an average of 38.56×.

Fast incremental reconfiguration of dynamic time-sensitive networks at runtime

Static configurations in Time-sensitive Networking (TSN) using the Time-aware Shaper allow precise calculations of deterministic, tight bandwidth and latency guarantees for real-time industrial application streams. However, this static configuration makes introducing flexible changes to a TSN system at runtime very hard. Scenarios of adaptive TSN networks envision that the network configuration evolves with time in accordance with anticipated changes, such as the dynamicity of machine formations and machine reconfigurations.In this paper, we propose a notion of flexibility of scheduler configurations along a network path that facilitates introducing changes to TSN network configurations at runtime. Based on this notion, we develop and analyze algorithms to incrementally reconfigure TSN using the Time-Aware Shaper. These reconfigurations include determining the admissibility of new or changed streams that may possess individual deadlines.

Development of the fundamentals for organizing the transportation of local goods on the railways of the republic of Uzbekistan

Target: The article discusses the approach to variant calculations of a phased increase in line capacity, modeling of a traffic management system aimed at meeting transportation needs and finding a balance between schedules of various categories of trains in the train schedule configuration to improve the efficiency of local freight transportation. Methods: The article uses methods from the theory of operational work, development of train schedules, graph theory, methods of system and cluster analysis, mathematical statistics, economic and mathematical modeling. Results: two-level model of transport and logistics regional network; iterative algorithm for assigning reference stations; approach to calculating the optimal weight of a local train; algorithm and recommendations for drawing up daily train schedules with local cargo. Practical significance: the results will make it possible to develop rational options for the movement of trains with local cargo on schedule in conditions of increasing transit freight traffic.

An Adaptable and Agnostic Flow Scheduling Approach for Data Center Networks

Cloud applications have reshaped the model of services and infrastructure of the Internet. Search engines, social networks, content delivery and retail and e-commerce sites belong to this group of applications. An important element in the architecture of data centers where these applications run is the communication infrastructure, commonly known as data center networks (DCNs). A critical challenge DCNs have to address is the processing of the traffic of cloud applications, which due to its properties is essentially different to the traffic of other Internet applications. In order to improve the responsiveness and throughput of applications, DCNs should be able to prioritize short flows (a few kB) over long flows (several MB). However, given the time and space variations the traffic presents, the information about flow sizes is not available in advance in order to plan the flow scheduling. There has been a wealth of solutions developed in this space, and prior work includes flow scheduling mechanisms optimizing for a specific workload but fall short when workloads are not known in advance, or comprise a collection of applications changing dynamically. In this paper, we present an adaptable mechanism called Adaptable Workload-Agnostic Flow Scheduling (AWAFS). It is an adaptable approach that can adjust in an agnostic way the scheduling configuration of DCN forwarding devices. This agnostic adjustment contributes to reduce the Flow Completion Time (FCT) of those short flows, representing around 85% of the traffic handled by cloud applications. AWAFS operates by observing the traffic and detecting statistical properties that provide a hint to adapt the scheduling parameters. Our evaluation results based on simulation show that AWAFS can reduce the average FCT of short flows between 16.9% and 45.2% when compared to the best existing agnostic non-adaptable solution, without inducing starvation on long flows. Indeed, it can provide improvements as high as 39% for long flows. Additionally, AWAFS can improve the FCT for short flows in scenarios with high heterogeneity in the traffic present in the network, with a reduction up to 5% for the average FCT and 15% for the tail FCT.

Optimal Energy Management of Microgrids Using Quantum Teaching Learning Based Algorithm

Quantum inspired computational intelligence is gaining momentum in the interest of enhancing the performance of existing metaheuristic optimization while solving multi-dimensional nonlinear problems. The microgrid optimal energy scheduling is one such problem that involves multiple distributed energy resources (DER) with volatile characteristics and proficient energy management is essential for their coordination and reducing global carbon emissions. Relatively very few works in the existing literature have attempted to solve this problem using quantum-based algorithms. In this article, a stochastic framework associated with the Quantum Teaching Learning-based optimization (QTLBO) algorithm is devised for the first time to optimize energy flow in the microgrids. Four scenarios concerning seasonal variations are chosen to address the uncertainties related to generated power from DERs with better accuracy. The day-ahead optimum power scheduling configuration of DERs is evaluated for each scenario. The performance of QTLBO is assessed on a grid-connected microgrid network and compared with existing metaheuristic algorithms such as the Real-coded Genetic Algorithm, Differential Evolution, and TLBO. The obtained simulation results prove the superiority of QTLBO in terms of convergence and achieving a global optimum solution by overcoming premature convergence. Further, the proposed stochastic framework is helpful to attain techno-economic benefits to both customers and market operators.

Demand response of grid-connected microgrid based on metaheuristic optimization algorithm

ABSTRACT Demand Response Programs (DRPs) have gained the microgrid (MG) operators phenomenal attention for mobilizing the end-users in alleviating the uncertainties associated with renewable energy sources. In this research work, the effective MG energy management system (EMS) in conjunction with price-driven DRPs is proposed to achieve synergistic coordination between the energy providers and consumers and reduce operational costs. The flexible price elasticity model is implemented instead of using the price elasticity models with a preordained constant value like most existing literature. This results in a more realistic characterization of customer responsiveness to energy price changes and promotes the DRPs under a grid-connected MG environment. With this regard, a stochastic day-ahead energy management strategy is proposed to incorporate four distinct DRPs and schedule the MG distributed energy resources. The proposed strategy is verified on a practical 3-feeder MG test system with a majority of 50% industrial load considered. The short-term scheduling period of 15 min ahead solar and wind power forecast is considered to optimize the microgrid dispatch costs accurately. The intermittent nature of renewable energy sources is addressed by employing a stochastic-based scenario generation and reduction approach. A novel and nature-inspired Black Widow Optimization (BWO) is applied to determine the optimal scheduling configuration. The effectiveness of the BWO is validated in terms of rate of convergence, computational time, and solution efficacy. Finally, the best DRP has been chosen based on its technical and economic performance indices by employing a multi-criteria decision-making approach.

Service Delivery Schedule Effects on Speech Sound Production Outcomes

Purpose Children with speech sound disorders feature prominently on the caseloads of speech-language pathologists working in schools, with many receiving services once or twice weekly for 20-30 min. This study compared the outcomes of services provided twice weekly for 30 min to those provided 4 times weekly for 15 min to examine their effectiveness in remediating speech sound disorders in an elementary school setting. Method A total of 35 students were recruited from an existing public school caseload for participation. Participants were randomly assigned to receive school-based speech therapy services for either 30 min twice weekly or 15 min 4 times weekly. There were no differences between groups in age, gender, or the amount of time spent in general education. Growth was measured by the percentage of Individualized Education Program goals mastered and the percentage of sounds produced correctly in isolation. Results After one calendar year, there was a negligible difference between groups on both the percentage of Individualized Education Program goals mastered and the percentage of sounds produced correctly in isolation. On average, both scheduling configurations were effective in meeting students' needs. Conclusions The results of this study suggest that children with speech sound disorders receiving school-based speech therapy services can benefit from a variety of scheduling options. Awareness of such options is an invaluable resource to speech-language pathologists wanting to provide effective and efficient services. Future research should continue investigating service delivery models' effects in applied settings.

Resource scheduling strategy for uncertain factors in mobile cloud computing

At present, resource configuration of mobile cloud computing has received extensive attention from the outside world. Most of the similar resource scheduling configuration fails to comprehensively consider the dynamics of mobile terminals and the difference in user requested resources. Therefore, considering uncertainty in paging scheduling under mobile cloud resource environment from the perspective of consumers has become the key to solving the problem of resource allocation in the mobile cloud computing environment. This paper proposes an adaptive matching resource allocation algorithm based on uncertain factors under mobile cloud computing environment. Uncertain factors of the mobile terminal are derived via QoS attribute, and then user information and load characteristics of the user requested resources are analyzed through CLIQUE similarity matching. Afterwards, based on the mapping between similarity and resources, resource paging allocation can be carried out based on adaptive matching resource allocation algorithm. From the perspective of consumers, dynamics of mobile terminals and uncertainty of paging scheduling in the mobile cloud resource environment under different user requested resources can be considered to allow minimized delay and optimized paging strategies.

Designing schedule configuration of a hybrid appointment system for a two-stage outpatient clinic with multiple servers.

Even though several clinics serve patients in more than one stage (e.g., visit nurse and then visit doctor) and employ multiple providers in each stage, most of the previous work on appointment system design considers a simplified single-stage single-server clinic. Motivated by a real-life clinic setting, this paper aims to determine the schedule configuration of a hybrid appointment system (i.e., the number of pre-booking and same-day time slots reserved for a physician along with their positions in the schedule) for a two-stage multi-server clinic. A stochastic optimization model is developed to obtain a schedule configuration that minimizes the expected total cost - a weighted sum of excessive patient waiting time, resource idle time, resource overtime, and denied appointment requests. Owing to its computational complexity, we estimate the expected total cost using the sample average approximation method. The proposed model is verified and validated using small test instances and subject matter experts. A case study of a family medicine clinic in Pennsylvania is used to illustrate the proposed approach. The schedule generated by the proposed model results in a significantly lower expected cost compared to the approximated single-stage system's best schedule configuration and clinic's existing configuration. Further, sensitivity analysis is conducted to assess the impacts of no-show rate, service time variation, and cost ratios on the schedule configuration. Our findings demonstrate that the schedule configuration is sensitive to changes in the average no-show rate and cost ratios but is not significantly impacted by service time variation. Several managerial insights are also drawn from our analysis. Finally, we provide directions for future research that also highlights the potential to use the revenue management approach to address the problem under study.

A Matheuristic for Joint Optimal Power and Scheduling Assignment in DVB-T2 Networks

Because of the introduction and spread of the second generation of the Digital Video Broadcasting—Terrestrial standard (DVB-T2), already active television broadcasters and new broadcasters that have entered in the market will be required to (re)design their networks. This is generating a new interest for effective and efficient DVB optimization software tools. In this work, we propose a strengthened binary linear programming model for representing the optimal DVB design problem, including power and scheduling configuration, and propose a new matheuristic for its solution. The matheuristic combines a genetic algorithm, adopted to efficiently explore the solution space of power emissions of DVB stations, with relaxation-guided variable fixing and exact large neighborhood searches formulated as integer linear programming (ILP) problems solved exactly. Computational tests on realistic instances show that the new matheuristic performs much better than a state-of-the-art optimization solver, identifying solutions associated with much higher user coverage.

Impact of Scheduling Configurations on State-Mandated Social Studies Test Scores

Impact of Scheduling Configurations on State-Mandated Social Studies Test Scores Kenneth E. Vogler, Susan Schramm-Pate Abstract This study compared the academic performance of seventh-grade students on a state-mandated social studies accountability test by scheduling configuration used, explored principals’ perceptions regarding the impact scheduling configurations have on social studies instruction and student preparedness for the next grade level in social studies, and examined the barriers affecting time allocated for social studies. Results of South Carolina’s accountability assessment system’s social studies seventh-grade test scores in 117 schools, as well as a survey completed by the principals of those schools, were analyzed. After controlling for poverty, no significant difference was found between student social studies accountability test performance and scheduling configuration used. However, findings showed statistically significant differences between scheduling configuration used and principals’ perceptions of its impact on social studies instruction and students’ preparedness for the next grade level in social studies. Additionally, results exposed no clear consensus among principals regarding barriers affecting time allocated for social studies. Full Text: PDF DOI: 10.15640/jehd.v9n3a2

Workload-Adaptive Configuration Tuning for Hierarchical Cloud Schedulers

Cluster schedulers provide flexible resource sharing mechanism for best-effort cloud jobs, which occupy a majority in modern datacenters. Properly tuning a scheduler's configurations is the key to these jobs’ performance because it decides how to allocate resources among them. Today's cloud scheduling systems usually rely on cluster operators to set the configuration and thus overlook the potential performance improvement through optimally configuring the scheduler according to the heterogeneous and dynamic cloud workloads. In this paper, we introduce AdaptiveConfig, a run-time configurator for cluster schedulers that automatically adapts to the changing workload and resource status in two steps. First, a comparison approach estimates jobs’ performances under different configurations and diverse scheduling scenarios. The key idea here is to transform a scheduler's resource allocation mechanism and their variable influence factors (configurations, scheduling constraints, available resources, and workload status) into business rules and facts in a rule engine, thereby reasoning about these correlated factors in job performance comparison. Second, a workload-adaptive optimizer transforms the cluster-level searching of huge configuration space into an equivalent dynamic programming problem that can be efficiently solved at scale. We implement AdaptiveConfig on the popular YARN Capacity and Fair schedulers and demonstrate its effectiveness using real-world Facebook and Google workloads, i.e., successfully finding best configurations for most of scheduling scenarios and considerably reducing latencies by a factor of two with low optimization time.

Empirical study to explore the impact of ergonomics on workforce scheduling

This work is focused on the workforce scheduling problem, investigating how the ergonomic exposure of a worker may affect the results of workforce allocation and the relative impact on production performances. A research methodology has been developed within a case study of an assembly flow with the twofold objective of (i) setting up a system able to consider the ergonomic parameters of workers within the solution of a workforce scheduling problem and (ii) finding the possible impacts that ergonomic postures can have on workforce allocation parameters. The ergonomic analysis, joint with the development of a constraint optimisation problem, resulted in a mathematical depiction of the ergonomic exposures and in a workforce ergonomic scheduling model. The study assessed how ergonomics may impact on workforce scheduling and the relative production capacity. Then, an experimental campaign joint with a tuning activity of the model resulted in a workforce scheduling configuration able to front the apparently contrasting objectives of production capacity optimisation and ergonomic stress lowering. The empirical results allowed also to quantify the trade-off between production performances, in terms of production capacity and idle time, versus ergonomic stress of the workers.

Sensor and Dynamic Pricing Aware Vertical Transportation in Smart Buildings

In modern smart buildings, the electricity consumption of a building is monitored every time and costs differently at each time slot of a day. Smart buildings are also equipped with indoor sensors that can track the movement of human beings. In this paper, we propose a new elevator control system (ECS) that utilizes two kinds of context information in smart buildings: (1) human movements estimated by indoor sensors and (2) dynamic changes of electricity price. In particular, indoor sensors recognize elevator passengers before they press the elevator call buttons, and smart meters inform the dynamically changing price of the electricity to ECS. By using this information, our ECS aims at minimizing both the electricity cost and the waiting time of passengers. As this is a complex optimization problem, we use an evolutionary computation technique based on genetic algorithms (GA). We inject a learning module into the control unit of ECS, which monitors the change of the electricity price and the passengers’ traffic detected by sensors. Experimental results with the simulator we developed show that our ECS outperforms the scheduling configuration that does not consider sensor information or electricity price changes.

Research and Exploit of Resource Sharing Strategy at IHEP

At IHEP (Institute of High Energy Physics, Chinese Academy of Sciences), computing resources are contributed by different experiments including BES, JUNO, DYW, HXMT, etc. The resources were divided into different partitions to satisfy the dedicated experiment data processing requirements. IHEP had a local Torqu&Maui cluster with 50 queues serving for above 10 experiments. The separated resource partitions leaded to imbalance resource load. In a typical situation, BES resource partition was quite busy without free slot but still with lots of jobs in idle, while JUNO resources are free and wasted seriously. After moving resources from Torque&Maui to HTCondor in 2016, job scheduling efficiency has been improved a lot. In order to balance the imbalance resource load, we designed an efficient sharing strategy to improve the overall resourceutilization. We created an unified pool shared by all experiments. For each experiment, resources are divided into two parts: dedicated resource and sharing resource. The slots in dedicated resource only run jobs from its own experiment, and the slots in sharing resource are shared by jobs from all experiments. Default ratio of dedicated resource to sharing resource is 1:4. To maximize the sharing effectiveness, the ratio is dynamically adjusted between 0:5 and 4:1 based on the number of jobs submitted by each experiment. We have developed a central control system to decide how many resources can be allocated to each experiment group. This system is implemented at two sides: server side and client side. A management database is built at server side, which is storing resource, group and experiment information. Once the sharing ratio needs to be adjusted, resource group will be changed and updated into database. The resource group information is published to the server buffer in real-time. The client periodically pulls resource group information from server buffer via https protocol And resource scheduling configuration at client side is changed based on the resource group information. With this method, share ratio can be modified and deployed dynamically. Sharing strategy is implemented with HTCondor. ClassAd mechanism and accounting-group in HTCondor facilitate to utilizethe sharing strategy at IHEP computing cluster. With the sharing strategy, resource usage has been improved dramatically.

Correct‐by‐construction specification to verified code

AbstractEvent‐B is a formal notation and method for the systems development. The key feature of this method is to produce correct‐by‐construction system designs. Once the correct design is established, the remaining work is to generate or implement correct code from the design. Two main problems remain in the process from the correct‐by‐construction design to the correct software. First, the Event‐B design is “quasi‐correct” due to some technical limitations. For instance, it is still difficult to prove the liveness properties by the Rodin platform; it is not possible to construct the Event‐B design with floating‐point arithmetic, and sometimes, the Event‐B model is incomplete and must rely on the third‐party libraries. Therefore, a method is needed to complement these modeling and proof gaps. Secondly, proving the correctness of an automatic code generator is very difficult; therefore, a method is needed to guarantee the correctness of the produced code without proving the code generator. In this article, we address the above 2 problems by introducing an intermediate formal language called High‐Level Language (HLL) between the Event‐B models and the C code. The Event‐B model is translated to HLL with an additional schedule configuration, where Event‐B invariants and system invariants (here, deadlock‐freeness and liveness properties) are proved using a SAT‐based model checker called S3. This proof guarantees the correctness of the HLL model with respect to the Event‐B model. The C code is then automatically generated from the HLL model for most functions and is manually implemented for the third‐party ones according to the function contracts defined in Event‐B. The correctness of the generated C code is guaranteed using the equivalence proof, and the correctness of the implemented C code is guaranteed using the conformance proof. Through the article, we use a traffic light controller to illustrate the proposed method; then, we apply the method to an automatic protection function of a 3‐wheeled robot to evaluate its feasibility.

Empirical Evaluation and Enhancement of Enterprise Storage System Request Scheduling

Since little has been reported in the literature concerning enterprise storage system file-level request scheduling, we do not have enough knowledge about how various scheduling factors affect performance. Moreover, we are in lack of a good understanding on how to enhance request scheduling to adapt to the changing characteristics of workloads and hardware resources. To answer these questions, we first build a request scheduler prototype based on WAFL®, a mainstream file system running on numerous enterprise storage systems worldwide. Next, we use the prototype to quantitatively measure the impact of various scheduling configurations on performance on a NetApp®'s enterprise-class storage system. Several observations have been made. For example, we discover that in order to improve performance, the priority of write requests and non-preempted restarted requests should be boosted in some workloads. Inspired by these observations, we further propose two scheduling enhancement heuristics called SORD (size-oriented request dispatching) and QATS (queue-depth aware time slicing). Finally, we evaluate them by conducting a wide range of experiments using workloads generated by SPC-1 and SFS2014 on both HDD-based and all-flash platforms. Experimental results show that the combination of the two can noticeably reduce average request latency under some workloads.

ВОПРОСЫ ПОВЫШЕНИЯ СТАБИЛЬНОСТИ ВЫПОЛНЕНИЯ ГРАФИКА ДВИЖЕНИЯ ПОЕЗДОВ

Objective: At present the majority of railway lines experiences serious difficulties in handling of the increased flow of freight trains with considerable amount of passenger traffic. In view of this there is a necessity to improve the level of train schedule stability by creating certain time slacks in it, which make it possible to eliminate errors. Methods: The methods of simulation, computational theory and construction of a train schedule graph were applied. Results: The method of train routing was developed on the basis of simulation of schedule configuration. The characteristics of schedule configuration and conditions of its creation were presented. The influence of trainhandling capacity efficiency coefficient on the choice of a configured train routing diagram was studied, as well as one of the vital factors, causing degradation of train schedule fulfillment stability – disagreement in train traffic. It was shown that in case of selecting a configuration it was necessary to increase the headway between consecutive trains after a bunch of trains, and if train overtaking is inevitable – to use the time of extra removal. In order to eliminate the consequences of disagreement in train traffic, it was proposed to increase intervals not between all trains, but to compensate the disagreement after passage of a number of trains, the latter should be specified on an individual basis. The assessment of compensating interval efficiency was fulfilled by means of removal coefficient calculation for different conditions on three options. It was concluded that the compensating interval not only reduces disagreement impact, but also improves train-handling capacity. The example of train schedule stability improvement was considered on the basis of applying configurations at “Malaya Vishera – Bologoye” section on down trains within the period of time from 11.30 pm to 7.30 am. Practical importance: Application of configurations makes it possible to achieve higher implementable levels of speed and train-handling capacity, leads to the detection of time slacks and time buffers, which considerably increase train schedule stability and, consequently, the stability of its fulfillment.