Zhan Qiu, Peter G. Harrison
As systems scale up, their mean-time-to-failure reduces drastically. We consider parallel servers subject to permanent failures but such that only one needs to survive in order to execute a given task. This kind of failure-model is appropriate in at least two types of systems: systems in which repair cannot take place (e.g. spacecraft) and systems that have strict deadlines (e.g. navigation systems). We use multiple replicas to perform the same task in order to improve the reliability of systems. The server in the system is subject to failure while it is on and the time to failure is memoryless, i.e. exponentially distributed. We derive expressions for the Laplace transform of the sojourn time distribution of a tagged task, jointly with the probability that the tagged task completes service, for a network of one or more parallel servers with exponential service times and times to failure.
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