Overflow Probability Research Articles

Optimal control strategies for stormwater detention ponds

Stormwater detention ponds are essential stormwater management solutions that regulate the urban catchment discharge towards streams. Their purposes are to reduce the hydraulic load to avoid stream erosion, as well as to minimize the degradation of the natural waterbody by direct discharge of pollutants. Currently, static controllers are widely implemented for detention pond outflow regulation in engineering practice, i.e., the outflow discharge is capped at a fixed value. Such a passive discharge setting fails to exploit the full potential of the overall water system, hence further improvements are needed. We apply formal methods to synthesize (i.e., derive automatically) optimal active controllers. We model the stormwater detention pond, including the urban catchment area and the rain forecasts with its uncertainty, as hybrid Markov decision processes. Subsequently, we use the tool UppaalStratego to synthesize using Q-learning a control strategy maximizing the retention time for pollutant sedimentation (optimality) while also minimizing the duration of emergency overflow in the detention pond (safety). These strategies are synthesized for both an off-line and on-line settings. Simulation results for an existing pond show that UppaalStratego can learn optimal strategies that significantly reduce emergency overflows. For off-line controllers, a scenario with low rain periods shows a 26% improvement of pollutant sedimentation with respect to static control, and a scenario with high rain periods shows a reduction of overflow probability of 10%–19% for static control to lower than 5%, while pollutant sedimentation has only declined by 7% compared to static-control. For on-line controllers, one scenario with heavy rain shows a 95% overflow duration reduction and a 29% pollutant sedimentation improvement compared to static control.

Level-Crossing Characteristics of an Actively Managed Buffer

In this paper, we examine a buffer with active management that rejects packets basing on the buffer occupancy. Specifically, we derive several metrics characterizing how effectively the algorithm can prevent the queue of packets from becoming too long and how well it assists in flushing the buffer quickly when necessary. First, we compute the probability that the size of the queue is kept below a predefined level L. Second, we calculate the distribution of the amount of time needed to cross level L, the buffer overflow probability, and the average time to buffer overflow. Third, we derive the distribution of the amount of time required to flush the buffer and its average value. A general modeling framework is used in derivations, with a general service time distribution, general rejection function, and a powerful model of the arrival process. The obtained formulas enable, among other things, the solving of many design problems, e.g., those connected with the design of wireless sensor nodes using the N-policy. Several numerical results are provided, including examples of design problems and other calculations.

Video Relay Service Recording System Using Packet-Capture Multiple Buckets Architecture

This paper presents a research and development work for the automatic service recording system using network-based monitoring approach. The project is under the cooperation of National Science and Technology Development Agency (NSTDA) and Thai Telecommunication Relay Service (TTRS). The goal is to archive and record video relay services offered to the deaf and hard of hearing community. Using the network-based monitoring approach, we can develop a video recording system that is fully automated and intelligent to analyze different kinds of video relay services. In brief, the system functions to capture network traffic and analyze network packets, signaling, and related protocols such as TCP, UDP, SIP, SDP, RTP, as well as H.264, G.711 encoding. Then, it records the relevant media streams, creates a video file containing the whole video relay service conversation, and send the file to archive in the cloud storage. The benefits include verification in case of appeal, service evaluation, and service improvement. A technical challenge in this system development is how to process real-time interactive multi flows because it must detect and process a large number of call signaling and media streams that occur as interactive real time. The optimization is vital so that the system can swiftly do the processing in time, without causing the buffer overflow problem that can degrade the recording quality. In this regard, we developed a novel methodology for processing PCAP (Packet Capture) called Multiple Buckets Architecture. Our test results showed that it can significantly reduce the probability of buffer overflow, making the processing more efficient when compared to the traditional processing of single bucket.

Supremum Distribution of Weighted Sum of Random Processes from Orlicz Spaces of Exponential Type with Continuous Deviation

The paper studies distribution of sum of random processes from Orlicz spaces of exponential type weighted by continuous functions, in particular, processes from spaces Subϕ (Ω), SSubϕ (Ω) and class V (ϕ, ψ) are considered. Such spaces and classes of random variables and corresponding stochastic processes provide generalizations of Gaussian and sub-Gaussian random variables and processes and are important for various applications, for example, in queuing theory and financial mathematics. We derive the estimates for the distribution of supremum of weighted sum of such processes deviated by a continuous monotone function using the entropy method. As examples, weighted sum of Wiener and weighted sum of fractional Brownian motion processes with different Hurst indices from classes V (ϕ, ψ) are considered. Corresponding estimates of the probability of exceeding by trajectories of such weighted sums a positive level determined by a linear function are obtained. In the insurance risk theory, such aproblem arises during estimating a ruin probability of the corresponding risk process with a constant premium income, and in the communications theory, it appears for the buffer overflow probability for a single server with a constant service rate.

Evaluation of the probability of overflow from the Abadia de Goiás repository by the Fokker-Planck equation using the Trotter’s formula

A model was constructed with the objective of developing the Fokker-Planck equation for the calculation of the reliability attributes required for risk-informed decision-making involved in the analysis of water infiltration inside the repository located in the Abadia de Goiás municipality, in the metropolitan region of the city of Goiânia. The solution of the Fokker-Planck equation was analytically obtained by the Trotter’s method for a near surface repository. This solution provides the probability density and the probability functions for the height of the liquid (water + radionuclides) column, generated by the infiltrated water in the concrete crypt of the repository. The modeling was unidimensional, and the calculations were performed for the geometric center of the repository crypt, which is the place of greater sensitivity of occurrence of accidental scenarios. The concept of the present model can be extended to other places in the crypt without loss of generality. The developed model is appropriate to analyze the repository overflow, a kind of event that occurs when the height of the liquid column inside the repository reaches the value of the inner height of the concrete crypt of the facility. This accident scenario produces the greatest release of radioactive material to the region outside the repository and, consequently, it is responsible for the main radiological impact for both members of the public and the environment. Calculations performed for the Abadia de Goiás repository indicated that the overflow probability for this facility is strongly dependent on the rainfall rate and also on the institutional time period, varying from about 3% with no rainfall penetration up 99% with the maximum rainfall rate for an institutional time period control of 300 yr. Such results can help making decisions on the problem of risk scenarios related to the disposal of radioactive waste.

Performance of Multidevice Downlink Cell-Free System Under Finite Blocklength for uRLLC With Hard Deadlines

As an important part of beyond the fifth-generation (B5G) and the sixth-generation (6G) mobile communication systems, ultra-reliable and low latency communications (uRLLC) puts forward strict requirements for delay and reliability (e.g., 99.9999% reliability and 500 μs latency). At present, the evaluation measures of delay and reliability are usually based on infinite block length and rely on long-term statistics, which cannot meet the requirement of low latency. The cell-free system, with a very large number of distributed antennas, has the characteristics of macro-diversity and spatial sparsity, which can further enhance the performance of uRLLC. In this paper, the downlink multidevice cell-free system with hard deadlines is considered and analyzed in the finite block length (FBL) regime. The communication’s delay and reliability are described based on two instantaneous evaluation measures: transmission error (TE) and time overflow (TO) probability. From the perspective of information theory, this paper analyzes the analytic expression of TE probability for a single device and the performance impact of FBL on the traditional channel capacity analysis. Considering the multidevice TO probability in a cell-free system, the closed-form expressions of upper and lower bounds are derived and compared with the gamma approximation results. This paper further provides three methods, namely, transmission rate selection, device grouping and space division multiplexing, to balance the delay and reliability of the system and analyzes the performance.

Determination of Characteristics of Associative Storage Devices in Radio Telemetry Systems with Data Compression

In the radio telemetry systems of spacecraft, various data compression methods are used for data processing. When using any compression methods, the data obtained as a result of compression is formed randomly, and transmission over radio communication channels should be carried out evenly over time. This leads to the need to use special buffer storage devices. In addition, existing spacecraft radio telemetry systems require grouping of compressed data streams by certain characteristics. This leads to the need to sort compressed data by streams. Therefore, it is advisable to use associative buffer storage devices in such systems. This article is devoted to the analysis of the processes of formation of output streams of compressed data generated at the output of an associative storage device (ASD). Since the output stream of compressed data is random, queue theory and probability theory are used for analysis. At the same time, associative memory is represented as a queue system. Writing and reading in an ASD can be interpreted as servicing orders in a queue system. The purpose of the analysis is to determine the characteristics of an associative storage device (ASD). Such characteristics are the queue length M{N} in the ASD, the deviation of the queue length D{N} in the ASD and the probability pn of a given volume n of compressed data in the ASD (including the probability of emptying and the probability of memory overflow). The results obtained are of great practical importance, since they can be used to select the amount of memory of an associative storage device (ASD) when designing compression devices for telemetry systems of spacecraft.

On the need to go beyond bucket modelling to evaluate NBS risk of failure under urban constraints

The need to combine simple analytical solutions to control the full spectrum of stochastic events, not just extreme rainfall events related to flood risk, in order to restore the natural water cycle has led to the adoption of probability analysis (PA) as a powerful design tool for urban drainage systems. Applications of PA to sustainable urban drainage and nature-based solution (NBS) design are numerous but often rely on a bucket modelling (BM) approach to assess the efficiency of retention and detention structures.Managing urban growth and climate change requires careful attention to 1) the shape of NBSs to fit into an existing urban grid and 2) the intensity of rainfall, which is expected to increase significantly. The BM approach is insensitive to the shape of technical solutions and the variability of rainfall intensity, so the PA was revised, coupled with a hydrodynamic modelling (HM) approach and compared with previous BM-based approaches.In the low-intensity rainfall regime, HM and BM predict completely different infiltration system (IS) overflow probabilities. In the high-intensity precipitation regime, both provide a bell-shaped probability density function of overflow volumes, although BM tends to underestimate IS overflow volumes with low shape factor and overestimate IS overflow volumes with high shape factor.

Rare-Event Analysis of Packet-Level Coding for URLLC via Virtual Queue

In this paper, we propose a method to analyze the performance of ultra-reliable low-latency communication (URLLC) with packet-level coding when no feedback from a receiver is available. Unlike conventional methods of analyzing URLLC performance using <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">average</i> error rate, we focus on the events of burst or clustered (reception) errors <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> as they can be fatal for certain real-time wireless control systems. In the proposed method, to see the impact of clustered errors on the performance, a virtual queue is considered, where the reception error sequence is regarded as the arrival process and the departure process is characterized by the target error rate. This virtual queue allows to find how often the events of clustered errors of certain sizes occur using large deviations theory. For packet-level channels modeled by an independent and identically distributed process and a two-state Markov chain, the quality-of-service exponents are derived, and the asymptotic probability of buffer overflow is obtained, which agrees with simulation results. This demonstrates that the proposed method using virtual queue is useful to find the probability of system failure due to clustered errors and allows to determine the values of key parameters of URLLC for a certain probability of system failure under given conditions.

Design Optimization Methodology for Diversion Structure with Concrete Cofferdam Using Risk-Based Least-Cost Design Method

The optimal size of a diversion structure should be carefully studied to ensure economic viability and safety during construction. In practice, to determine the size of a diversion structure, design flood frequency is selected as the suggested return period presented by the design standard, which is presented differently. This study proposes a methodology for the design of a diversion structure with a concrete cofferdam adopting risk analysis to reflect the more practical hazard and risk of diversion structure during dam construction. The proposed methodology is based on a risk-based least-cost design process and risk analysis. The optimization result is presented as the lowest expected monetary value, which accounts for construction cost, reconstruction cost, and delay liquidated damage with the failure probability and recovery cost with the overflow probability. This methodology was applied to the case study of the Gulpur hydropower project in Pakistan. The results showed that the optimal design flood frequency is 1 year for a recovery cost of USD 0.5 mil. and 1~2 years for a recovery cost of USD 1.0~2.0 mil. with 3, 4, and 5 years of the usage period of the diversion structure. Furthermore, 2~10 years is the optimal value for a recovery cost of USD 3.0~4.0 mil. These results indicated that the optimal design flood frequency increases as the recovery cost and usage period of the diversion structure increase. The results of the study reveal that the recovery cost and the period of use of the diversion structure affect the design flood frequency of the diversion structure. From a design perspective, the period of use is determined by the construction period of the project or the construction method, whereas the recovery cost depends on the countermeasure method. Therefore, after preparing a proactive plan and estimating the recovery cost, the design flood frequency for the diversion structure should be determined.

Effective Energy Efficiency and Statistical QoS Provisioning Under Markovian Arrivals and Finite Blocklength Regime

In this article, we evaluate the effective energy efficiency (EEE) and propose delay-outage aware resource allocation strategies for energy-limited Internet of Things (IoT) devices under the finite blocklength (FBL) regime. The EEE is a cross-layer model, measured by the ratio of effective capacity to the total consumed power. To maximize the EEE, there is a need to optimize transmission parameters, such as transmission power and rate efficiently. Whereas it is quite complex to study the impact of transmission power, or rate alone, the complexity is aggravated by the simultaneous consideration of both variables. Hence, we formulate power allocation (PA) and rate allocation (RA) optimization problems individually and jointly to maximize EEE. Furthermore, we investigate the performance of the EEE under constant and random arrivals, where statistical QoS constraints are imposed on buffer overflow probability. Using effective bandwidth and effective capacity theories, we determine the arrival rate and the required service rate that satisfy the QoS constraints. After that, we compare the performance of different iterative algorithms, such as Dinkelbach’s and cross entropy, which guarantee the convergence for the optimal solution. By numerical analysis, the influence of source characteristics, fixed transmission rate, error probability, coding blocklength, and QoS constraints on the throughput are identified. Our analysis reveals that the joint PA and RA is the optimal resources allocation strategy for maximizing the EEE in the presence of constant and random data arrivals. Finally, the results illustrate that modified Dinkelbach’s algorithm has high performance and low complexity compared to others.

Estimating Buffer Occupancy sans Message Exchange in Mobile Opportunistic Networks

The multi-copy routing schemes in a mobile opportunistic network (MON) lead to buffer congestion, thereby affecting the network performance. This calls for a proactive buffer management policy for congestion mitigation. Existing works on buffer management in MONs require additional message exchange and are reactive in nature. In this letter, we devise a generalized probabilistic routing model to analyze and estimate the average buffer occupancy, without message exchange. We then estimate the buffer overflow probability using the Chernoff’s bound. The accuracy of the theoretical model is validated through simulation using a synthetic mobility model and a real-life mobility trace.

Про оцінку ймовірності переповнення буферу для мереж зв’язку

In recent years, a large number of research of telecommunications traffic have been conducted. It was found that traffic has a number of specific properties that distinguish it from ordinary traffic. Namely: it has the properties of self-similarity, multifractality, long-term dependence and distribution of the amount of load coming from one source. At present, many other models of traffic with self-similarity properties and so on have been built in other researched works on this topic. Such models are investigated in this paper, which considers traffic in telecommunications networks, the probability of overflow traffic buffer. Statistical models are built to analyze traffic in telecommunications networks, in particular to research the probability of buffer overflow for communication networks. The article presents the results of the analysis of processes in telecommunication networks, in particular traffic; research of possibilities of representation of real processes in the form of random processes on the basis of use of statistical simulation model; the necessary mathematical and statistical models are selected and analyzed; software-implemented models using the Matlab environment; visual graphs for comparison of the received data are given; the analysis of the received models is carried out.

Performance of Multiuser Downlink Cell-Free Massive MIMO Systems With Hard Deadlines

Cell-free massive MIMO (mMIMO) is expected to be a novel network architecture to support massive connections, ultra-high transmission rate, and ultra-reliability low-latency transmission. Therefore, applications in ultra-reliable low-latency communications (URLLC) can be served by the cell-free mMIMO network in the future. This paper considers a multiuser downlink cell-free massive MIMO communication system and defines two events to evaluate the system&#x2019;s failure in latency and reliability performance of the transmission. The first kind of event is defined as Transmission Error, where the value of the downlink rate becomes too high to be supported by the channel between the access points (APs) and user equipments (UEs), while the second event is defined as Time Overflow, where the time of packet delivery violates the hard deadline. The probabilities of these events can help evaluate the URLLC performance of the system because the probability of Transmission Error reflects the reliability of the transmission while the probability of Time Overflow reflects the latency of the transmission. We derive the expressions of the probabilities of these two events and the final probability system outage, with maximum ratio transmission (MRT) and zero-forcing (ZF) precoding, based on the properties of Gamma distribution and the approximation for non-isotropic vectors. We finally provide the numerical results by system-level simulations to show that the expressions are accurate and discuss the influence of the noise variance, the number of UEs, and the precoding scheme on the URLLC performance.

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. We propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

Probability assessment of the Kyiv reservoir overflow

Reservoirs are an integral part of the world’s hydraulic infrastructure and form the basis of modern water management in most countries including Ukraine. However, reservoirs are also sources of an essential danger to the environment, infrastructure, and population. The potential danger and risks to the population living near reservoirs especially downstream may be no less than to people living near nuclear facilities or chemical plants, with which experts and the public usually associate problems of technogenic safety. Moreover, statistics show that about a third of all accidents on dams and levees occurred due to overflow of reservoirs when upstream water levels exceeded allowable values.There are 1103 reservoirs in Ukraine with a total water volume of about 55,500 million m3. The Kyiv reservoir is the third one by volume and water surface area in the country. In addition, the reservoir is created by one of the longest dams in the world; the total dam length of the reservoir reaches 70 km.Admittedly, the overflow of a reservoir can be caused by an extreme flood with inflow parameters exceeding the capacity of hydraulic structures. The challenge is that the capacity of water passage structures may be insufficient both due to the inaccuracy of the hydrological forecast and because of faults, poor functioning, or failures of the hydraulic structures during a design flood. In particular, long-term forecasts of floodwater discharges maxima of the inflow into the Kyiv reservoir based on using various probability distribution functions show the essential divergence of the obtained results. As well, as practice shows, the unavailability of some water passage tracts of the reservoir can reach several months in a year. Sometimes repair works were performed even during floods.The aim of the study consisted of probabilistic forecasting the emergency situation on the Kyiv reservoir as a result of its uncontrolled overflow through the possible inaccuracy of the hydrological forecast concerning an actual water inflow into the reservoir and due to failures of water passage hydraulic structures during floods. To achieve the study aim the following tasks were solved: (1) there was proposed a method of hydrological forecasting, which allows taking into account results of long-term forecasts of floodwater discharges maxima based on using various probability distribution functions and fuzzy modelling; (2) there was performed hydrological forecasting of floodwater discharges maxima of the Dnieper affecting the condition of the Kyiv reservoir based on the actual data collected the Vyshgorod water level gauge; (3) there was assessed the probability of the Kyiv reservoir overflow taking into account the occurrence possibility of a shortage of the capacity of water passage structures with using the failure and fault tree method. Totally, six incompatible hypothetical emergency situations at the Kyiv reservoir were considered. The calculations showed the total probability of the Kyiv reservoir overflow equal to 3.84*10–4 (year–1), which is acceptable to guarantee the hydrological safety of infrastructure and the population.

Performance Analysis of Gamma/M/1 Model for IoT-Based Sensor Data Traffic

Recent investigations of Internet of Things network traffic suggest the failure of traditionally used Poisson process-based models. The paper substantiates this finding by performing statistical analysis of packets inter-arrival time in publicly available datasets of IoT-based sensor data traffic. It is observed that gamma distribution fits well to the inter-arrival time of packets. Motivated by this outcome, a detailed performance evaluation of Gamma/M/1 model is carried out. The closed form expressions of mean queue length, mean waiting time in the queue and overflow probability are derived. Numerical computations show that the mean queue length of Gamma/M/1 model explodes much faster than Poisson process based M/M/1 model when its shape parameter is low and scale parameter is high, whereas, the opposite is observed when the values of parameters are reversed. Monte-Carlo simulation of the Gamma/M/1 model also validates these findings. These results will be useful in dimensioning resources like buffers and in designing congestion-control algorithms for IoT systems.

Case History of Risk Evaluation of Earth-Fill Dams Due to Heavy Rain

The present paper describes an assessment method for risks brought on by heavy rain in order to determine the priority of countermeasures for small earth-fill dams. To evaluate the failure risks of an earth-fill dam, defined as the product of failure probability and damage costs, an unsaturated seepage flow analysis is carried out based on the measured rainfall conditions. The damage costs are calculated using the correlation between the results of a flood analysis after breaching and land use and asset data. Subsequently, an evaluation to prioritize the countermeasures is conducted based on the failure risks. The larger of the two comparative failure probabilities—namely, the probability of overflow and the probability of slip failure—will showcase the dominant factor in the failure of small earth-fill dams, and the failure risk evaluation will determine the priority of the countermeasures for repairing and/or reinforcing decrepit earth-fill dams.

Fast Storm Surge Ensemble Prediction using Searching Optimization of a Numerical Scenario Database

AbstractAccurate storm surge forecasts provided rapidly could support timely decision-making with consideration of tropical cyclone (TC) forecasting error. This study developed a fast storm surge ensemble prediction method based on TC track probability forecasting and searching optimization of a numerical scenario database (SONSD). In a case study of the Fujian Province coast (China), a storm surge scenario database was established using numerical simulations generated by 93,150 hypothetical TCs. In a GIS-based visualization system, a single surge forecast representing 2562 distinct typhoon tracks and the occurrence probability of overflow of seawalls along the coast could be achieved in 1–2 min. Application to the cases of Typhoon Soudelor (2015) and Typhoon Maria (2018) demonstrated that the proposed method is feasible and effective. Storm surge calculated by SONSD had excellent agreement with numerical model results (i.e., mean MAE/RMSE: 7.1/10.7 cm, correlation coefficient: &gt;0.9). Tide prediction also performed well with MAE/RMSE of 9.7/11.6 cm versus the harmonic tide, and MAE/RMSE of phase prediction for all high waters of 0.25/0.31 h versus observations. The predicted high-water level was satisfactory (MAE of 10.8 cm versus observations) when the forecasted and actual positions of the typhoon were close. When the forecasted typhoon position error was large, the ensemble surge prediction effectively reduced prediction error (i.e., the negative bias of −58.5 cm reduced to −5.2 cm versus observations), which helped avoid missed alert warnings. The proposed method could be applied in other regions to provide rapid and accurate decision-making support for government departments.

An Opportunity Downlink Interference Alignment Algorithm Based on Punch Scheduling in Cognitive Heterogeneous Networks

For the hierarchical structure and frequency reuse of cognitive heterogeneous networks, it is inevitable to effectively deal with interference while gaining capacity. In this article, we consider the downlink cognitive heterogeneous network, in which a macro base station can serve a certain number of macro users, and each macro cell is composed of a certain number of micro cells. An opportunistic downlink interference alignment (ODIA) algorithm for cognitive heterogeneous networks based on puncture scheduling is proposed. First, we designed a pair of precoding and decoding matrices to eliminate co-layer interference. Second, in order to reduce the overhead required to transmit system state information(CSI), we proposed a user scheduling algorithm that not only can obtain a larger interference-free size, but also improvements in fairness, system capacity and overflow probability. The simulation results show that the proposed ODIA scheme is superior to the existing interference management algorithms in terms of interference, system capacity and fairness of system resource allocation.