Network Calculus Approach Research Articles

End-to-end delay and backlog bound analysis for hybrid vehicular ad hoc network: a stochastic network calculus approach

End-to-end delay and backlog bound analysis for hybrid vehicular ad hoc network: a stochastic network calculus approach

End-to-end delay and backlog bound analysis for hybrid vehicular ad hoc network: a stochastic network calculus approach

End-to-end delay and backlog bound analysis for hybrid vehicular ad hoc network: a stochastic network calculus approach

Network Calculus Approach for Packet Delay Variation Analysis of Multi-Hop Wired Networks

The Industrial Internet of Things (IIoT) has revolutionized businesses by changing the way data are used to make products and services more efficient, reliable, and profitable. To achieve the improvement goals, the IIoT must guarantee the real-time performance of industrial applications such as motion control, by providing stringent quality of service (QoS) assurances for their (industrial applications) communication networks. An application or service may malfunction without adequate network QoS, resulting in potential product failures. Since an acceptable end-to-end delay and low jitter or packet delay variation (PDV) are closely related to quality of service (QoS), their impact is significant in ensuring the real-time performance of industrial applications. Although a communication network topology ensures certain jitter levels, its real-life performance is affected by dynamic traffic due to the changing number of devices, services, and applications present in the communication network. Hence, it is essential to study the jitter experienced by real-time traffic in the presence of background traffic and how it can be maintained within the limits to ensure a certain level of QoS. This paper presents a probabilistic network calculus approach that uses moment-generating functions to analyze the delay and PDV incurred by the traffic flows of interest in a wired packet switched multi-stage network. The presented work derives closed-form, end-to-end, probabilistic performance bounds for delay and PDV for several servers in series in the presence of background traffic. The PDV analysis conducted with the help of a Markovian traffic model for background traffic showed that the parameters from the background traffic significantly impact PDV and that PDV can be maintained under the limits by controlling the shape of the background traffic. For the studied configurations, the model parameters can change the PDV bound from 1 ms to 100 ms. The results indicated the possibility of using the model parameters as a shaper of the background traffic. Thus, the analysis can be beneficial in providing QoS assurances for real-time applications.

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.

ALOHA Receivers: A Network Calculus Approach for Analyzing Coded Multiple Access With SIC

Motivated by the need to hide the complexity of the physical layer from performance analysis in a layer 2 protocol, a class of abstract receivers, called Poisson receivers, was recently proposed by Yu <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">et al.</i> (2021) as a probabilistic framework for providing differentiated services in uplink transmissions in 5G networks. In this paper, we further propose a deterministic framework of ALOHA receivers that can be incorporated into the probabilistic framework of Poisson receivers for analyzing coded multiple access with successive interference cancellation. An ALOHA receiver is characterized by a success function of the number of packets that can be successfully received. Inspired by the theory of network calculus, we derive various algebraic properties for several operations on success functions and use them to prove various closure properties of ALOHA receivers, including (i) ALOHA receivers in tandem, (ii) cooperative ALOHA receivers, (iii) ALOHA receivers with traffic multiplexing, and (iv) ALOHA receivers with packet coding. By conducting extensive simulations, we show that our theoretical results match extremely well with the simulation results.

Worst-Case Latency Analysis for AVB Traffic Under Overlapping-Based Time-Triggered Windows in Time-Sensitive Networks

Deterministic and low end-to-end latency communication is an urgent demand for many safety-critical applications such as autonomous vehicles and automated industries. The time-sensitive network (TSN) is introduced as Ethernet-based amendments in IEEE 802.1 TSN standards to support time-triggered (TT) traffic in these applications. In the presence of TT flows, TSN is designed to integrate Audio/Video Bridging (AVB) and Best Effort (BE) traffic types. Although AVB traffic has a lower priority than TT, it still requires low and deterministic latency performance, which may not be guaranteed under strict predefined TT scheduling constraints. For this reason, a window-overlapping scheduling algorithm is recently proposed in different works as analytical forms for TT latency under overlapping-windows based. But worst-case AVB latency evaluation under overlapped TT windows is also essential for critical optimizations and tradeoffs. In this paper, a worst-case end-to-end delay ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WCD</i> ) for AVB traffic under overlapping-based TT windows (AVB-OBTTW) algorithm is proposed. Separate analytical models are derived using the network calculus (NC) approach for AVB-OBTTW with both non-preemption and preemption mechanisms. Using an actual vehicular use case, the proposed models are evaluated with back-to-back and porosity configurations under light and heavy loading scenarios. For specific AVB credit bounds, a clear <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WCD</i> reduction has been achieved by increasing the overlapping ratio ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OR</i> ), especially under back-to-back configuration. Preemption and non-preemption modes are compared under different loading conditions, resulting in lower <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WCD</i> s using preemption mode than non-preemption, especially with porosity style. Compared to the latest related works, AVB-OBTTW reduces <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">WCD</i> bounds and increases unscheduled bandwidth, leading to the highest enhancements with the maximum allowable <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">OR</i> .

Interleaved Weighted Round-Robin: A Network Calculus Analysis

Weighted Round-Robin (WRR) is often used, due to its simplicity, for scheduling packets or tasks. With WRR, a number of packets equal to the weight allocated to a flow can be served consecutively, which leads to a bursty service. Interleaved Weighted Round-Robin (IWRR) is a variant that mitigates this effect. We are interested in finding bounds on worst-case delay obtained with IWRR. To this end, we use a network calculus approach and find a strict service curve for IWRR. The result is obtained using the pseudo-inverse of a function. We show that the strict service curve is the best obtainable one, and that delay bounds derived from it are tight (i.e., worst-case) for flows of packets of constant size. Furthermore, the IWRR strict service curve dominates the strict service curve for WRR that was previously published. We provide some numerical examples to illustrate the reduction in worst-case delays caused by IWRR compared to WRR.

Network Calculus-Based Latency for Time-Triggered Traffic under Flexible Window-Overlapping Scheduling (FWOS) in a Time-Sensitive Network (TSN)

Deterministic latency is an urgent demand to pursue the continuous increase in intelligence in several real-time applications, such as connected vehicles and automation industries. A time-sensitive network (TSN) is a new framework introduced to serve these applications. Several functions are defined in the TSN standard to support time-triggered (TT) requirements, such as IEEE 802.1Qbv and IEEE 802.1Qbu for traffic scheduling and preemption mechanisms, respectively. However, implementing strict timing constraints to support scheduled traffic can miss the needs of unscheduled real-time flows. Accordingly, more relaxed scheduling algorithms are required. In this paper, we introduce the flexible window-overlapping scheduling (FWOS) algorithm that optimizes the overlapping among TT windows by three different metrics: the priority of overlapping, the position of overlapping, and the overlapping ratio (OR). An analytical model for the worst-case end-to-end delay (WCD) is derived using the network calculus (NC) approach considering the relative relationships between window offsets for consecutive nodes and evaluated under a realistic vehicle use case. While guaranteeing latency deadline for TT traffic, the FWOS algorithm defines the maximum allowable OR that maximizes the bandwidth available for unscheduled transmission. Even under a non-overlapping scenario, less pessimistic latency bounds have been obtained using FWOS than the latest related works.

Critical Offset Optimizations for Overlapping-Based Time-Triggered Windows in Time-Sensitive Network

Deterministic and low latency communications are increasingly becoming essential requirements for several safety-critical applications, such as automotive and automation industries. Time-sensitive networking (TSN) is an element of the new IEEE 802.1 standards that introduced Ethernet-based amendments to support these applications. One of these enhancements was presented in IEEE 802.1Qbv to define the time-aware shaping (TAS) technique for time-triggered (TT) traffic scheduling. The TAS mechanism is window-based scheduling using a gating system controlled by the gate control list (GCL) schedules in all nodes. Although several scheduling algorithms have been proposed to investigate the effects of window-related parameters on network performance, the offset difference ( $OD$ ) between the same-class windows in the adjoining nodes has not been optimized yet. These optimizations are extremely crucial to implement less pessimistic latency schedules. This paper proposes an optimized flexible window-overlapping scheduling (OFWOS) algorithm that optimizes TT window offsets based on latency evaluations considering the overlapping between different priority windows at the same node. First, we formulate the GCL timings as mathematical forms under variable $OD\text{s}$ between the same-priority windows. Then, an analytical model is implemented using the network calculus (NC) approach to express the worst-case end-to-end delay ( $WCD$ ) for TT flows and evaluated using a realistic vehicular use case. The OFWOS model optimizes $OD$ under all overlapping situations between TT windows at the same node. Compared with the latest works of 3-hop and 30-hop TSN connections, the OFWOS reduces the $WCD$ bounds by 8.4% and 32.6%, respectively, accomplishing less pessimistic end-to-end latency bounds.

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.

Transient Analysis for Multihop Wireless Networks Under Static Routing

In this article, we investigate the transient behavior of a sequence of packets/bits traversing a multi-hop wireless network under static routing. Our work is motivated by novel applications from the domain of process automation, Machine-Type Communication (MTC) and cyber-physical systems, where short messages are communicated and statistical guarantees need to be provided on a per-message level. In order to optimize such a network, apart from understanding the stationary system dynamics, an understanding of the short-term dynamics (i.e. transient behavior) is also required. To this end, we derive novel Wireless Transient Bounds (WTB) for end-to-end delay and backlog in a multi-hop wireless network using stochastic network calculus approach. We start by analyzing a single end-to-end path, i.e. a line topology, and then we show how the obtained results can be applied to a mesh network with static routing using a concept called ’ leftover service ’. WTB depends on the initial backlog at each node as well as the instantaneous channel states. We numerically compare WTB with Kernel-Based-Transient Bound (KBTB), which can be obtained by adapting existing stationary bound, as well as simulated end-to-end delay of the investigated network. While KBTB and stationary bounds are not able to capture the short-term system dynamics well, WTB provides relatively tight upper bound and has a decay rate that closely matches the simulation. This is achieved by WTB only with a slight increase in the computational complexity, by a factor of $O(T+N)$ , where $T$ is the duration of the arriving sequence and $N$ is the number of hops in the network. We believe that the presented analysis and the bounds are necessary tools for future work on transient network optimization for many important emerging applications, e.g., massive MTC, critical MTC, edge computing and autonomous vehicle.

Energy-Efficient Pushing With Content Consumption Constraints: A Network Calculus Approach

Joint pushing and caching (JPC) holds the promise of achieving high spectral and energy efficiency in future networks, thereby attracting much attention most recently. However, few attention has been paid to the content consumption process that describes how a content item leaves the receiver buffer after the request time. Such a process bounds the amount of data that have arrived in the buffer, thereby constraining the content transmission. By taking content consumption processes into account, this paper aims to present optimal JPC policies that minimize the transmission energy under receiver buffer size and content consumption constraints. In particular, two common types of content consumption processes, instantaneous reading and sequential reading, along with two content transmission strategies, orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA), are respectively considered. Energy minimization problems are first formulated as variational problems based on the network calculus approach, and are then equivalently transformed into convex optimization problems in order to reduce the computational complexity. It is shown that JPC policies are capable of significantly reducing the energy consumption when receiver buffer sizes are large. Furthermore, the NOMA based JPC achieves higher energy efficiency than the OMA based JPC by effectively exploiting physical layer multicasting opportunities.

A Revised Trajectory Approach for the Worst-Case Delay Analysis of an AFDX Network

AFDX (Avionics Full-Duplex Switched Ethernet) standardized as ARINC 664 is a major upgrade for safety-critical applications in avionics systems. Worst-case delay analysis of all the flows transmitted on the AFDX network is mandatory for certification reasons. Different approaches have been proposed for end-to-end (ETE) delay upper bound, such as network calculus and trajectory approach, but these methods still introduce some pessimism in the computations and overestimate the exact worst-case delay of the flows. In addition, the existing trajectory approaches may underestimate the exact worst-case delay of the flows for some corner cases. In this article, we revised the trajectory approach to make the flow analysis more accurate for the computation of the worst-case ETE delay. The results had been shown that the worst-case delay analysis of an AFDX network can be improved by using our revised trajectory approach.

Improving Worst-Case Delay Analysis for Traffic of Additional Stream Reservation Class in Ethernet-AVB Network.

With the increase in the number of Electronic Control Units (ECUs) and future requirements for vehicle functions, two SR (Stream Reservation) traffic classes may not be sufficient to ensure fulfilment of constraints for multiple traffic types with individual timing requirements transmitted in the Ethernet-AVB (Audio Video Bridging) networks. The goal of this paper is to determine the worst-case delay for an additional SR traffic class under the CBS (Credit-Based Shaper) algorithm. Delay evaluation is based on the impact analysis of CBS on different priority flows, particularly depending on when the credits of both SR class A and B drain from the worst-case perspective. More specifically, both the impact of CBS and the evolution trends of credit on different priority class flows are first analyzed from the worst-case perspective. Then, for an additional SR class, two types of worst-case delay models are established with the CBS configuration suggestions. Finally, an approach to calculate the worst-case queuing delay is proposed. Moreover, the worst-case end-to-end delay is determined by the network calculus approach and simulation. Numerical results show that the delay bounds of our models are tighter than those of other models, which is beneficial to the development of Ethernet-AVB for in-vehicle networking.

Bound-based power optimization for multi-hop heterogeneous wireless industrial networks under statistical delay constraints

The noticeably increased deployment of wireless networks for battery-limited industrial applications in recent years highlights the need for tractable performance analysis methodologies as well as efficient QoS-aware transmit power management schemes. In this work, we seek to combine several important aspects of such networks, i.e., multi-hop connectivity, channel heterogeneity and the queuing effect, in order to address these needs. We design delay-bound-based algorithms for transmit power minimization and network lifetime maximization of multi-hop heterogeneous wireless networks using our previously developed stochastic network calculus approach for performance analysis of a cascade of buffered wireless fading channels. Our analysis shows an overall transmit power saving of up to 95% compared to a fixed power allocation scheme in case when the service is modeled via a Shannon capacity. For a more realistic set-up, we evaluate the performance of the suggested algorithm in a WirelessHART network, which is a widely used communication standard for industrial process automation applications. We find that link heterogeneity can significantly reduce network lifetime when no efficient power management is applied. Using extensive simulation study we further show that the proposed bound-based power allocation performs reasonably well compared to the real optimum, especially in the case of WirelessHART networks.

Improving Worst-Case Latency Analysis for Rate-Constrained Traffic in the Time-Triggered Ethernet Network

Traditional performance analysis models based on the network calculus approach are not fit for the time-triggered Ethernet (TTEthernet) network due to the porosity characteristic of timed-triggered (TT) traffic in the TT-schedule. This paper introduces the porosity concept into the arrival curve model of TT traffic and gives a general method for the worst-case end-to-end latency analysis of rate-constrained (RC) traffic. Experiments show that our models give tighter latency bounds than results from other already known models and may be used to guide the design of the TT-schedule.

Quality of Service Modelling of Virtualized Wireless Networks: A Network Calculus Approach

Wireless network virtualization is an emerging technology that logically divides a wireless network element, such as a base station (BS), into multiple slices with each slice serving as a standalone virtual BS. In such a way, one physical mobile wireless network can be partitioned into multiple virtual networks each operating as an independent wireless network. Wireless virtual networks, as composed of these virtual BSs, need to provide quality of service (QoS) to mobile end user services. Key QoS parameters include buffer queue length, network delay and effective bandwidth, in particular their upper bound forms. This paper presents a QoS model for such a wireless virtual network addressing these parameters. This QoS model considers resources of both physical nodes and virtual nodes and provides a realistic modelling of the delay and bandwidth behaviours of wireless virtual networks. Network calculus (NC), which usually provides finer insight into a system, is utilized to fulfil the modelling task. The numerical results have shown the effectiveness of the proposed model. The model is useful for both off-line network planning and online network admission control.

A Stochastic Network Calculus Approach for the End-to-End Delay Analysis of LTE Networks

Long Term Evolution(LTE),which was proposed by the 3rd Generation Partnership Project(3GPP),is an important standard in future wireless network communication.However,the time-varying characteristic of wireless channel capacity in LTE networks poses big challenges in performance analysis.In this paper,we construct a framework of analyzing stochastic End-to-End(E2E) delay of the LTE network by modeling the arrival model and service model using Stochastic Network Calculus(SNC).Numerical analyses are conducted to prove the effectiveness of the framework.

Delay Bounds in Communication Networks With Heavy-Tailed and Self-Similar Traffic

We provide upper bounds on the end-to-end backlog and delay in a network with heavy-tailed and self-similar traffic. The analysis follows a network calculus approach where traffic is characterized by envelope functions and service is described by service curves. A key contribution of this paper is the derivation of a probabilistic sample path bound for heavy-tailed self-similar arrival processes, which is enabled by a suitable envelope characterization, referred to as `htss envelope'. We derive a heavy-tailed service curve for an entire network path when the service at each node on the path is characterized by heavy-tailed service curves. We obtain backlog and delay bounds for traffic that is characterized by an htss envelope and receives service given by a heavy-tailed service curve. The derived performance bounds are non-asymptotic in that they do not assume a steady-state, large buffer, or many sources regime. We also explore the scale of growth of delays as a function of the length of the path. The appendix contains an analysis for self-similar traffic with a Gaussian tail distribution.

Worst-case flow model of VL for worst-case delay analysis of AFDX

Worst-case delay analysis is important for avionics full duplex switched Ethernet (AFDX) standardised as ARINC 664. The flow model of virtual link (VL) in the worst-case delay analysis of AFDX is inaccurate, which depends only on the parameters of VL and ignores the impact from the network, so it makes the worst-case delay analysis of AFDX impractical. A worst-case flow model of VL, which takes the worst impact from the network into account, is proposed to mend the worst-case delay analysis of AFDX. This worst-case flow model of VL is applied in one of the main theoretical approaches for worst-case delay analysis, the network calculus approach. It assists the network calculus approach to get the real upper bound of delay for VL.