Consistency Asymptotic Normality Research Articles

Statistical Analysis of Tandem Queues with Blocking

Abtsrcat A maximum likelihood estimator (MLE), a consistent asymp- totically normal (CAN) estimator and asymptotic condence limits for the expected number of entities in the system (LS) in a two service point tandem queue with at most one entity in between the service points and busy service point 1 are obtained. Further, for a three service point tandem queue with busy service points 1 and 2 and at most one entity in between the last two service points, the MLE, CAN estimator and asymptotic confidence limits for LS are obtained.

Statistical Inference for a two station tandem queue with atmost one customer to wait between the stations

A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected number of customers in the system for a sequential two station, single server system with Poisson input and exponential service, where no queue is allowed in front of station 1 and atmost one customer is allowed to wait between the stations and with blocking are obtained.

A study on a two unit parallel system with erlangian repair time

A two unit parallel system where in the failure rate of a unit is a constant and the repair time distribution is a two stage erlangian distribution is considered. Measures of system performance such as reliability, MTBF, system availability and steady state availability are derived. Also, a consistent asymptotically normal (CAN) estimator, a 100(1-α) % asymptotic confidence interval for the steady state availability of the system and the maximum likelihood estimator (MLE) of the system reliability are obtained.

Confidence limits for expected waiting time of two queuing models

A maximum likelihood estimator (MLE), a consistent asymptotically normal (CAN) estimator and asymptotic confidence limits for the expected waiting time per customer in the queues of M |M |1|∞ and M |M |1|N are obtained.

ESTIMATION OF THE MAXIMAL MOMENT EXPONENT OF A GARCH(1,1) SEQUENCE

We propose an estimator for the maximal moment exponent of a GARCH(1,1) sequence. We establish its consistency asymptotic normality with rate n−1/2. Finite sample properties are investigated by means of a small simulation study.The research for this paper was partially supported by NSF grant INT-0223262. István Berkes and Lajos Horváth were supported by the Hungarian National Foundation for Scientific Research, grant T 29621. Piotr Kokoszka and Lajos Horváth were supported by NATO grant PST.CLG.977607.