Negative Customers Model Queues with Breakdowns
Negative customers in queueing networks are used to model breakdowns at a server which cause some customers to be lost. We consider an unreliable M/M/l queue with both instantaneous and exponential repairs, and derive expressions for the Laplace transform of the sojourn time density. We apply the model to approximate the performance of a bank of parallel, unreliable servers by modifying the arrival process to a Markov Modulated Poisson Process and considering an approximate decomposition of the underlying Markov chain under the assumption that arrivals and service occur much faster than breakdowns and repairs. Validation is by simulation.
KeywordsArrival Rate Queue Length Sojourn Time Batch Size Breakdown Rate
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