Srinivas, V.; Jayakrishna Udupa, H. Best unbiased estimation and CAN property in the stable M/M/1 queue. (English) Zbl 06599052 Commun. Stat., Theory Methods 43, No. 2, 321-327 (2014). Summary: The Uniform Minimum Variance Unbiased (UMVU) estimators of \(\rho^\ell\), the probability of having \(\ell\) or more customers, \(L\), the expected system size, \(L_q\), the expected number of customers in the queue, and \(L'_q\), the expected number of customers in a non empty queue, are derived based on a random sample of fixed size \(n\) on system size at departure points from the geometric distribution on the support \(\{0, 1, 2,\ldots\}\) with mean \(\frac{\rho}{1-\rho}\), which is the distribution of system size in M/M/1 queueing system in equilibrium. The derivations are based on application of Lehmann-Scheffe theorem. Also, CAN estimators of performance measures are derived. In addition the probability distribution of UMVU estimators are obtained. Cited in 4 Documents MSC: 62-XX Statistics Keywords:consistent asymptotic normality; M/M/1 queueing system; uniform minimum variance unbiased estimator PDFBibTeX XMLCite \textit{V. Srinivas} and \textit{H. Jayakrishna Udupa}, Commun. Stat., Theory Methods 43, No. 2, 321--327 (2014; Zbl 06599052) Full Text: DOI References: [1] Armero C., Multivariate, Design and Sampling pp 579– (1999) [2] DOI: 10.1002/(SICI)1099-0747(199803)14:1<35::AID-ASM305>3.0.CO;2-O · Zbl 0915.60080 · doi:10.1002/(SICI)1099-0747(199803)14:1<35::AID-ASM305>3.0.CO;2-O [3] DOI: 10.1023/A:1019121506451 · Zbl 0942.90018 · doi:10.1023/A:1019121506451 [4] Ausin , M. C. , Wiper , M. P. , Lillo , R. E. ( 2008 ). Transient Bayesian inference for short and long-tailed GI/G/1 queueing systems. Statistics and Econometrics Series 05, Universidad Carlos III De Madrid. Working article 05-35 . [5] DOI: 10.1007/BF01149536 · Zbl 0668.60084 · doi:10.1007/BF01149536 [6] Bhat U. N., Frontiers in Queueing-Models and Applications in Science and Engineering (1997) [7] DOI: 10.2307/3315981 · Zbl 0986.62016 · doi:10.2307/3315981 [8] DOI: 10.1007/s00184-007-0138-3 · Zbl 1433.90045 · doi:10.1007/s00184-007-0138-3 [9] Gross D., Fundamentals of Queueing Theory., 2. ed. (1985) · Zbl 0658.60122 [10] DOI: 10.1111/1475-3995.t01-1-00329 · Zbl 1004.90020 · doi:10.1111/1475-3995.t01-1-00329 [11] Jayakrishna Udupa H., J. Sci. 8 (2) pp 20– (2009) [12] Kale B. K., A First Course in Parametric Inference., 2. ed. (2005) · Zbl 1044.62500 [13] DOI: 10.1002/nav.20342 · Zbl 1163.90405 · doi:10.1002/nav.20342 [14] Mukherjee S. P., IAPQR transactions 30 (2) pp 89– (2005) [15] Patel J., Handbook of Statistical Distributions (1976) · Zbl 0367.62014 [16] DOI: 10.1080/03610910701753861 · Zbl 1160.62025 · doi:10.1080/03610910701753861 [17] Ramirez , P. , Lillo , R. E. , Wiper , M. P. ( 2008a ). Inference for double Pareto lognormal queues with applications. Statistics and Econometrics Series 02, Universidad Carlos III De Madrid. Working article 08-04 . [18] DOI: 10.1023/A:1019173206509 · Zbl 0917.90137 · doi:10.1023/A:1019173206509 [19] Sharma K. K., Opsearch 36 (1) pp 26– (1999) [20] DOI: 10.1080/03610926.2010.498653 · Zbl 1225.62119 · doi:10.1080/03610926.2010.498653 [21] DOI: 10.1016/S0167-6377(00)00030-4 · Zbl 0973.90024 · doi:10.1016/S0167-6377(00)00030-4 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.