Parametric and Nonparametric Estimation of the Mean Number of Customers in Service for an M/G/Infinity Queue.
NAVAL POSTGRADUATE SCHOOL MONTEREY CA
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This thesis studies the estimation from interarrival and service time data of the mean number of customers in service at time t for an MG infinity queue. Two situations are considered. In one the parametric form of the service time distribution is known. In the special case in which the service time distribution is exponential the approximate bias and variance of the estimate are derived and simulation is used to study an approximate normal confidence interval procedure. Simulation is also used to illustrate that assuming a wrong parametric model can lead to misleading results. In the other situation, the parametric form of the service time distribution is unknown and the empirical distribution of the service times is used in the estimate of the mean number of customers in service. In the case in which the customer arrival rate is known the distribution of the estimate is derived and an approximate normal confidence interval procedure is suggested. The use of the bootstrap and jackknife procedure to estimate variability and construct confidence intervals for the estimate is also studied both analytically and by simulation. Keywords Nonparametric estimation Statistical inference. Author
- Statistics and Probability