Comparing the influencing factors of M/G/1 performance indices in queuing theory across different scheduling approaches

The M/G/1 queue holds significant research value within the realm of queuing theories and systems due to its broad applicability. However, the multifaceted nature of the M/G/1 queue makes its characteristics and scheduling challenges particularly intricate. Key performance metrics include the average response time, average waiting time, system expectancy, and queue expectancy. This study predominantly concentrates on the average response time, average waiting time, and the increasingly emphasized metric, average slowdown. These metrics provide a more holistic view of system performance, unhindered by system size variations. Appropriate scheduling can do more than just decrease the average response and wait times; it holds a specific relevance to achieving equitable scheduling. Among the myriad metrics employed to gauge system efficiency, the fairness index is gaining traction. The crux of this investigation centers on this metric, aiming to delineate the discrepancies in average slowdown between non-preemptive and preemptive scenarios. Furthermore, a delve into the z-transform within the M/G/1 system will unravel the intricacies of the update-reward mechanism, illuminating the performance oscillations of the M/G/1 system across varied timelines.