2D Markov Chain Research Articles

Constructing representative driving cycle for heavy duty vehicle based on Markov chain method considering road slope

Electrification of heavy duty vehicles (HDVs) is critical to realization of the target of carbon neutralization in the future. For most HDVs, the influence of road slope on vehicle power usually cannot be ignored due to significant road slope variation during long driving mileages. In order to design the powertrain system for electrified HDVs effectively, it is necessary to construct representative driving cycles with road slope information. There are two difficulties for this task. (1) Road slope measuring devices are usually costly. A cheaper yet effective method for measuring road slope needs to be developed. (2) A 3D (three dimension) Markov chain method is usually utilized for constructing cycles with velocity and road slope. This method is complex and time consuming, and needs to be improved. In this paper, a 2D (two dimension) Markov chain method for addressing these issues is proposed. A road slope observation is designed based on normal GPS (Global Positioning System) signals and a high order Butterworth filter. The effectiveness of the method is validated. Driving velocity and road slope are collected and observed for the area between Beijing and Zhangjiakou in northern China. Representative cycles with road slope are constructed using a 2D Markov chain method and a matching algorithm based on average speed. With the introduced technology, three representative driving cycles with road slope for urban, suburban and highway routes are designed. Statistic results on vehicle power show that, the representative driving cycles are effective with relative errors less than 4% compared to the real driving conditions. These driving cycles will be utilized in designing electric HDVs, such as hydrogen fuel cell vehicles in the future.

Evaluation of wind turbine power outputs with and without uncertainties in input wind speed and wind direction data

This paper analyses importance of including wind direction (WD) as an additional explanatory variable to the wind speed (WS) for evaluating uncertainty in wind turbine (WT) power output (P out). Using available measurements of an actual WT, the paper compares a ‘two-dimensional’ (2D) P out-WS model with a ‘three-dimensional’ (3D) P out-WS-WD model for two general cases: (a) for the specific input WS and WD values (i.e. WS and WD without uncertainties), and (b) for the forecasted input WS and WD values (i.e. WS and WD with uncertainties). In paper, 2D and 3D Gaussian mixture Copula model and vine Copula framework are combined with 2D and 3D Markov chain models, which are used to forecast input WS and WD data with uncertainties. The obtained results show that inclusion of WD will provide noticeable improvement for models with no uncertainties in input WS and WD data, while in the case of forecasted WS and WD data with uncertainties, WS is a much stronger contributor to the total WT P out uncertainty than WD.

Simple Short-Term Probabilistic Drought Prediction Using Mediterranean Teleconnection Information

Timely forecasts of the onset or possible evolution of droughts is an important contribution to mitigate their manifold negative effects; therefore, in this paper, we propose a mathematically-simple drought forecasting framework gaining Mediterranean Sea temperature information (SST-M) to predict droughts. Agro-metrological drought index addressing seasonality and autocorrelation (AMDI-SA) was used in a Markov model in Urmia lake basin, North West of Iran. Markov chain is adopted to model drought for joint occurrence of different classes of drought severity and sea surface temperature of Mediterranean Sea, which is called 2D Markov chain model. The proposed model, which benefits suitability of Markov chain models for modeling droughts, showed improvement results in prediction scores relative to classic Markov chain model not including SST-M information, additionally.

Investigation on random access in a VLC system with multipacket reception in the presence of hidden devices and obstructions

Due to the directionality of light, the hidden device problem and the obstruction cannot be ignored for carrier sense multiple access with collision avoidance (CSMA/CA)-based uplink visible light communication (VLC). In this paper, we introduce multipacket reception (MPR) to handle the hidden device problem in VLC system. We model the traffic of the device with on/off Markov source. With the unsaturated traffic, we formulate a two dimensional (2D) Markov chain to model the CSMA/CA-based slotted random access procedure to evaluate the effects of hidden devices and obstructions on the performance of MPR-aided VLC system, which are mapped into the transition probabilities of the Markov chain. Then, we analyze the throughput and the reception power efficiency (RE) of MPR-aided VLC system with the obstructed optical channel. Numerical results show that the effect is negative when hidden devices or obstructions appear solely. But when they appear simultaneously, they will interact with each other to mitigate the negative effects.

Semi-Distributed Backoff: Collision-Aware Migration from Random to Deterministic Backoff

Collision is imminent in wireless networks (WNs) capacitated with randomized distributed channel access. In such networks, the probability of frame drop (Pdrop) is greater than zero due to successive collisions with a finite retry limit m. The IEEE 802.11 DCF is one such widely accepted protocol used in wireless local area networks (WLANs). The objective of the work reported in this paper is to provide guaranteed channel access to colliding frames for avoiding successive collisions for any loss-sensitive application, and thus, increase network throughput under finite m. We propose the semi-distributed backoff (SDB) algorithm, which operates in two modes: S-mode and R-mode. The key idea of the SDB scheme is to perform receiver-side backoff, if a mobile station encounters collision even after performing the existing sender-side backoff procedures. Using the SDB scheme, we design Semi-DCF, a MAC protocol for WLANs, which performs opportunistic migration from random to deterministic backoff. Semi-DCF functions independent of m. This protocol exploits the collision detection capability of receivers for disseminating information on optimal backoffs to the contenders using signature vectors. An analysis of Semi-DCF using the 2D Markov chain, coupled with results of network simulation establishes its superior performance in WLANs.

Approximating spatially exclusive invasion processes.

A number of biological processes, such as invasive plant species and cell migration, are composed of two key mechanisms: motility and reproduction. Due to the spatially exclusive interacting behavior of these processes a cellular automata (CA) model is specified to simulate a one-dimensional invasion process. Three (independence, Poisson, and 2D-Markov chain) approximations are considered that attempt to capture the average behavior of the CA. We show that our 2D-Markov chain approximation accurately predicts the state of the CA for a wide range of motility and reproduction rates.

A Distance-Aware Safety-Related Message Broadcasting Algorithm for Vehicular Networks

A new distance-aware broadcasting algorithm was proposed to enhance the propagation distance in the latency time of safety-related message broadcasting. The IEEE 802.11p standard states that if the medium is detected as idle, a station would defer its transmission within a backoff time to avoid collisions with other stations. The backoff times follow uniform distribution over [0, CW]. In this way, fairness among all the stations can be guaranteed. However, propagation distance was ignored and in safety-related message broadcasting fairness is not the most important issue. In the proposed algorithm, the lengths of backoff times are generated from a nonuniform distribution. They are related with the distances between the source station and its forwarding stations. The farthest forwarding station has the highest probability to forward messages. Performance of the proposed algorithm is analyzed by using a 2D Markov chain. Analytical and simulation results demonstrate that the proposed algorithm can enhance the performance of safety-related message broadcasting in terms of propagation distance, which is reflected by the successful transmission probability. The proposed algorithm does not need additional waiting time, RTS/CTS, and ACK, therefore having better compatibility with the IEEE 802.11p standard than earlier distance-aware algorithms.

Research of Early Warning Mechanism for Traffic Safety Based on Internet of Things

This paper focuses on the study of the optimization of accuracy rate for traffic safety early warning mechanism. The traffic safety problem has become one of harms to the global society. A prediction technology and emergency management mechanism for traffic safety has been put forward to solve the problem of traffic congestion and road traffic imbalance, especially the parameter of traditional warning algorithm is too demanding and the algorithm is too complex. The plan adopts the technology of Internet of Things, monitoring the real-time traffic condition which affords the reliable data for the traffic management department, and designs the targeted safety early warning index according to the collected traffic information, and sets up the emergency management mechanism based on the time and space model of 2D Markov chain. The simulation experiment and mathematical analysis show that the improved early warning methods can help the traffic management department to timely forecast the traffic safety risks and hidden dangers and take the effective solutions to guarantee the benign and stable state of overall transport system.

Performance Evaluation of the WiMAX Network Based on Combining the 2D Markov Chain and MMPP Traffic Model

WiMAX is intended for fourth generation wireless mobile communications where a group of users are provided with a connection and a fixed length queue. In present literature traffic of such network is analyzed based on the generator matrix of the Markov Arrival Process (MAP). In this paper a simple analytical technique of the two dimensional Markov chain is used to obtain the trajectory of the congestion of the network as a function of a traffic parameter. Finally, a two state phase dependent arrival process is considered to evaluate probability states. The entire analysis is kept independent of modulation and coding schemes.

A 2D Markov chain for modelling powder mixing in alternately revolving static mixers of Sysmix® type

A two-dimensional model of the flow and mixing of particulate solids has been developed on the basis of the Markov chain theory for an alternately revolving static mixer of Sysmix® type. In such a system, mixing occurs in both vertical and horizontal directions. Simulations are presented here to investigate the effect of the initial loading of the components, as well as the effect of the values of the transition probabilities that constitute the main parameters of the model. It is shown that a horizontal arrangement of the components always leads to better mixture quality and improved mixing kinetics. This research is presented for non-segregating mixtures, as well as potentially segregating mixtures, for which the empirically well-known oscillations in variance are represented by the model. Results suggest that there is a rational way of approaching a static-mixing problem with regard to the initial loading of the component and the optimal number of revolutions. Comparison of model results with experimental data published previously for a Sysmix® apparatus contributes to validating the viability of the model.

Influence of Preconditioning and Blocking on Accuracy in Solving Markovian Models

Influence of Preconditioning and Blocking on Accuracy in Solving Markovian ModelsThe article considers the effectiveness of various methods used to solve systems of linear equations (which emerge while modeling computer networks and systems with Markov chains) and the practical influence of the methods applied on accuracy. The paper considers some hybrids of both direct and iterative methods. Two varieties of the Gauss elimination will be considered as an example of direct methods: the LU factorization method and the WZ factorization method. The Gauss-Seidel iterative method will be discussed. The paper also shows preconditioning (with the use of incomplete Gauss elimination) and dividing the matrix into blocks where blocks are solved applying direct methods. The motivation for such hybrids is a very high condition number (which is bad) for coefficient matrices occuring in Markov chains and, thus, slow convergence of traditional iterative methods. Also, the blocking, preconditioning and merging of both are analysed. The paper presents the impact of linked methods on both the time and accuracy of finding vector probability. The results of an experiment are given for two groups of matrices: those derived from some very abstract Markovian models, and those from a general 2D Markov chain.

Performance analysis of channelized cellular systems with dynamic channel allocation

We present an analytical model to compute the blocking probability in channelized cellular systems with dynamic channel allocation. We model the channel occupancy in a cell by a two-dimensional (2D) Markov chain, which can be solved to obtain the blocking probability in each cell. We apply our analytical model to linear highway systems with and without lognormal shadowing and then extend it to 2D cellular systems with lognormal shadowing. We show that, for linear highway systems, distributed dynamic channel-allocation schemes perform similarly to the centralized dynamic channel-allocation schemes in terms of blocking probability. However, for 2D cellular systems, the improvement in the performance is significant and the reduction in the blocking probability in systems with distributed dynamic channel allocation is by almost one order of magnitude, when compared to that in systems with centralized dynamic channel allocation. In practice, our analysis of linear highway systems is applicable to Digital European Cordless Telephony (DECT) and that of 2D cellular systems is applicable to global systems for mobile communications (GSM).

2D Markov chains

The separation property that characterizes the dynamics of Markov chains is extended to a class of discrete 2D models where the time support, given by the discrete plane Z × Z , is partially ordered by the product of the orderings. The paper analyzes the matrix representation structure of the probability transition map in a 2D Markov chain and some properties of the associated characteristic polynomial in two variables. These allow one to show how the long-term behavior depends on the intersections between the variety of the characteristic polynomial and the distinguished boundary of the unit closed bidisk.