On Tenth‐Order Hybrid Numerov‐Type Methods

A new 4th order Runge-Kutta method for solving initial value problems is derived by replacing the arithmetic means in the formula where etc., by their geometric means i.e. etc. to yield initially a low order accuracy formula. However by re-comparing the Taylor series expansions of k 1 k 2 k 3 and k 4 in terms of the functional derivatives and the α ij parameters, a fourth order accuracy formula is obtained which is confirmed by numerical experiments. Then, a new fourth order Runge-Kutta method for solving linear initial value problems of the form y′ = Ay is derived which provides an estimate of the truncation error without any extra function evaluations. The idea follows from the fact that two numerical solutions of similar order can be obtained by using the arithmetic mean (AM) and the geometric mean (GM) averaging of the functional values. The numerical results given confirm that this new method is suitable to be used as an error control strategy.

This article reviewed how to enhance safety rules through human error and behavioural control strategies. To understand what strategies could be applied safety rules, types of safety rules, safety violations, organisational factors, and behavioural types were explored. To complete this article twelve peer-reviewed articles and three statistical data sets were used based on the Fast-Moving Consumer Goods (FMCG) industry. The importance of safety is undisputed and the need for a holistic approach to enhance safety rules through human error and behavioural control strategies is required. Five key strategies to enhance safety rules through human error and behavioural control strategies include 1. Reducing the number and complexity of safety rules, 2. Consultation, 3. Data Banks, 4. Feedback 5. Proactive and Positive Leadership.

Wireless links are known to suffer location-dependent, time-varying, and bursty errors. This paper considers a class of adaptive error-control schemes in the data link layer for reliable communication over wireless links in which the error-control code and the frame length are chosen adaptively, based on the estimated channel state/condition. Three error-control schemes are considered according to: (1) the number of Reed Solomon code segments a packet is divided into and (2) the way a lost packet is retransmitted. Through throughput performance and computation complexity analyses, these three schemes are compared, and then one of them is claimed to be the most attractive in terms of computation complexity and practicality even though its throughput performance is not the best. The simulation results also verify that this scheme works well over a time-varying fading channel. Error control for the medium access control (MAC) header and its effect on the performance of each error-control scheme are also considered since, without proper error protection for the header, it would be futile to exercise error control on the user data.

Since wireless channel is always band-limited with multi-path fading and highly burst errors, flexible error control is needed in wireless asynchronous transfer mode (WATM) networks. This paper proposes a hybrid automatic repeat request (HARQ) architecture which has on-demand quality of services (QoS). By choosing different options in the architecture, we get different error control schemes. In this paper, we investigate the performance of three different error control schemes, namely HARQ, HARQ with different redundancy, and adaptive HARQ with traffic-type-dependent redundancy. The simulation results show that the HARQ with FEC adaptation offers the best performance.

Exploiting the adaptive properties of a probing device for TCP in heterogenous networks

We study the interaction between error control and media synchronization. We approach the problem by considering a virtual application data unit (ADU) network with error control within the network boundary and media synchronization outside the network boundary. We introduce the concept of cumulative inter-ADU jitter, which is the running total of the differences between inter-ADU spacings at the receiver and at the sender, to model the ADU departure process from the network observed at the entry of the playback buffer. We investigate how different error control schemes, network and source characteristics influence the process on one hand and how the process affects the choice of playback delay in order to minimize ADU losses on the other hand. Our numerical results, obtained through simulation, verify the analysis and reveals that jitter control within the network is not as important as controlling the bandwidth and the delay, especially in the presence of error control and variable bit rate source.

Observing the threshold effect of CDMA systems, this paper proposes a simple, fair protocol suitable for the CDMA environment, which does not need the additional feedback channel but can still achieve the goal of error control. Based on the same rationale as the CSMA/CD protocol, this protocol is designed to avoid collision or congestion of traffic before formal transmission of a packet. By the handshake procedure, the intended transmitter is able to test the channel quality and the receiver's status using a very short handshake packet. Therefore, channel traffic can be controlled to avoid overload. The throughput and reliability are analyzed based on the underlying Markovian models. Numerical results are compared to other error control schemes and show that with a reasonably short handshake time compared to the packet transmission time, this handshake protocol with simple forward error correction offers an excellent alternative for error control and can even improve the throughput performance.

This paper presents an adaptive rate error control scheme for digital communication over time-varying channels. The cyclic code with majority-logic decoding is used in a cascaded way as an inner code to create a simple and powerful hybrid-ARQ error control scheme. Inner code is used only for error correction and the outer code is used for both error correction and error detection. When an error is detected, retransmission is required. The unsuccessful packets are not discarded as with conventional schemes, but are combined with their retransmitted copies. Approximations for the throughput efficiency and the undetectable error probability are given. A high reliability coupled with a simple high-speed implementation makes it suitable for high data rate error control over both stationary and non-stationary channels. Adaptive error control scheme becomes the best solution for time-varying channels when the optimum code is selected according to the actual channel conditions to enhance the system performance. The main feature of this system is that the basic structure of the encoder and decoder need not be modified while the error-correction capability of the code increases. Results of a comparative analysis show that the proposed scheme outperforms other similar ARQ protocols. >

In this paper, we present a novel analytical framework for the study of a multiple access scheme for an ad hoc CDMA network with HARQ error control and MF-LSIC receivers. We focus on a scenario where users access the channel simultaneously, fully exploiting the PHY layer multiuser potential. To improve efficiency and reliability we consider a rate controlled system where nodes adapt their transmission rate to the channel conditions in terms of both fading and interference. We compare ARQ and type I-II HARQ error control schemes. We show that in this scenario the error control scheme used to ensure reliability is of particular importance, since it not only determines the average interference level in the network, but also heavily conditions the channel predictability since it affects the interference statistics.

The paper proposes an error control scheme that dynamically adjusts the polling schedule so that more corrupted messages can be manipulated within their deadlines for real-time communication on IEEE 802.11 wireless LAN. Monitoring the current traffic in the CFP (collision free period) interval as well as inspecting whether a node is executing an error control procedure, the AP (access point) terminates CFP, if possible, to extend the duration of the next CP (collision period). With the enlarged time, the AP gives more polls to the node in need to increase the number of timely recovered messages. Simulation result performed via SMPL shows that this adaptation scheme can reduce the message discard due to transmission error by 5.5%, compared with the existing error controls method for real-time communication on WLAN.

N-dimensional error control multiresolution algorithms for the point value discretization

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

We present an adaptive error control scheme that employs a link quality grading technique and a burst error prediction mechanism, in order to handle multi-wire and multicycle errors, respectively. Our approach enables the transmitter to select the most effective error-control scheme for the particular link quality. Using this method, we can improve switch-to-switch throughput by 4X and reduce power consumption by 70%, compared to retransmission-only and retransmission-plus-fixed-coding approaches.

Integration algorithm is a key to ensure the better application of the dynamic constitutive model. As for the bounding surface model based on swell–shrink rules in this paper, an explicit integration algorithm based on sub-stepping and error control scheme has be described in detail. For being adaptable to the constitutive model, several modifications have been made. The modified explicit algorithm includes two procedures: the first procedure is the second-order forward modified Euler scheme with sub-stepping and error control; the second procedure is the stress correction. However, due to the shrink rule of the bounding surface, the second procedure is not needed at the unloading phase. Finally, several numerical simulations have been conducted for assessing the performance of the explicit algorithm, which demonstrates that the corresponding algorithm is stable and accurate, and can simulate the mechanical characteristics of the clay pretty well.

A model is described that predicts the time required to broadcast a message to an arbitrary number of receivers over a meteor burst channel, taking into account the actual time-varying nature of the bit error rate. The model computes the broadcast waiting time for any modulation scheme and choice of system parameter values using both ARQ and Hybrid ARQ/FEC error control. Example calculations are performed that find optimal data rates and packet sizes as functions of message length. Waiting times for both error control schemes are also computed and compared.