A renewal theory based performance and configuration framework of the IEEE 802.11ah RAW mechanism

IEEE 802.11ah is a new Wi-Fi standard for sub-1Ghz communications,aiming to address the challenges of the Internet of Things(IoT).Significant changes in the legacy 802.11 standards have been proposed to improve the network performance in high contention scenarios,the most important of which is the Restricted Access Window(RAW)mechanism.This mechanism promises to increase the throughput and energy efficiency by dividing stations into different groups.Under this scheme,only the stations belonging to the same group may access the channel,which reduces the collision probability in dense scenarios.However,the standard does not define the RAW grouping strategy.In this paper,we develop a new mathematical model based on the renewal theory,which allows for tracking the number of transmissions within the limited RAW slot contention period defined by the standard.We then analyze and evaluate the performance of RAW mechanism.We also introduce a grouping scheme to organize the stations and channel access time into different groups within the RAW.Furthermore,we propose an algorithm to derive the RAW configuration parameters of a throughput maximizing grouping scheme.We additionally explore the impact of channel errors on the contention within the time-limited RAW slot and the overall RAW optimal configuration.The presented analytical framework can be applied to many other Wi-Fi standards that integrate periodic channel reservations.Extensive simulations using the MATLAB software validate the analytical model and prove the effectiveness of the proposed RAW configuration scheme.

Modeling Expected Failure Considering Repair Time and Degradation: A Rail System Case Study

The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering the length of repair and reduced degradation of the idle object. In addition to minimal repair and failure replacement, partial repairs are also discussed when the repair results in reduction of the number of future failures or decreases the effective age of the object. Numerical integration-based algorithm and simulation study are performed to solve the resulting integral equation. Since the geometry degradation in different dimensions of a rail track and controlling and maintaining defects are of importance, a numerical example using the rail industry data is conducted. Expected number of failures of different failure type modes in rail track is calculated within a two-year interval. Results show that within a two-year period, anticipated occurrences of cross level failures, surface failures, and DPI failures are 2.4, 3.8, and 5.8, respectively.

A Mass Transfer Model Based on Individual Bubbles and an Unsteady State Film Mechanism

A gas-liquid mass transfer model based on an unsteady state film mechanism applied to a single bubble is presented. The mathematical model was solved using Laplace transform to obtain an analytical solution of concentration profile in terms of the radial position r and time t. The dynamic mass transfer flux was deduced and the influence of the bubble size was also determined. A mathematical method for deducing the average mass transfer flux directly from the Laplace transformed concentration is presented. Its accuracy is verified by comparing the numerical results with those from the indirect method. The influences of the model parameters, namely, the bubble size R, liquid film thickness δ, and the surface renewal constant s on the average mass transfer flux were investigated. The proposed model is useful for a better understanding of the mass transfer mechanism and an optimum design of gas-liquid contact equipment.

A New Analytical Model for TCP Reno with Bursts Error Considered

In this paper, we present a new analytical model for TCP Reno, and thismethod can also be used in other versions of TCP. The first order two-state Markovian model is usedto describe the wireless link, so as to deal with the burst error in wireless links very well. Thetimeout mechanism of TCP is also considered and a geometric method describes the exponential growthof TCP timeout. Also this method is effective for the study of the growth of TCP transmissionwindow. Analytical results indicate that this model is effective.

Inspection-Based Policy Considering Human Errors for Three-Stage Delay Time Degradation Systems

A periodic inspection policy for a single component system based on a three-stage failure process is proposed, and two different kinds of failures covering "hard" and "human" are considered in the proposed policy.The system is periodically inspected and inspections are perfect so that they can identify the intended defect.If the severe defect is detected by an inspection, an immediate repair is needed. However, once the system is identified to be in the minor defective state, there are two options. The first is to do nothing till the arrival of identifying the severe defect or hard failure, and the second is to repair immediately. Repair for any defect can renew the system with a limited probability such that the system may fail after repair due to human errors, which is common in many industrial applications. Two models are constructed by minimizing the expected cost per unit time and compared. We provide a numerical example to demonstrate the proposed model.

Determining exact survival probability by setting discrete random variables in E. Sparre Andersen’s model

In this work,we propose an alternative to the Pollaczek-Khinchine formula for the ultimate time survival(or ruin)probability calculation in exchange for a few assumptions on the random variables that generate the renewal risk model.More precisely,we demonstrate the expressibility of the distribution function n P(sup n≥1^(n)∑_(i=1)(X_(i)-cθ_(i))<u),u∈N_(0)using the roots of the probability-generating function,expectation E(X-cθ)X-cθ,and probability mass function of.We assume that the random X_(1),X_(2),...cθ_(1),cθ_(2),...variables of the mutually independent sequences and are cθc>0 X cθindependent copies of X and respectively,wherein,and are independent,θnonnegative,and integer.We also assume that the support of is finite.To illustrate the applicability of the proven theoretical statements we present a few numerical outputs when the mentioned random variables adopt some particular distributions.