On EDF scheduler with the exponential deadlines

This work deals with the performance evaluation of EDF (Earliest Deadline First) packet scheduler with two classes. The primary metric of interest is the mean sojourn time for each class. The system is composed of two classes (two queues) with Poisson input to each of them, deterministic service times and exponentially distributed deadline values. The model is analysed as an embedded Markov chain at the instants of packet departures from the service. The solution i.e. the joint probability distribution of the number of packets in each queue is obtained using the matrix approach. The metrics such as the mean sojourn time or the mean number of packets in the system for each class are directly obtained from this joint probability distribution.