Comparison of Loss ratios of different scheduling algorithms

It is well known that in a firm real time system with a renewal arrival process, exponential service times and independent and identically distributed deadlines till the end of service of a job, the earliest deadline first (EDF) scheduling policy has smaller loss ratio (expected fraction of jobs, not completed) than any other service time independent scheduling policy, including the first come first served (FCFS). Various modifications to the EDF and FCFS policies have been proposed in the literature, with a view to improving performance. In this article, we compare the loss ratios of these two policies along with some of the said modifications, as well as their counterparts with deterministic deadlines. The results include some formal inequalities and some counter-examples to establish non-existence of an order. A few relations involving loss ratios are posed as conjectures, and simulation results in support of these are reported. These results lead to a complete picture of dominance and non-dominance relations between pairs of scheduling policies, in terms of loss ratios.
Comment: 8 pages, 10 figures