### Some Confidence Regions for Traffic Intensity Vector

#### Abstract

Using the Consistent and Asymptotically Normal (CAN) estimator and its covariance matrix (A), 100(1−α)% confidence region for traffic intensity vector ρ with no assumption of arrival and service time distribution is constructed in this paper. Also Standard Bootstrap (SB), Bayesian Bootstrap(BB) and percentile bootstrap (PB) are applied to develop the confidence regions for traffic intensity vector ρ with confidence level 100(1 − α)%. Simulation study is undertaken to evaluate the performances of the confidence regions in terms of their coverage area percentage, average area and relative coverage area. Calibration technique is used to improve the coverage area percentages of confidence regions.

#### Keywords

#### References

Anderson T.W., An Introduction to Multivariate Statistical Analysis, Second edition, Wiley series in probability and mathematical statistics, New York, 1984.

Beran R., Prepivoting to reduce level error of confidence sets, Biometrika,Vol.74, pp. 457-468, 1987.

Banik, S. and Kibria, B. M. G., Estimating the Population Standard Deviation with Confidence Interval: A Simulation Study under Skewed and Symmetric Conditions, International Journal of Statistics in Medical Research. Vol. 3(4), pp. 356-367,2014.

Disney R. L., Random flow in queueing networks: a review and a critique. Trans. A.I.E.E., Vol.7, pp. 268-288, 1975.

Efron B. and Tibshirani R.J., Bootstrap Method for standard errors, confidence intervals and other measures of statistical accuracy, Statistical Science, Vol. 1, pp. 54-77, 1986.

Efron B. and Tibshirani R.J., An Introduction to the bootstrap, Chapman and Hall, New York ,1993.

V.K. and Pathare S.B., Comparison of different confidence intervals of intensities for an open queueing network with feedback, Am J Oper Res, Vol.3 No.2, pp. 307?27, 2013.

Gedam V.K. and Pathare S.B., Calibrated confidence intervals for intensities of a two stage open queueing network with feedback,J Stat Math, Vol. 4, No.1 , pp.151?61, 2013.

Gedam V.K. and Pathare S.B., Calibrated confidence intervals for intensities of a two stage open queueing network, J Stat. Appl.Pro., Vol. 3, No.1, pp.33?4, 2014.

Gedam V.K. and Pathare S.B., Estimation approaches of mean response time for a two stage open queueing network model, Stat Optim Inform Comput, Vol.3, No.3, pp.249-258, 2015.

Gedam V.K. and Pathare S.B., Use of the calibration approach in confidence intervals for mean response times of an open queueing network with feedback, SIMULATION: Transactions of The Society for Modeling and Simulation International , Vol. 91, No 6 , pp.553-565, 2015.

Hall P. and Martin M.A., On bootstrap resampling and iteration, Biometrika Vol. 75, pp. 661-671, 1988.

Hall P. , On the bootstrap and confidence intervals, Ann Stat. Vol. 14, pp. 1431-1452, 1986.

Jackson J.R., Jobshop-Like Queueing Systems, Management Science, Vol. 10, pp. 131-142, 1963.

Kale B.K., A First Course on Parametric Inference, Narosa Publishing House, London, 1999.

Ke J. C. and Chu Y. K., Comparison on five estimation approaches of intensity for a queueing system with short run, Computational Statistics, Vol. 24 No. 4, pp. 567-582, 2009, Springer-Verlag.

Kibria, B. M. G. and Banik, S., Parametric and Nonparametri Confidence Intervals for Estimating the Difference of Means of Two Skewed Populations, Journal of Applied Statistics. Vol. 40, No. 12, pp. 2617-2636, 2013.

Kleinrock L., Queueing Systems, Computer Applications,Vol. 2 , 1976, John Wiley & Sons, New York.

Loh W.Y., Calibrating confidence coefficient, J Am Stat Assoc, Vol. 82, pp. 155-162, 1987.

Loh W.Y., Bootstrap calibration for confidence interval construction and selection, Stat sinica, Vol.1, pp. 477-491, 1991.

Pathare S.B. and Gedam V.K., Some estimation approaches of intensities for a two stage open queueing network, Stat Optim Inform Comput, Vol. 2, No.1, pp.33?6, 2014.

Rubin D.B., The Bayesian bootstrap, The Annals of Statistics,Vol.9, pp. 130-134, 1981.

Thiruvaiyaru D., Basawa I.V. and Bhat U.N., Estimation for a class of simple queueing network, Queueing Systems Vol. 9, pp.301-312, 1991.

DOI: 10.19139/soic.v7i2.356

### Refbacks

- There are currently no refbacks.