Narrow Results

The Fog computing is rising as a dominant and modern computing model to deliver Internet of Things (IoT) computations, which is an addition to the cloud computing standard to get it probable to perform the IoT requests in the network of edge. In those above independent and dispersed environment, resource allocation is vital. Therefore, scheduling will be a test to enhance potency and allot resources properly to the tasks. This paper offers a distinct task scheduling algorithm in the fog computing environment that tries to depreciate the makespan and maximize resource utilization. This algorithm catalogues the task based on the mean Suffrage value. The suggested algorithm gives much resource utilization and diminishes makespan. Our offered algorithm is compared with different alive scheduling for performance investigation, and test results confirm that our algorithm has a more significant resource utilization rate and low makespan than other familiar algorithms.

We consider two semi-online scheduling problems on a single batch (processing) machine with jobs' nondecreasing processing times and jobs' nonincreasing processing times, respectively. Our objective is to minimize the makespan. A batch processing machine can handle up to B jobs simultaneously. We study an unbounded model where B = ∞. The jobs that are processed together construct a batch, and all jobs in a batch start and complete at the same time. The processing time of a batch is given by the longest processing time of any job in the batch. Jobs arrive over time. Let p_j denote the processing time of job J_j. Given job J_j and its following job J_{j + 1}, we assume that p_{j + 1} ≥ α p_j, where α ≥ 1 is a constant number, for the first problem with jobs' nondecreasing processing times. For the second problem, we assume that p_{j + 1} ≤ α p_j, where 0 < α < 1 is a constant number. We propose an optimal algorithm for both problems with a competitive ratio for the first problem and for the second problem.

We study the problem of online scheduling parallel jobs with bounded processing times on 2 machines, and the objective is to minimize makespan. A parallel job requires simultaneous processing on a pre-specified, job-dependent number of machines. The problem is online in the sense that jobs are presented one by one. Once a job is presented, we must irrevocably assign it to some time slot before the next one shows up. We investigate the case where the processing times of jobs are bounded within interval [a, αa] where a > 0 and α > 1. We first prove a lower bound of competitive ratios for online algorithms equal when α ≥ 2 and when 1 < α < 2, respectively. We further prove that the Greedy algorithm proposed in Chan et al. (2008) is -competitive in the case but it cannot be better than -competitive. The results imply that when 1 < α < 2 Greedy has a competitive ratio better than 2, which is the competitive ratio of Greedy in the case without processing time bound.