  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.
