Nonparametric Estimation of the Probability of a Long Delay in the M/G/1 Queue
Copyright policy )Nonparametric Estimation of the Probability of a Long Delay in the M/G/1 Queue
SUMMARY A Poisson stream of customers with known arrival rate λ approaches a single server having independent identically distributed service times with unknown distribution. A nonparametric estimator of the probability of a long customer delay is obtained from an asymptotic renewal theoretic result giving an exponential approximation to the tail of the virtual waiting time distribution for a stable M/G/1 queue. Asymptotic properties of the estimator are obtained. Results of a simulation study of the small sample size behaviour are given.
- Naval Postgraduate School United States
domain of attraction of a stable law, Markov processes: estimation; hidden Markov models, central limit theorem, M/G/1 Queue, terminating renewal process, Queueing theory (aspects of probability theory), jackknife, independent identically distributed service times with unknown distribution, tail of the virtual waiting time distribution, asymptotic exponential tail, single server, virtual waiting time distribution, stable M/G/1 queue, known arrival rate, Poisson stream of customers, Nonparametric estimation, exponential approximation
domain of attraction of a stable law, Markov processes: estimation; hidden Markov models, central limit theorem, M/G/1 Queue, terminating renewal process, Queueing theory (aspects of probability theory), jackknife, independent identically distributed service times with unknown distribution, tail of the virtual waiting time distribution, asymptotic exponential tail, single server, virtual waiting time distribution, stable M/G/1 queue, known arrival rate, Poisson stream of customers, Nonparametric estimation, exponential approximation
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