Urn models and their applications: an approach to modern discrete probability theory, by Norman L. Johnson and Samuel Kotz. Pp xiii, 402. £16·45. 1977. SBN 0 471 44630 0 (Wiley)

LEVERAGING RESOURCES ON ANONYMOUS MOBILE EDGE NODES Ahmed Salem Old Dominion University, 2018 Director: Dr. Tamer Nadeem Co-Director: Dr. Ravi Mukkamala Smart devices have become an essential component in our lives. The rapid rise of smartphones, IoTs, and wearable devices has enabled applications that were not possible few years ago, e.g., health monitoring and online banking. Meanwhile, smart sensing has laid the infrastructure for smart homes and smart cities. The intrusive nature of smart devices has granted access to huge amounts of raw data. Researchers have seized the moment with complex algorithms and data models used to process the data over the cloud in order to extract as much information as possible. However, with the pace and amount of data generation, in addition to the networking protocols transmitting data to cloud servers only 20% of what has been generated on the edge of the network was processed. On the other hand, smart devices carry a large set of resources, e.g., CPU, memory, and camera, and these resources sit idle most of the time. Studies have shown that, for much of the time, resources are either idle, e.g., sleeping and eating, or underutilized, e.g. inertial sensors during phone calls. These findings articulate a problem in processing large data sets, while having idle resources in close proximity. In this dissertation, we propose harvesting underutilized edge resources then using them in processing the huge amount of data generated, and currently wasted, through applications running at the edge of the network. We propose to flip the concept of cloud computing; instead of sending massive amounts of data for processing over the cloud, we distribute lightweight applications to process data on users’ smart devices. We envision that this approach will enhance the network’s bandwidth, grant access to larger datasets, provide low latency responses, and most importantly include user’s contextual information in processing. However, such benefits come with a set of challenges: How to locate suitable resources? How to match resources with data providers? How to inform resources about what to do and when to do it? How to orchestrate applications’ execution on multiple devices? and How to communicate between devices at the edge? Communication between devices at the edge uses different parameters in terms of device mobility, topology, and data rate. Standard protocols, e.g., Wi-Fi or Bluetooth, were not designed for edge computing, hence, they do not offer a perfect match. Edge computing requires a lightweight protocol that provides quick device discovery, a decent data rate, and multicasting to devices in the proximity. Bluetooth features wide acceptance within the IoT community; however, its low data rate and unicast communication limits its use on the edge. Despite its being the most suitable communication protocol for edge computing and despite the fact that it is unlike other protocols, Bluetooth uses a closed source code that blocks its lower layer from all forms of research study, enhancement, and customization. Hence, we offer an open source version of Bluetooth and then we customize it for edge computing applications. In this dissertation, we propose Leveraging Resources on Anonymous Mobile Edge Nodes (LAMEN ), a three-tier framework in which edge devices are clustered by proximity. On finding an application to execute, LAMEN clusters discover and allocate resources, share the application’s executable with resources, and estimate incentives for each participating resource. In a cluster, a single head node, i.e. the mediator, is responsible for resource discovery and allocation. Mediators orchestrate cluster resources and present them as a virtually large homogeneous resource. For example, two devices, each offering either a camera or a speaker are presented outside the cluster as a single device with both camera and speaker; this can be extended to any combination of resources. Then, the mediator handles applications’ distribution within a cluster, as needed. Also, we provide a communication protocol that is customizable to the edge environment and the application’s need. Pushing lightweight applications that end devices can execute over their locally generated data has the following benefits: First, it avoids sharing user data with a cloud server, which is a privacy concern for many users; Second, it introduces mediators as local cloud controllers, closer to the edge; Third, it hides the user’s identity behind the mediators; and finally, it enhances bandwidth utilization by keeping the raw data at the edge and by transmitting processed information. Our evaluation shows both an optimized resource lookup and application assignment schemes, in addition to scalability in handling networks with a large number of devices. In order to overcome the communication challenges, we provide an open source communication protocol that we customize for edge computing applications; however, it can be used beyond the scope of LAMEN. Finally, we present three applications to show how LAMEN enables various application domains on the edge of the network. In summary, we propose a framework to orchestrate underutilized resources at the edge of the network and use them in processing data generated in their proximity. Using the approaches explained later in the dissertation, we show how LAMEN enhances the performance of applications and enables a new set of applications that were not previously feasible.

/pdf/leveraging-resources-on-anonymous-mobile-edge-nodes-26a6nmt996.pdf

Leveraging Resources on Anonymous Mobile Edge Nodes

Hyperbolic, trigonometric, rational function solutions are obtained for a nonlinear Schrödinger type equation in an optical fiber. The numerical investigations for the examined solutions have been remarks that rational, shock, envelopes, periodic, explosive, solitonic and bright new waves may be usable in fiber communications. The presented methods are effective and powerful in the applications of comparisons in optical fibers. The optical propagating wave characteristics inside fiber boundaries are theoretically expected to become a very significantly improved by introducing fiber dispersions, nonlinear and fiber losses effects. Furthermore, both the wave amplitudes and widths may be controlled by these parameters. • Nonlinear analysis technique is used to solve the physical models. • The nonlinear Schrödinger equation with different physical fiber coefficients is considered. • Highly performance and efficient of the proposed solver. • Physical parameters effects are introduced. • The behavior of presented solutions is depicted by 2D, 3D and contour graphs. 

Modulations of some physical parameters in a nonlinear Schrödinger type equation in fiber communications

This research investigates on the numerical methods for computing the greatest common divisors (GCD) of two polynomials in the orthogonal basis without having to convert to the power series form. Previous implementations were conducted using the Gauss Elimination with partial pivoting (GEPP) and QR Householder algorithms, respectively. This work proceeds to seek for a better approximate solution by comparing the results of the implementations with the QR with column pivoting (QRCP) algorithm. The results reveal that QRCP is as competent as the GEPP algorithm, up to a certain degree, giving a reasonably good approximate solution. It is also found that normalizing the columns of the associated coefficient matrix slightly reduces the condition number of the matrix but has no significant effect on the GCD solutions when applying the GEPP and QR Householder algorithms. However equilibration of the columns by computing its ∞-norm is capable to improve the solution when QRCP is applied. Comparing the three algorithms on some test problems, QR Householder outperforms the rest and is able to give a good approximate solution in the worst case condition when the smallest element of the matrix is 1, the entries ranging up to 15 digits integers.

/pdf/analysis-and-comparison-of-numerical-algorithms-for-finding-48tmpl9v8z.pdf

Analysis and comparison of numerical algorithms for finding the GCD of certain types of polynomials in the Chebyshev basis

In this paper a finite difference method for solving 2-dimensional diffusion equation is presented. The method employs Crank-Nicolson scheme to improve finite difference formulation and its convergence and stability. The obtained solution will be a recursive formula in each step of which a system of linear equations should be solved. Given the specific form of obtained matrices, rather than solving the problem in each step using conventional iterative methods, a closed-form solution is formulated..

https://jac.ut.ac.ir/article_71297_5397798f2c99c329aa87ce4d7a549428.pdf

A Closed-Form Solution for Two-Dimensional Diffusion Equation Using Crank-Nicolson Finite Difference Method

Solving nonlinear Schrodinger equation using stable implicit finite difference method in single‐mode optical fibers

Neighborhood discovery (ND) in a wireless sensor network is a process of identifying the sensors that a given node can communicate directly. In this paper, our main contribution is to model the ND protocol in a wireless sensor network. In ND task, each node is assigned its own N timeslots, with equal slot intervals. In each slot, each node chooses either to transmit or listen, with probabilities p and 1 -- p. Our objectives are to analyze the optimal value of p, and model the formulation of N by mapping the problem into the coupon's collector problem. The simulation results show close match to the theoretical results.

Neighborhood discovery in a wireless sensor networks

In this research, the method for computing the GCD of two polynomials in the orthogonal basis, using the comrade matrix approach is further investigated Generally, polynomials in the orthogonal basis may be better conditioned than that of the power series form when finding polynomial roots However when transforming the GCD problem into a linear algebra problem requires the determination of the matrix rank and solving corresponding systems of linear equations As such, conditioning issues may arise in certain types of inputs In this report preliminary results using the Gauss elimination method with partial pivoting and the QR decomposition algorithm for solving systems of linear equations are implemented to find the GCD of certain class of polynomials and the results presented

Numerical matrix methods in the computation of the greatest common divisor (GCD) of polynomials

We model an important aspect of the problem of sensor information integration that arises in wireless communications, where N sensors try to communicate with a receiver using a single un-shareable radio channel. If several sensors transmit at the same time their transmissions collide at the receiver resulting in garbled messages and the need for re-transmission. This is highly undesirable since the sensor nodes are energy-constrained and the radio interface is known to be the most significant source of energy expenditure. Consequently, it is of paramount importance to design arbitration protocols that are highly efficient in stamping out collisions and are, at the same time, as lightweight as possible. The main contribution of this paper is to present a distributed probabilistic mechanism that aims to arbitrate between several competing requests by sensor nodes for the radio channel. Our mechanism is simple, energy-efficient and does not rely on the existence of unique sensor identifiers (IDs).

Shazirawati Mohd Puzi

Papers

Solving nonlinear Schrodinger equation using stable implicit finite difference method in single‐mode optical fibers

Neighborhood discovery in a wireless sensor networks

Numerical matrix methods in the computation of the greatest common divisor (GCD) of polynomials

A distributed probabilistic arbitration in sensors integration

Transformation of DCG onto DAG for task assignment problem