Arrival Curves Research Articles

Network Calculus Theory and Application: A New Graduate Course for Engineering Students

With the development of modern networks, the quality of service guarantee has become even more important than before. However, various new types of traffic and heterogeneous network architecture make it quite challenging to evaluate the quality of service, such as delay and reliability. Therefore, a novel analysis method is needed to solve this situation. Network calculus is a theory used to analyze the queueing problems in networks, which is the main content to be taught in this graduate course. Before network calculus theory is introduced, the classical queueing theory will be taught. Then, the mathematical fundamentals of network calculus, such as min-plus algebra and cumulative arrival/service process, will be introduced. Next, two branches of network calculus, i.e., deterministic network calculus and stochastic network calculus, will be introduced separately, including the definition of deterministic/stochastic arrival curve and service curve, as well as important theorems, such as delay theorem, flow aggregation theorem, server concatenation theorem. After the theoretical knowledge, practical content will be taught in two parts. First, students are encouraged to establish system models based on their graduate research topics, analyze the service guarantee of their models, and present their work in class. Second, a traffic data collection platform will be taught, and students will collect various traffic data and analyze traffic characteristics based on network calculus theory. Based on the feedback from students during the past three years, students are satisfied with this new course because it focuses on frontier technology and the teaching activities are well-organized.

Improved Network-Calculus Nodal Delay-Bounds in Time-Sensitive Networks

In time-sensitive networks, bounds on worst-case delays are typically obtained by using network calculus and assuming that flows are constrained by bit-level arrival curves. However, in IEEE TSN or IETF DetNet, source flows are constrained on the number of packets rather than bits. A common approach to obtain a delay bound is to derive a bit-level arrival curve from a packet-level arrival curve. However, such a method is not tight: we show that better bounds can be obtained by directly exploiting the arrival curves expressed at the packet level. Our analysis method also obtains better bounds when flows are constrained with g-regulation, such as the recently proposed Length-Rate Quotient rule. It can also be used to generalize some recently proposed network-calculus delay-bounds for a service curve element with known transmission rate.

Deficit Round-Robin: A Second Network Calculus Analysis

Deficit Round-Robin (DRR) is a widespread scheduling algorithm that provides fair queueing with variable-length packets. Bounds on worst-case delays for DRR were found by Boyer et al., who used a rigorous network calculus approach and characterized the service obtained by one flow of interest by means of a convex strict service curve. These bounds do not make any assumptions on the interfering traffic hence are pessimistic when the interfering traffic is constrained by some arrival curves. For such cases, two improvements were proposed. The former, by Soni et al., uses a correction term derived from a semi-rigorous heuristic; unfortunately, these bounds are incorrect, as we show by exhibiting a counter-example. The latter, by Bouillard, rigorously derive convex strict service curves for DRR that account for the arrival curve constraints of the interfering traffic. In this paper, we improve on these results in two ways. First, we derive a non-convex strict service curve for DRR that improves on Boyer et al. when there is no arrival constraint on the interfering traffic. Second, we provide an iterative method to improve any strict service curve (including Bouillard’s) when there are arrival constraints for the interfering traffic. As of today, our results provide the best-known worst-case delay bounds for DRR. They are obtained by using the method of the pseudo-inverse.

Cumulative Flow Diagram Estimation and Prediction Based on Sampled Vehicle Trajectories at Signalized Intersections

Although considerable methods have been developed for the performance evaluation of signalized intersections using sampled vehicle trajectories, most of them aim at estimating a single parameter and cannot describe the entire arrival–departure process of the traffic flow. This significantly constrains the application of these methods for a comprehensive evaluation and efficient optimization of signalized intersections. In this paper, we propose a cumulative flow diagram (CFD) estimation and prediction method using sampled vehicle trajectories. It can be used to calculate multiple performance measures—traffic volume, queue length, average delay, and total delay—based on the estimated CFD for the current signal timing plan. Concurrently, it can be further employed for signal control optimization based on the predicted CFDs for candidate signal timing plans. The core idea of the proposed method is to generate the cumulative arrival curve based on the arrival characteristics of the sampled vehicles, and then fit the queue leaving points to obtain the cumulative departure curve. Thereby, given the current or any candidate signal timing plan, we can estimate or predict the CFDs by updating the sampled vehicle arrivals. The proposed method is evaluated using both simulation and empirical data. The simulation results yield that the average estimation error of the four performance measures is 10.3% under a real-world level penetration rate of 10%. Meanwhile, similar accuracies are achieved for the CFD prediction. The empirical results show that under a penetration rate of 8.6%, the estimation errors of the traffic volume and queue length are 2.7% and 3.3%, respectively.

On Packet Reordering in Time-Sensitive Networks

Time-sensitive networks (IEEE TSN or IETF DetNet) may tolerate some packet reordering. Re-sequencing buffers are then used to provide in-order delivery, the parameters of which (timeout, buffer size) may affect worst-case delay and delay jitter. There is so far no precise understanding of per-flow reordering metrics nor of the dimensioning of re-sequencing buffers in order to provide worst-case guarantees, as required in such networks. First, we show that a previously proposed per-flow metric, reordering late time offset (RTO), determines the timeout value. If the network is lossless, another previously defined metric, the reordering byte offset (RBO), determines the required buffer. If packet losses cannot be ignored, the required buffer may be larger than RBO, and depends on jitter, an arrival curve of the flow at its source, and the timeout. Then we develop a calculus to compute the RTO for a flow path; the method uses a novel relation with jitter and arrival curve, together with a decomposition of the path into non order-preserving and order-preserving elements. We also analyse the effect of re-sequencing buffers on worst-case delay, jitter and propagation of arrival curves. We show in particular that, in a lossless (but non order-preserving) network, re-sequencing is “for free”, namely, it does not increase worst-case delay nor jitter, whereas in a lossy network, re-sequencing increases the worst-case delay and jitter. We apply the analysis to evaluate the performance impact of placing re-sequencing buffers at intermediate points and illustrate the results on two industrial test cases.

Root architecture development in stony soils

AbstractSoils with high stone content represent a challenge to root development, as each stone is an obstacle to root growth. A high stone content also affects soil properties such as temperature or water content, which in turn affects root growth. We investigated the effects of all soil properties combined on root development in the field using both experiments and modeling. Field experiments were carried out in rhizotron facilities during two consecutive growing seasons (wheat [Triticum aestivum L.] and maize [Zea mays L.]) in silty loam soils with high (>50%) and low (<4%) stone contents. We extended the CPlantBox root architecture model to explicitly consider the presence of stones and simulated root growth on the plot scale over the whole vegetation period. We found that a linear increase of stone content resulted in a linear decrease of rooting depth across all stone contents and developmental stages considered, whereas rooting depth was only sensitive to cracks below a certain crack density and at earlier growth stages. Moreover, the impact of precipitation‐influenced soil strength had a relatively stronger impact on simulated root arrival curves during the vegetation periods than soil temperature. Resulting differences between stony and non‐stony soil of otherwise the same crop and weather conditions show similar trends as the differences observed in the rhizotron facilities. The combined belowground effects resulted in differences in characteristic root system measures of up to 48%. In future work, comparison of absolute values will require including shoot effects—in particular, different carbon availabilities.

An Accelerated-Time Simulation of Queues at Ticket Offices at Railway Stations

Although nowadays many railway tickets are bought online, still many are bought through rail appointed travel agents and ticket offices at stations. There are several works on microscopic and accelerated-time simulations, some of them related to the topic of this paper, treating passengers movements in railway stations (both of general purpose and also with a focus on specific topics like evacuation, stations design, ticketing, etc.). We focus on a very specific topic: modelling queuing at ticket offices at a main Spanish station where “AVE” (“High-Speed”), “Larga Distancia” (“Long-Distance”), “Media Distancia” (“Middle-Distance”), and “Cercanías” (“Suburban Services”) dedicated windows exist. The existence of “Last Minute” desks is also considered. The goal is to provide the user with a tool that allows to choose the best option for windows distribution along time, after different microscopic simulations based on given data and windows possible distribution are performed (as done in a previous work of one of the authors for airport terminals check-in counters). Special attention is paid to “Last Minute” windows and shared windows (for example simultaneously selling tickets for “Larga Distancia” and “Media Distancia”). Input is given by arrival curves or can be generated by the package. The output is the detailed situation of any window at any moment and the evolution of queues by train or window type. There are different further possible extensions of this work. The implementation has been developed in a computer algebra system in order to minimize the development time.

Delay bound estimation for multicarrier 5G systems considering lognormal beta traffic envelope and stochastic service curve

AbstractIn this article, we propose an approach for estimating delay bound on user data in the downlink of wireless multicarrier 5G networks. To this end, we propose a stochastic arrival curve based on the parameters of a lognormal beta multifractal traffic model. More specifically, we present a delay bound equation that takes into account this novel stochastic arrival curve and a stochastic service curve for multicarrier systems. Simulations are carried out to confirm that the precision of the delay bound estimation using network calculus is enhanced by considering the proposed arrival envelope and service curve.

The Approaches for the Estimation of Control System Parameters in “Network Calculus”

Abstract The paper considers the problem of experimental estimation of important control system characteristics like signal delay and buffering parameters in the framework of Network Calculus method. A brief review of the method is provided. The techniques of estimation of the flow arrival curve (envelope) and system services curve are discussed. Piecewise-linear approximation or affine approximation using support vector machines method are considered for the arrival curve estimation. Two approaches are proposed for the estimation of minimum system service curve. The first one is an inexact estimation based on a maxi-plus deconvolution property; the property is proven in the paper. The second one is applicable for the cases of systems having an analytical dependence between minimum and maximum service curves as a FIFO or Priority Queue type schedulers.

Loss Analysis for Networks based on Heavy-Tailed and Self-Similar Traffic

Many businesses on the computer network appear heavy-tailed self-similarity (long range dependency), which means network traffic exists burst. Various service source with burst characteristic which show self-similar have a significant effect on transmission performance, network traffic control strategy and network performance indicators such as loss. Loss is an important QoS parameter at the network node, which need to be considered and controlled in all types of traffic, but there is no paper study loss analysis based on heavy-tailed self-similarity. Thus, only analyze and evaluate loss under self-similar traffic can reduce the adverse effects which caused by traffic self-similarity and optimize network performance. We adopt stochastic network calculus approach to bewrite loss lssue. Based on this, we present the loss analysis in the case of a single node network using heavy-tailed service curve and heavy-tailed self-similar arrival curve, and loss analysis under cross traffic, multi-node networks with concatenation. And we also get the relational graph between the loss and the arrival rate, service rate.

Stochastic simulation of fully nonstationary aftershock ground motions from known preceding main shock

Aftershocks can cause significant additional damage to a structure that already got damaged during the preceding main shock. Past studies showed that the ground motion characteristics of an aftershock, in statistical sense, are related to those of the preceding main shock. Hence, statistical assessment of additional damage during future aftershocks given a main shock requires conditional simulation of aftershock ground motions. In the present study, a methodology is proposed to obtain an ensemble of fully nonstationary aftershock ground motions at a site of interest from the known seismic scenarios of both the main shock and the anticipated aftershock. The proposed method is based on the Priestley process assumption in order to characterize both amplitude and frequency nonstationarities via some frequency-dependent deterministic amplitude modulations. The amplitude modulations of a probable aftershock process belonging to the anticipated aftershock seismic scenario are considered to be statistically dependent on those of the recorded main shock process. Since the amplitude modulation is obtained from the frequency-dependent energy arrival curves, a conditional scaling model for the energy arrival of aftershocks is newly proposed. An improved methodology is also proposed in order to extract the frequency-dependent amplitude modulations from the energy arrival curves, obtained either via the scaling model or from a recorded motion, as well as to generate process-specific random samples from the knowledge of such modulations. It is found that the simulated ground motion ensemble shows better agreement with the recorded aftershock process, especially for larger aftershocks, when the aftershock's dependency on its main shock (via the conditional scaling model) is considered than what it shows when the dependency is not considered.

Modeling Nakagami Fading channel in Underwater wireless sensor network using Stochastic Network Calculus

Underwater acoustic communication is growing famously day to day because of its important in many applications like offshore search, underwater search. In UWNS while signal is transmitting source to destination the signals are suspected by fading and noise. The QoS guarantees like small backlog, low packet delay are need to be in good condition for Real-time applications. Important role of this designing is Performance evaluation. Analytical models constructed by using (a) queuing theory, (b) effective bandwidth, and (c) deterministic network calculus. These were not adequate to sustain and assess the present packet switched networks. Stochastic Network Calculus is the solution for these issues. The SNC tool can be used to model and network performance assessment, especially for UWSN. In this paper, we have developed an underwater acoustic channel that is subjected to Nakagami fading channel based on SNC to arrive at Stochastic Arrival Curve and Stochastic Service Curve. Backlog bound and delay bounds stochastic performance are derived by using this model.

RC performance analysis based on model optimization with the aid of network calculus

Time-Triggered Ethernet (TTE) Network is a communication network which combines the time-triggered traffic and event-triggered traffic. Based on network calculation, the adopted model in TTE considers the worst case which assumes a number of traffic simultaneously arrive at a node and each virtual link work is fully loaded. Such assumptions lead to the analysis of a certain RC data flow’s delay performance obsessing too much pessimism. In this paper, based on the partition scheduling model, we introduced the loss packet period of the time-triggered data flow $$ p $$ and the correction parameter of rate-constrained (RC) data flow $$ \mu $$ and then optimized the model of service curve and arrival curve of a certain RC data flow. The delay performance of RC data flow is analyzed under proposed optimized model. Simulation results verify that our optimized model relieves the pessimism on delay analysis. The smaller the $$ p $$ value is and the larger the $$ \mu $$ value is, the stricter delay bound can be obtained by our optimized model than by the traditional model. According to the optimized delay analysis model, the scheduling table can be better rearranged and the system resources can be used reasonably.

Performance modelling for data monitoring services in smart grid: A network calculus-based approach

This paper focuses on solving the modeling issues of monitoring system service performance based on the network calculus theory. First, we formulate the service model of the smart grid monitoring system. Then, we derive the flow arrival curve based on the incremental process related functions. Next, we develop flow arrival curves for the case of the incremental process being a fractional Gaussian process, and then we obtain the generalized Cauchy process. Three technical theorems related to network calculus are presented as our main results. Mathematically, the variance of arrival flow for the continuous time case is derived. Assuming that the incremental process of network flow is a Gaussian stationary process, and given the auto-correlation function of the incremental process with violation probability, the formula of the arrival curve is derived. In addition, the overall flow variance under the discrete time case is explicitly derived. The theoretical results are evaluated in smart grid applications. Simulations indicate that the generalized Cauchy process outperforms the fractional Gaussian process for our considered problem.

I&C System Availability Assessment Using Upper Bound Delay Estimation

Abstract Nowadays, a cybersecurity assessment is at the core of the safety and security assurance for all of software and hardware complexes. For instrumentation and control systems of nuclear facilities, the availability is proved to be the most important in the whole confidentiality, integrity, and availability triad representing cybersecurity. However, no any relevant method for the industrial control system availability evaluation is at hand now. The article presents a novel approach for the availability assessment by upper bound delay estimation with the help of a theory of deterministic queuing systems Network calculus. As an example of applying proposed approach, the availability of IntServ model under internal insider’s and external denial-of-service cyberattacks is investigated; in particular, the dependences of the maximum delay on arrival flow and server parameters are revealed. For utilizing the approach with empirical data, a technique for a linear service curve calculation, similar to a linear arrival curve regression, is proposed.

A Theory of Traffic Regulators for Deterministic Networks With Application to Interleaved Regulators

We introduce Pi-regulation, a new definition of traffic regulation which extends both the arrival curves of network calculus and Chang's max-plus g-regulation, and also includes new types of regulation, such as packet rate limitations. We provide a new exact equivalence between min-plus and max-plus formulations of traffic regulation. We show the existence and a max-plus representation of per-flow minimal regulators, which extends the concepts of packetized greedy shapers and minimal g-regulators. We show that any minimal regulator, placed after any arbitrary system that is FIFO for the flow of interest, does not increase the worst-case delay of the flow. We extend the theory to interleaved regulation and introduce the concept of minimal interleaved regulator. It generalizes the urgency-based shaper that was recently proposed by Specht and Samii as a simpler alternative to per-flow regulators in deterministic networks with aggregate scheduling. With this regulator, packets of multiple flows are processed in one FIFO queue and only the packet at the head of the queue is examined against the regulation constraints of its flow. We show that any minimal interleaved regulator, placed after any arbitrary FIFO system does not increase the worst-case delay of the combination.

Applying Periodic Thermal Management on Hard Real-Time Systems to Minimize Peak Temperature

Due to growing power density, on-chip temperature increases rapidly, which has hampered the reliability and performance of modern real-time systems. This paper studies how to minimize the peak temperature of real-time systems under hard real-time constraints with periodic thermal management. A closed-form representation of the peak temperature for such a periodic scheme is derived to tackle this problem. Based on this closed form and the arrival curve model, one offline approach and one online approach are proposed to minimize the peak temperature for a given event stream. The offline one does thermal optimization in design phase and introduces negligible runtime overhead. The online one computes dynamic power-control schemes which are adaptive to actual event arrivals and execution states. We conduct experiments on a real single-core processor and compare our approaches to two existing works. The temperature results measured from a physical thermal sensor demonstrate that the achieved maximal and average temperature reductions are 5[Formula: see text]K and 2.6[Formula: see text]K, respectively.

Enabling Rapid Construction of Arrival Curves From Execution Traces

Editor’s note: This article presents an approach toward rapid construction of empirical arrival curves—a widely used abstraction for modeling temporal workloads in real-time systems—from the execution traces. —Tulika Mitra, National University of Singapore —Jurgen Teich, Friedrich-Alexander-Universitat Erlangen-Nurnberg —Lothar Thiele, ETH Zurich

Capture versus tagging impacts on chum salmon freshwater spawning migration travel times

AbstractThe spawning migration travel times of chum salmon, Oncorhynchus keta (Walbaum), fitted with gastrically implanted radio tags vs external spaghetti tags were tested for a short [≈60 river km (rkm)] and long migration route (≈730 rkm) on the Koyukuk River, Alaska, USA. Using a novel application of statistical arrival curve models to infer travel times for uncaptured fish, migrations by chum salmon not directly handled during the study were also assessed. Results demonstrated negligible differences in travel times within migration routes between fish fitted only with spaghetti tags and fish fitted with radio tags, indicating low impacts on migration travel behaviour associated with gastric tags once deployed. Conversely, travel times for unhandled fish as inferred by statistical arrival models may have been 12%–24% shorter than those for fish captured with gillnets for tagging. These results suggest that, if present, chum salmon migration behaviour impacts may be more strongly associated with fish capture than tag deployment.

QoS-Predicted Energy Efficient Routing for Information-Centric Smart Grid: A Network Calculus Approach

As the proportion of information content in the power grid increased, information-centric smart grid (iCenS) has drawn much attention in recent years. By introducing features of information-centric networking on decentralization, multi-path transmission, and in-network caching to distributed power systems, the iCenS enabled more efficient demand response, disruption tolerant, and mobility support. However, due to the strict quality of services (QoSs) requirement of power grid and a large number of resource-limited infrastructures existed in iCenS, it still faces the following challenges. First, multi-path addressing will cause redundant packets and the transmission of duplicate packet consumes the node energy which may lead to link failure; the delayed transaction of key component information like tele-protection will induce electricity accidents. Second, it is hard to model the traffic of iCenS without introducing extra computing burden because of its interest-driven feature and constantly updated forwarding information base. In this paper, we propose a QoS-predicted energy efficient routing (QPER) scheme for iCenS, which leverage on the network calculus. Upon collecting the real-time state information of the iCenS nodes, the QPER rapidly predicts the QoS boundary and energy consumption of each link for upcoming traffic flows by establishing the service curve and arrival curve. The simulation results validate that our method is superior to traditional multicast routing algorithm in terms of delay, energy consumption, packet loss, and others. Simultaneously, providing various routing methods for different service information can ensure the stability and minimize the security risks.