Mathematical framework towards the analysis of a generic traffic marker

Traffic shaping for MPEG video transmission over the next generation internet

A successful mathematical description of natural landscapes relies upon a class of random processes known as fractional Brownian motions (fBms), which may exhibit correlation with long-range dependence (LRD). In remote sensing applications, the sensor observes a certain real scene <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> and records data <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> for successive signal processing tasks. Assuming that <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B </i> is modeled as an fBm, does the recorded signal <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">I</i> preserve the LRD character of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">B</i> ? More in general, can we relate the Hurst coefficient (an index of LRD) of the real scene to that of the recorded data? We address the problem in a simplified setup in which the data are related to (the slope of) the original scene through a zero-memory mapping. A mathematical framework is presented in which the above questions can be answered in the asymptotic regime of infinite data size. The effect of the finite sample size is also investigated. The mathematical model is also validated by real data, which are collected by a synthetic aperture radar that is mounted onboard of ERS-1/2 satellites.

The equilibrium behavior of Jackson queueing networks (Poisson arrivals, exponential servers and Bernoulli switches) has recently been investigated in some detail. In particular, it was found that in equilibrium, the traffic processes on the so-called exit arcs of a Jackson network with single server nodes constitute Poisson processes—a result extending Burke's theorem from single queues to networks of queues. A conjecture made by Burke and others contends that the traffic processes on non-exit arcs cannot be Poisson in equilibrium. This paper proves this conjecture to be true for a variety of Jackson networks with single server nodes. Subsequently, a number of characterizations of the equilibrium traffic streams on the arcs of open Jackson networks emerge, whereby Poisson-related stochastic properties of traffic streams are shown to be equivalent to a simple graph-theoretical property of the underlying arcs. These results then help to identify some inherent limitations on the feasibility of equilibrium decompositions of Jackson networks, and to point out conditions under which further decompositions are ‘approximately’ valid.

This paper presents and analyzes test results of the single rate Three Color Marker (srTCM) algorithm middleware implementation. The srTCM, defined at the RFC 2697, basically performs traffic shaping through two token buckets and packet marking according to their traffic parameters. The test environment evaluates a client-server application performance in terms of bandwidth usage and data throughput when all client requests to the server are intercepted and the server output traffic controlled by the srTCM. The test results allowed a fine-tuning of the stTCM parameter configuration aiming bandwidth allocation fairness and better throughput average to individual data streams.

In order to guarantee the quality of a service that uses the Differentiated Service QoS mechanisms, knowledge and predictions about the characteristics of the network elements and the type of traffic that is used is an important resource for service providers to configure traffic parameters on Router conditioner properly. Selection of the value and type of conditioner is often not appropriate for the performance of a DiffServ network also relies on other network elements — as a result of selection and parameter values conditioner will intuitively result in inefficient network utilities. The selection must be tailored to the application of the model policy and traffic conditioning according to Service Level Agreement (SLA) between the user and the service provider. This paper offers a solution for the selection of the parameters and the type of conditioner. The simulated traffic conditioner is TSW2CM, TSW3CM, Token Bucket, srTCM, and trTCM

We study finite size corrections to the semiclassical string solutions of the Schrödinger spacetime. We compute the leading order exponential corrections to the infinite size dispersion relation of the single spin giant magnon and of the single spin single spike solutions. The solutions live in a S3 subspace of the five-sphere and extent in the Schrödinger part of the metric. In the limit of zero deformation the finite size dispersion relations flow to the undeformed AdS5 × S5 counterparts and in the infinite size limit the correction term vanishes and the known infinite size dispersion relations are obtained.

The paper proposes a new class of traffic profiles that is better suited for metering bursty Internet traffic streams than the traditional token bucket profile. A good traffic profile should satisfy two criteria: first, it should consider packets from a conforming traffic stream as in-profile with high probability to ensure a strong QoS guarantee; second, it should limit the network resources consumed by a non-conforming traffic stream to no more than that consumed by a conforming stream. We model a bursty Internet traffic stream as an ON/OFF stream, where both the ON-period and the OFF-period have a heavy-tailed distribution. Our study shows that the heavy-tailed distribution leads to an excessive randomness in the long-term session rate distribution. Therefore, it is inherently difficult for any profile that limits the long-term average session rate to give a strong QoS guarantee for the conforming traffic streams. Our simulation demonstrates that a token bucket profile that couples the average rate control and the burst size control has a weak QoS guarantee. Based on this result, we propose a new class of traffic profiles that decouples the long term average rate control from the burst size control. Compared to a token bucket profile, this profile improves the level of QoS for a conforming traffic stream, yet limits the effective bandwidth consumed by a non-conforming traffic stream.

The back-projection algorithm is the most common method for the reconstruction of circular-scanning-based photoacoustic tomography (CSPAT) due to its simplicity, computational efficiency, and robustness. It usually can be implemented in two models: one for ideal point detector, and the other for planar transducer with infinite element size. However, because most transducers in CSPAT are planar with a finite size, the off-center targets will be blurred in the tangential direction with these two reconstruction models. Here in this paper, we put forward a new model of the back projection algorithm for the reconstruction of CSPAT with finite size planar transducer, in which the acoustic spatial temporal response of the employed finite size transducer is approximated with a virtual detector placed at an optimized distance behind the transducer, and the optimized distance is determined by a phase square difference minimization scheme. Notably, this proposed method can also be suitable for reconstruction with the ideal point detector and infinite planar detector, and thus is a generalized form of the back-projection algorithm. Compared with the two conventional models of the back-projection method and the modified back-projection method, the proposed method in this work can significantly improve the tangential resolution of off-center targets, thus improving the reconstructed image quality. These findings are validated with both simulations and experiments. We propose a generalized model of the back projection algorithm to restore the elongated tangential resolution in CSPAT in case of a planar transducer of finite size, which can also be applicable for point and large-size planar transducers. This proposed method may also guide the design of CSPAT scanning configurations for potential applications such as human breast imaging for cancer detection.

Finite size behavior of the asymmetric avalanche process

The objective of this study is to model the complex behavior of non-lane based heterogeneous traffic which is predominantly occupied by vehicles with varying physical and dynamical characteristics and their staggered car following behavior. This study proposes a new continuum model by considering the properties of two-sided lateral gap in a non-lane based heterogeneous traffic stream. The model is built on a strong empirical background and modified car following theory. In particular, the model consists of density dependent disturbance propagation speed, viscosity term and a frictional clearance term to describe the complex vehicular interactions in a traffic stream. Viscosity term in the model represents the driver’s reaction to a sudden change in density and further, it helps in smoothening out the shock fronts. Frictional clearance term in the model considers the effect of slow moving vehicles on the dynamics of fast moving vehicles. The results of mathematical and numerical analysis show that the proposed model satisfies all the qualitative and physical properties of the real world system. Moreover, two sided lateral gap in the model improves the stability region of traffic flow and increases the capacity and density of traffic stream. In addition, it is able to dissipate the traffic perturbation rapidly when compared to one-sided lateral gap model. It is anticipated that the new model provides the basis for evaluating alternative transport policy measures and helps in analyzing the system performance in the future.

Nominal flight time optimization for arrival time scheduling through estimation/resolution of delay accumulation

A general methodology for population analysis

A system of two parallel queues is considered, where each customer must leave after service through a common gate G. It is assumed that service times at the two stations I and II are independent and identically distributed, and that exit service takes a fixed length of time. A I-customer may be served at station I only if the previous I-customer has completed exit service. Integral equations are formulated from which the distribution of the total service time may be obtained when the two queue sizes are infinite. These equations are solved for exponential and generalized erlangian service times. Extensions to the case of k parallel queues and to the case of Poisson arrivals and finite queue sizes are discussed briefly.

Matrix structures are ubiquitous in linear algebra problems stemming from scientific computing, engineering and from any mathematical models of the real world. They translate, in matrix language, the specific properties of the physical problem. Often, structured matrices reveal themselves in a clear form and apparently seem to show immediately all their properties. Very often, structures are hidden, difficult to discover, and their properties seem to be hardly exploitable. In this note, we rely on the research area of queueing models and Markov chains to present, motivate, and analyze from different points of view the main matrix structures encountered in the applications. We give an overview of the main tools from the structured matrix technology including Toeplitz matrices—with their asymptotic spectral properties and their interplay with polynomials—circulant matrices and other trigonometric algebras, preconditioning techniques, the properties of displacement operators and of displacement rank, fast and superfast Toeplitz solvers, Cauchy-like matrices, and more. Among the hidden structures, besides the class of Toeplitz-like matrices, we just recall some properties of rank-structured matrices like quasi-separable matrices. Then we focus our attention to finite dimensional and to infinite dimensional Markov chains which model queueing problems. These chains, which involve block Hessenberg block Toeplitz matrices of finite and infinite size, are efficiently solved by using the tools of the structured matrix technology introduced in the first part. In this note we also provide pointers to some related recent results and to the current research.

ABSTRACTThis work focuses on a mobile edge computing (MEC) assisted IoT status update network with multi‐objective sensing, which consists of a wireless sensing network, MEC network, and an information receiver (IR). To simultaneously guarantee information freshness and system throughput, a layer‐superposed non‐orthogonal multiple access (NOMA) HARQ (LS‐NOMA‐HARQ) scheme is proposed. In the proposed LS‐NOMA‐HARQ scheme, an entire status update delivery circle consists of multiple rounds for NOMA symbol feedforward transmission. In each round, the source constructs and transmits a NOMA symbol to the AP that first performs feedforward decoding (FD). Each NOMA symbol includes the newly generated packet, termed the primary packet, and the part of the currently failed packet, termed the secondary one. If the received primary packet can not be correctly recovered by the AP, the NOMA symbol is offloaded to the edge server and stored in the buffer of the edge server. The source continuously generates and sends new NOMA symbols to AP until a successful FD occurs. On the contrary, the decoded result is directly delivered to IR, and backtrack decoding (BD) is triggered at the edge server. Then, the edge server successively decodes the previously stored NOMA symbols by using sophisticated successive interference cancellation (SIC), and delivers the recovered packet to IR. Once SIC‐based BD fails, it is declared that a circle of LS‐NOMA‐HARQ status update delivery completes. Because the primary and secondary packets are independently modulated and superposed in the MAC layer, the proposed LS‐NOMA‐HARQ outperforms the layer‐coded HARQ scheme that is executed in the physical layer. Moreover, this work also considers the two cases of finite and infinite buffer size at the edge server, and truncated HARQ is used for the retransmission of a single NOMA symbol. Under the finite buffer size case, the circle‐shift preemption is used at the buffer edge server. The edge service follows exponentially distributed processes due to the user schedule and can be interrupted by one In‐Out process due to the energy computation at the edge server, which results in a huge data processing delay at the edge server. To characterize this specific issue, this work investigates the age of process information (AoPI). In addition, considering the joint impact of both FD and BD, two modified AoPI metrics, that is, FD‐based AoPI (FD‐AoPI) and BD based AoPI (BD‐AoPI), are proposed. The FD‐AoPI is defined as the elapsed time since the generation of the last successfully feedforward decoded update, but the BD‐AoPI is based on the classical definition of AoI. While the FD‐AoPI simultaneously captures both throughput and information freshness, the BD‐AoPI results in a loss in information timeliness. With the statistical characterization of related statistics, the closed‐form expressions of both FD‐AoPI and BD‐AoPI are derived. The simulated and numerical results give insight into the impact of system parameters on both AoPI and throughput.