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Completing a Task with Interruptions

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Completing a Task with Interruptions
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12
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CC Attribution - NonCommercial - NoDerivatives 4.0 International:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
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Assume that the time to complete a task without interruption is T. Assume interruptions occur according to a Poisson process with rate lambda. If a process is interrupted, it must begin again. Let W be the total time to completion. We find the Laplace transform of W. One application is a solution of the classic problem of the time to cross a one way street assuming Poisson traffic.