Delay Probability Density Function Research Articles

Synchronization of Delayed Fuzzy Neural Networks with Probabilistic Communication Delay and Its Application to Image Encryption

This article studies the design of fuzzy synchronization controller of Takagi—Sugeno (T-S) fuzzy neural networks with distributed time-varying delay and probabilistic network communication delay. Compared with the existing model of neural networks with distributed time-varying delay without kernel, a more general model containing a distributed delay kernel is considered. By utilizing the probability distribution of random communication delays, a distributed but deterministic delay model is established. In this model, the delay probability density function is treated as the distributed delay kernel. By developing a new Lyapunov-Krasovskii functional (LKF) related to the distributed delay kernels and using an integral inequality, new sufficient conditions for the existence of a synchronization controller are presented. Finally, a numerical simulation and an application of encrypting the image are carried out to illustrate the effectiveness of the developed strategy.

Optimal control to improve reliability of demand responsive transport priority at signalized intersections considering the stochastic process

Bus priority has been proposed for many years to improve traffic congestion, energy conservation, and emissions reduction. Transit signal priority is a main measure of executing bus priority. Moreover, because the time that buses arrive at an intersection should be predicted quite precisely to make a signal control scheme in advance, bus lane is an important segment in transit priority at signalized intersections to avoid disturbances from other vehicles on the road. However, in practice, the bus route of demand responsive transport is widespread, which is not inappropriate to set bus lane for each bus route because of low frequency. Therefore, in this paper, a robust optimization control method is proposed to solve the bus priority problem at signalized intersections without exclusive bus lanes and improve reliability of demand responsive transport priority at signalized intersections. First, the bus delay probability density function is formulated to describe the interaction mechanism about the bus and other vehicles at the signalized intersection. Then, the accurate bus delay expectation and variance calculation mathematical models are formulated based on the bus delay probability density function. Furthermore, a robust optimal signal control method is proposed followed by the discussions of boundary conditions. Finally, simulation test and case study were conducted to illustrate the performance of the robust optimization control method proposed in this paper. The results show that the proposed control method could significantly improve bus delay compared to considering the bus operation process as stable.

On the Deadline Miss Probability of Various Routing Policies in Wireless Sensor Networks

Moving data across communication networks is often subject to deadline requirements. An example is early warning of disasters of natural origin, where sensor measurements at the disaster location must be communicated across a network within a predefined maximum delay in order for a consequent warning to be timely. In this work, we present a probabilistic model that allows for characterizing the delay experienced by sensor measurements in a wireless sensor network from source to sink depending upon the routing metric used for forwarding the data through the network. Using link delay probability distributions and the probabilities of following different paths to the sink, source-to-sink delay distributions are found for routing policies based on minimum hop-count, minimum mean delay and the Joint Latency (JLAT) protocol. An algorithm for calculating the end-to-end source to sink delay probability density function (PDF) is presented for the general case of networks that use routing tables whose input for routing decisions is the remaining time-to-deadline. The work provides a general tool for routing delay analysis, allowing for comparison of the deadline miss probability between different routing policies. An improved form of JLAT is proposed. Its deadline miss probability is found using the presented algorithm and compared to the ones determined for minimum hop-count, minimum mean delay and JLAT by means of an example.

Statistical estimation of delay in nano-scale CMOS circuits using Burr Distribution

the process of modern integrated circuit (IC) design has been challenged by many factors. One of the most important challenges is the variation of device and circuit parameters during the manufacturing process. In this paper, the effects of manufacturing process variations on the gate delay have been modeled and an accurate yet low-cost simulation method for estimation of the circuit performance has been proposed. This additive method takes advantage of a 3-parameter probability density function (PDF), known as Burr distribution, to estimate the delay of each gate on the critical path. In this work, it is demonstrated that our proposed method is more accurate than previously proposed methods by taking into account the skewness of delay PDF. Although our proposed method is based on a 3-parameter PDF, we demonstrate that the simulation cost of our proposed method is no more than the conventional 2-parameter Gaussian PDF. We have compared the accuracy of our proposed method against the HSPICE simulation results. Moreover, we have compared the accuracy of our method with the most recent works with a 2-parameter PDF. The results for ISCAS85 benchmark circuits in our work have shown for 99 percentile points with average errors of 3.62, 3.49 and 2.78% in 90 nm, 45 nm and 22 nm technologies respectively.

Queuing Models for Dimensioning Interactive and Streaming Services in High-Speed Downlink Packet Access Networks

We consider modeling the statistical behavior of interactive and streaming traffics in high-speed downlink packet access (HSDPA) networks. Two important applications in these traffic categories are web-browsing (interactive service) and video streaming (streaming service). Web-browsing is characterized by its important sensitivity to delay. Video streaming on the other hand is less sensitive to delay, however, due to its large frame sizes, video traffic is more affected by the packet loss resulting from a limited buffer size at the base station. Taking these characteristics into account, we consider modeling the queuing delay probability density function (PDF) of the Web-browsing traffic, and modeling the queuing buffer size distribution of video streaming traffic. Specifically, we show that the queuing delay of the Web-browsing traffic follows an exponential distribution and that the queuing buffer size of video streaming traffic follows a weighted Weibull distribution. Model fitting based on simulated data is used to provide simple mathematical formulations for the different parameters that characterize the PDFs under consideration. The provided equations could be used, directly, in HSDPA network dimensioning and, as a reference, to satisfy a certain quality of service (QoS).

Theoretical Characterization and System Impact of the Hinge Model of PMD

Modeling of the polarization-mode dispersion (PMD) temporal changes in long fiber routes represents a critical aspect of system outage characterization. In this paper, an analysis of the PMD temporal statistics in links obeying the recently proposed hinge model is presented. The analytical expression of the differential group delay probability density function is derived and used to show that the outage probability is channel specific in a wavelength-division-multiplexed system. The existence of outage-free channels, which represents one of the most important implications of the hinge model, is demonstrated and quantified. The frequency dependence of the temporal statistics is also characterized, and an expression for PMD-induced pulse broadening is derived

Unicast-based inference of network link delay distributions with finite mixture models

Providers of high quality-of-service over telecommunication networks require accurate methods for remote measurement of link-level performance. Recent research in network tomography has demonstrated that it is possible to estimate internal link characteristics, e.g., link delays and packet losses, using unicast probing schemes in which probes are exchanged between several pairs of sites in the network. We present a new method for estimation of internal link delay distributions using the end-to-end packet pair delay statistics gathered by back-to-back packet-pair unicast probes. Our method is based on a variant of the penalized maximum likelihood expectation-maximization (PML-EM) algorithm applied to an additive finite mixture model for the link delay probability density functions. The mixture model incorporates a combination of discrete and continuous components, and we use a minimum message length (MML) penalty for selection of model order. We present results of Matlab and ns-2 simulations to illustrate the promise of our network tomography algorithm for light cross-traffic scenarios.

A stochastic model of the temporal and azimuthal dispersion seen at the base station in outdoor propagation environments

A simple statistical model of azimuthal and temporal dispersion in mobile radio channels is proposed. The model includes the probability density function (PDF) of the delay and azimuth of the impinging waves as well as their expected power conditioned on the delay and azimuth. The statistical properties are extracted from macrocellular measurements conducted in a variety of urban environments. It is found that in typical urban environments the power azimuth spectrum (PAS) is accurately described by a Laplacian function, while a Gaussian PDF matches the azimuth PDF. Moreover, the power delay spectrum (PDS) and the delay PDF are accurately modeled by an exponential decaying function. In bad urban environments, channel dispersion is better characterized by a multicluster model, where the PAS and PDS are modeled as a sum of Laplacian functions and exponential decaying functions, respectively.

Turn-on jitter in zero-biased single-mode semiconductor lasers

An analytical expression for the turn-on delay probability density function (pdf) of single-mode lasers biased below threshold is derived, which is in good agreement with results based on computer simulations and measurements. It is shown, that the pdf obtained only depends on the on-state yielding simple requirements for the transmitter in order to achieve a given BER. The results are of particular interest for designing optical interconnects, where zero-biased lasers are used.

Buffer Sizing of a Packet-Voice Receiver

Some analytical results have been developed for the analysis and design of a packet-voice receiver in previous work [1], namely, the delay suffered by packets because of the reassembly mechanism is described in terms of the overall delay probability density function (pdf) <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w(t)</tex> . This basic analytical result is used here in order to obtain the pdf <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">b(t)</tex> of the time spent by packets in the receiver buffer. In this way, the previous work [1] is extended to analysis of the delay distribution of the receiver buffer where arriving talkspurts are delayed to compensate for the variable network delay of all packets within a talkspurt. The tools developed here facilitate a choice of the buffer size at the prescribed level of packet-loss probability.