Evaluating Dynamic Failure Probability for Streams with (m, k)-Firm Deadlines

A real-time stream is said to have (m, k)-firm deadlines if at least m out of any k consecutive customers from the stream must meet their respective deadlines. Such a stream is said to have encountered a dynamic failure if fewer than m out of any k consecutive customers meet their deadlines. Hamdaoui and Ramanathan recently proposed a scheduling policy called Distance Based Priority (DBP) in which customers are serviced with a higher priority if their streams are closer to a dynamic failure. In terms of reducing the probability of dynamic failure, Hamdaoui and Ramanathan also showed, using simulation, that the DBP policy is better than a policy in which all customers are serviced at the same priority level. In this paper, an analytic model is developed for computing the probability of dynamic failure of a real-time stream for the DBP and the single priority schemes. This model is useful for providing statistical quality of service guarantees to real-time streams. The probability of dynamic failure computed using this model is compared to the results from a discrete-event simulator. The comparison shows that the model is accurate for low and moderate loads.