Two load sharing processors with failures

We analyze two load-sharing single-server queues in a parallel processing environment. The arrival processes are Poisson and the service processes are Erlang type. Servers are subject to failures with exponentially distributed time to failures and repair times. A failure in one queue transfers all the tasks in that queue to the other queue if its server is not already down. Otherwise, the system is cleared of all the jobs. No new tasks arrive during the rollback recovery procedures. We have developed an approximation method that treats the queues in isolation and yet approximately models the interactions among them. The approximate steady-state probabilities of the number of tasks in each queue are computed using a recursive procedure that utilizes generating functions. We present numerical examples and discuss the accuracy of the approximation.