On the Existence of Steady-State Solutions to the Equations Governing Fluid Flow in Networks

The steady-state solution of fluid flow in pipeline infrastructure networks driven by junction/node potentials is a crucial ingredient in various decision support tools for system design and operation. While the non-linear system is known to have a unique solution (when one exists), the absence of a definite result on existence of solutions hobbles the development of computational algorithms, for it is not possible to distinguish between algorithm failure and non-existence of a solution. In this letter we show that a unique solution exists for such non-linear systems if the term solution is interpreted in terms of potentials and flows rather than pressures and flows. The existence result for flow of natural gas in networks also applies to other fluid flow networks such as water distribution networks or networks that transport carbon dioxide in carbon capture and sequestration. Most importantly, by giving a complete answer to the question of existence of solutions, our result enables correct diagnosis of algorithmic failure, problem stiffness and non-convergence in computational algorithms.Comment: 5 pages, 2 figure

Relaxations of the Steady Optimal Gas Flow Problem for a Non-Ideal Gas

Natural gas ranks second in consumption among primary energy sources in the United States. The majority of production sites are in remote locations, hence natural gas needs to be transported through a pipeline network equipped with a variety of physical components such as compressors, valves, etc. Thus, from the point of view of both economics and reliability, it is desirable to achieve optimal transportation of natural gas using these pipeline networks. The physics that governs the flow of natural gas through various components in a pipeline network is governed by nonlinear and non-convex equality and inequality constraints and the most general steady-flow operations problem takes the form of a Mixed Integer Nonlinear Program. In this paper, we consider one example of steady-flow operations -- the Optimal Gas Flow (OGF) problem for a natural gas pipeline network that minimizes the production cost subject to the physics of steady-flow of natural gas. The ability to quickly determine global optimal solution and a lower bound to the objective value of the OGF for different demand profiles plays a key role in efficient day-to-day operations. One strategy to accomplish this relies on tight relaxations to the nonlinear constraints of the OGF. Currently, many nonlinear constraints that arise due to modeling the non-ideal equation of state either do not have relaxations or have relaxations that scale poorly for realistic network sizes. In this work, we combine recent advancements in the development of polyhedral relaxations for univariate functions to obtain tight relaxations that can be solved within a few seconds on a standard laptop. We demonstrate the quality of these relaxations through extensive numerical experiments on very large scale test networks available in the literature and find that the proposed relaxation is able to prove optimality in 92% of the instances.Comment: 28 page

Intelligent transportation system and smart traffic flow with IOT

64-67There has been an increase in vehicles across the globe. Also, the congestion due to traffic has leapfrogged in India. The traffic flow information has been required to find out the route with minimum congestion and forecast the traffic. And this has been a part of the Intelligent Transportation System (ITS) which would help build smart cities. A lot of work has been done on the traffic measurement system. But the integration of emerging techniques such as the Internet of Things (IoT) and cloud computing has provided a lot of research scope in ITS. This paper has proposed an IoT-based method to determine the real-time traffic flow in a road section with ultrasonic sensors, Arduino, ESP8266 Wi-Fi module, and an open-source cloud. There has been an average traffic flow every five minutes to be displayed in the cloud platform. This method can be very much cost-effective with less power consumption and improved accuracy. Hence, the proposed IoT-based technique has provided the traffic flow data, and this data shall further be used for traffic predictions using machine learning algorithms

Trends In Task Allocation For Multicore System

As the functionality in real-time embedded systems becoming complex, there has been a demand for higher computation capability, exploitation of parallelism and effective usage of the resources. Further, technological limitations in uniprocessor in terms of power consumption, instruction level parallelism reaching saturation, delay in access of memory blocks; directed towards emergence of multicore. Multicore design has its challenges as well. Increase in number cores has raised the demand for proper load distribution, parallelizing existing sequential codes, enabling effective communication and synchronization between cores, memory and I/O devices. This paper brings out the demand for effective load distribution with analyzes and discussion about the various task allocation techniques and algorithms associated with decentralized task scheduling technique for multicore systems. This paper also addresses on the multithreaded architecture, where parallel tasks are formulated from sequential code blocks and finally on the techniques to parallelize the sequential code block