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Deducing Queueing from Transactional Data: The Queue Inference Engine, Revisited
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0
References
1992
Year
EngineeringTransactional SystemTransaction ProcessingTransient Queue LengthsDiscrete-event SimulationQueueing TheoryQueue Inference EngineOperations ResearchData ScienceData ManagementStatisticsQuantitative ManagementStochastic SystemProbability TheoryComputer ScienceQueueing SystemsQueue LengthsTransactional ApplicationPerformance ModelingBusinessR. LarsonQueuing TheoryFluid QueueData Modeling
R. Larson proposed a method to statistically infer the expected transient queue length during a busy period in O(n 5 ) solely from the n starting and stopping times of each customer's service during the busy period and assuming the arrival distribution is Poisson. We develop a new O(n 3 ) algorithm which uses these data to deduce transient queue lengths as well as the waiting times of each customer in the busy period. We also develop an O(n) on-line algorithm to dynamically update the current estimates for queue lengths after each departure. Moreover, we generalize our algorithms for the case of a time-varying Poisson process and also for the case of i.i.d. interarrival times with an arbitrary distribution. We report computational results that exhibit the speed and accuracy of our algorithms.