Two load sharing processors with failures

Scope and Purpose3-Distributed processing (or transaction processing) is quite common in large corporations, such as international banks, communication companies and airlines. There exist numerous nodes (displayed globally), each equipped with multiple processes and possibly with processors. Each process is a software capable of performing many tasks ranging from personal banking transactions to look-ups to large data bases. These processes fail randomly, and the interrupted tasks and the tasks waiting to be processed in their queues are transferred to other processes in the same node or in other nodes. Performance of the entire system heavily depends on the performance of the individual processes. This paper deals with one such process and introduces an algorithm to analyze its performance. 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 umerical examples and discuss the accuracy of the approximation.