The Annals of Probability · 1973 · 16 citations · 0 references
EngineeringMathematicsProbability TheoryStochastic ProcessesMarkov ProcessesPoisson ProcessesQueueing ProcessesQueueing TheoryRenewal ProcessesRenewal TheoryRegularity CriteriaWaiting Times
Under a slight regularity condition we prove that if the spent and residual waiting times at $t$ in a renewal process are independent random variables for one value of $t = t_0$, then the process is Poisson.