Grid system is used by many researchers' and scholars all over the world to solve the complicated and complex problems in different sciences. Job ranking backfilling is the most used model by many researchers in grid system to improve the performance of job scheduling algorithm. The model aims on serving the smallest job in the queue. As a second improvement of job backfilling, researchers proposed job ranking backfilling that serve job based on ranking equation. This paper proposes an enhance job ranking algorithm based on using linear and logarithmic ranking equations. Both proposed ranking equations used curve estimation model to predict on the variables' coefficients. By simulation and after different tests, the average results of job ranking backfilling with linear ranking equation outperform conventional job ranking backfilling with improvement equal 3.2% and 56.53% in total execution time and average waiting time, respectively. In addition, job ranking backfilling with logarithmic ranking equation shows average improvement equal 1.78% and 46.62% in total execution time and average waiting time, respectively. The results indicate that the proposed ranking equations would improve conventional job ranking backfilling in high and low demand grid system under different conditions.
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