Closed-Form Solutions of Performability

If computing system performance is degradable, then as recognized in a number of recent studies, system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's "performability," which relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. In this paper we examine the feasibility of closed-form solutions of performability when Y is continuous. In particular, we consider the modeling of a degradable buffer/multiprocessor system whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, we show that a closed-form solution can indeed be obtained.