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one percon alla n on n jobs. job i first spends s; time on the supercomputer and then n; time on the normal computer. A job can only start running on any of the normal computers after it has finished on the supercomputer. However, as soon as any job finishes on the supercomputer, it can immediately start on one of the free normal computers. The goal is to finish running all the jobs as soon as possible. Note that since there is only one supercomputer, you'll always have to wait si time so that the jobs finish running on the supercomputer. However, you can optimize when you run the jobs on the normal computers to try to finish running all the jobs as soon as possible. i=n i=1 Show that by executing jobs after sorting them in decreasing order by nį, you have an optimal schedule.

one percon alla n on n jobs. job i first spends s; time on the supercomputer and then n; time on the normal computer. A job can only start running on any of the normal computers after it has finished on the supercomputer. However, as soon as any job finishes on the supercomputer, it can immediately start on one of the free normal computers. The goal is to finish running all the jobs as soon as possible. Note that since there is only one supercomputer, you'll always have to wait si time so that the jobs finish running on the supercomputer. However, you can optimize when you run the jobs on the normal computers to try to finish running all the jobs as soon as possible. i=n i=1 Show that by executing jobs after sorting them in decreasing order by nį, you have an optimal schedule.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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### Scheduling Jobs on a Supercomputer and Normal Computers You have one supercomputer and \( n \) normal computers on which you need to run \( n \) jobs. Each job \( i \) first spends \( s_i \) time on the supercomputer and then \( n_i \) time on the normal computer. A job can only start running on any of the normal computers after it has finished on the supercomputer. However, as soon as any job finishes on the supercomputer, it can immediately start on one of the free normal computers. The goal is to finish running all the jobs as soon as possible. Note that since there is only one supercomputer, you will always have to wait \(\sum_{i=1}^{n} s_i\) time so that the jobs finish running on the supercomputer. However, you can optimize when you run the jobs on the normal computers to try to finish running all the jobs as soon as possible. ### Optimal Schedule Strategy To achieve an optimal schedule, execute the jobs after sorting them in decreasing order by \( n_i \). This prioritization helps ensure that jobs requiring the longest normal computer time are addressed promptly, leading to an overall reduction in the total time needed to complete all jobs. By employing this strategy, you can streamline the process and achieve efficient job scheduling on the supercomputer and normal computers.
Transcribed Image Text:### Scheduling Jobs on a Supercomputer and Normal Computers You have one supercomputer and \( n \) normal computers on which you need to run \( n \) jobs. Each job \( i \) first spends \( s_i \) time on the supercomputer and then \( n_i \) time on the normal computer. A job can only start running on any of the normal computers after it has finished on the supercomputer. However, as soon as any job finishes on the supercomputer, it can immediately start on one of the free normal computers. The goal is to finish running all the jobs as soon as possible. Note that since there is only one supercomputer, you will always have to wait \(\sum_{i=1}^{n} s_i\) time so that the jobs finish running on the supercomputer. However, you can optimize when you run the jobs on the normal computers to try to finish running all the jobs as soon as possible. ### Optimal Schedule Strategy To achieve an optimal schedule, execute the jobs after sorting them in decreasing order by \( n_i \). This prioritization helps ensure that jobs requiring the longest normal computer time are addressed promptly, leading to an overall reduction in the total time needed to complete all jobs. By employing this strategy, you can streamline the process and achieve efficient job scheduling on the supercomputer and normal computers.
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