Communications in Statistics Stochastic Models · 1995 · 19 citations · 5 references
EngineeringComputer ScienceMathematicsAlgorithmsProbability TheoryStochastic ProcessesFirst Passage TimesMarkov ProcessesQueueing ProcessesQueueing SystemsQueueing TheoryWaiting Time AnalysisDensityFirst Passage Time DensityFirst-passage ProblemsFirst-passage Time DistributionsProbability Density FunctionsQueueing ModelsState-space StructureWaiting Time Distributions
For a general Markov process on a denumerable state space with any initial state probability vector, the vectors of density functions of the first passage times to each state of a given set and their LS transforms are obtained and their algorithms are discussed. Some numerical examples are presented. These results are useful in studying busy periods and waiting times in queues
5