A Stochastic Reliability Model of a Server under a Random Workload

Abstract

Traffic to any server is rarely constant over time. In addition, the workload brought by each service request is typically unknown in advance, and each request may bring a different workload to the server. Cha and Lee (2011) proposed a reliability model where each request brings an identical and constant workload. In this paper, we generalize the model to allow for requests to bring an unknown random stress to the server. Jobs arrive to the server via a nonhomogeneous Poisson process. Service times are random and i.i.d. Each job adds a random stress Hj ~ H to the breakdown rate of the server until the job is completed. The survival function of such a server and the efficiency of the server are derived.