Using fundamental electrical theory for varying time quantum uni-processor scheduling

Given the total number of instructions to be completed on a uni-processor system and the average cycle time per instruction we introduce a method of calculating time quantum allocation to individual fine grain tasks. The main theory behind our method is based on fundamental equations describing electrical phenomenon. We show how electric circuit analysis can be used to describe the fundamental scheduling problem, and provide a framework for defining more elaborate scheduling problems such as multiprocessor and multicomputer task scheduling. As a matter of physical soundness we demonstrate through unit derivation that our electrical analogy provides proper physical quantities that are supported by current literature. Our analysis shows that variable time round-robin scheduling (VTRR) provides a more appropriate means of scheduling fine-grain tasks than constant time round-robin scheduling (CTRR). We prove that, our VTRR scheduler always completes at least one task per cycle. We show through numerical comparisons some differences between VTRR and CTRR performance.