This paper introduces an analytical method for approximating the fraction of jobs that miss their deadlines in a real-time system when earliest-deadline-first scheduling policy (EDF) is used. In the system, jobs either all have deadlines until the beginning of service or deadlines until the end of service. In the former case, EDF is known to be optimal and, in the latter case, it is optimal if preemption is allowed. In both cases, the system is modeled by an M/M/1/EDF+M queue, i.e., a single server queue with Poisson arrival, and service times and customer impatience, which are exponentially distributed. The optimality property of EDF is used for the estimation of a key parameter, &gamma;<sub>n</sub>, which is the loss rate when there are n customers in the system. The estimation is possible by finding an upper bound and a lower bound for &gamma;<sub>n</sub> and linearly combining these two bounds. The resulting Markov chains are then easy to solve numerically. Comparing numerical and simulation results, we find that the existing errors are relatively small.
Kargahi, M., & Movaghar, A. (2006). A method for performance analysis of earliest-deadline-first scheduling policy. Journal of Supercomputing, 37(2), 197–222. https://doi.org/10.1007/s11227-006-5944-2