China
Africa
Explore chapters and articles related to this topic
Approximate Methods
Published in Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou, ViscousFluid Flow, 2021
Tasos C. Papanastasiou, Georgios C. Georgiou, Andreas N. Alexandrou
Asymptotic analysis is the study of a problem under the assumption that an involved parameter is vanishingly small or infinitely large. Consider the following initial value problem, (1+ϵ)dudx+u=0,u(0)=a, which involves one dimensionless parameter, ϵ. The exact solution to problem (7.28) is u=ae−x/(1+ϵ).
Work-conserving disciplines are asymptotic optimal in completion time minimization
Published in IISE Transactions, 2023
To compare the performance of different disciplines, deterministic models always consider the worst possible input, which does not correspond to any inherent properties of the input. In addition to the aforementioned results in the deterministic setting, there has also been a considerable amount of work on stochastic models, which helps to explain the empirical performance. Specifically, there is a line of work that utilizes asymptotic analysis to evaluate system performance in a large scale, often with certain stochastic assumptions on the input data. Chou et al. (2006) studied the weighted completion time minimization problem with release dates in a single-machine model, and proved that the expected weighted completion time under the non-preemptive Weighted Shortest Expected Processing Time Algorithm (WSEPTA) among available jobs is asymptotically optimal when the number of jobs increases to infinity, if job workload and weights are bounded and the job workloads are mutually independent random variables. Kaminsky and Simchi-Levi (2001) proved the asymptotic optimality of the SPT for the total completion time objective in a flow shop model, where each job must be sequentially processed on the machines and every job has the same routing.
Stack-Based Dynamic Resource Access Control Protocol for Real-Time Systems
Published in IETE Journal of Research, 2022
Rumpa Hazra, Shouvik Dey, Ananya Kanjilal, Swapan Bhattacharya
Asymptotic analysis of an algorithm refers to define the mathematical boundation or framing of its run-time performance [12]. This analysis evaluates the performance of an algorithm in terms of input size (we don't measure the actual running time). The SRP and the SDRP depend on the two input parameters, number of tasks (n) and number of resources (m).