Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues

References

[1] I. Adan and J. Resing, Queueing Theory, Eindhoven University of Technology, Eindhoven, 2002. Suche in Google Scholar

[2] S. R. Asmussen, Applied Probability and Queues, 2nd ed., Appl. Math. (New York) 51, Springer, New York, 2003. Suche in Google Scholar

[3] U. N. Bhat, A statistical technique for the control of traffic intensity in Markovian queue, Ann. Oper. Res. 8 (1987), 151–164. 10.1007/BF02187088Suche in Google Scholar

[4] U. N. Bhat and S. Subba Rao, A statistical technique for the control of traffic intensity in the queuing systems M/G/1 and G⁢I/M/1, Oper. Res. 20 (1972), 955–966. 10.1287/opre.20.5.955Suche in Google Scholar

[5] D. Brook and D. A. Evans, An approach to the probability distribution of cusum run length, Biometrika 59 (1972), 539–549. 10.1093/biomet/59.3.539Suche in Google Scholar

[6] N. Chen, Y. Yuan and S. Zhou, Performance analysis of queue length monitoring of M/G/1 systems, Naval Res. Logist. 58 (2011), no. 8, 782–794. 10.1002/nav.20483Suche in Google Scholar

[7] N. Chen and S. Zhou, CUSUM statistical monitoring of M/M/1 queues and extensions, Technometrics 57 (2015), no. 2, 245–256. 10.1080/00401706.2014.923787Suche in Google Scholar

[8] A. K. Erlang, Sandsynlighedsregning og telefonsamtaler (The theory of probabilities and telephone conversations), Nyt Tidsskrift Mat. B (Copenhagen) 20 (1909), 33–39. Suche in Google Scholar

[9] A. K. Erlang, Løsning af nogle problemer fra sandsynlighedsregningen af betydning for de automatiske telefoncentraler (Solution of some problems in the theory of probabilities of significance in automatic telephone exchanges), Elektrotkeknikeren (Copenhagen) 13 (1917), 5–13. Suche in Google Scholar

[10] A. K. Erlang, Telefon-ventetider. Et stykke sandsynlighedsregning (The application of the theory of probability in telephone administration), Mat. Tidsskrift B (Copenhagen) 31 (1920), 25–42. Suche in Google Scholar

[11] W. Feller, An Introduction to Probability Theory And its Applications. Vol. II, 2nd ed., John Wiley & Sons, New York, 1971. Suche in Google Scholar

[12] I. Greenberg, Markov chain approximation methods in a class of level-crossing problems, Oper. Res. Lett. 21 (1997), no. 3, 153–158. 10.1016/S0167-6377(97)00033-3Suche in Google Scholar

[13] D. Gross and C. M. Harris, Fundamentals of Queueing Theory, 2nd ed., John Wiley & Sons, New York, 1985. Suche in Google Scholar

[14] Y.-C. Hung, G. Michailidis and S.-C. Chuang, Estimation and monitoring of traffic intensities with application to control of stochastic systems, Appl. Stoch. Models Bus. Ind. 30 (2014), no. 2, 200–217. 10.1002/asmb.1961Suche in Google Scholar

[15] S. Jain, Estimating changes in traffic intensity for M/M/1 queueing systems, Microelec. Reliab. 35 (1995), 1395–1400. 10.1016/0026-2714(95)00047-6Suche in Google Scholar

[16] S. Jain, An autoregressive process and its application to queueing model, Metron Int. J. Stat. 58 (2000), 131–138. Suche in Google Scholar

[17] S. Jain and J. G. C. Templeton, Problem of statistical inference to control the traffic intensity, Sequential Anal. 8 (1989), no. 2, 135–146. 10.1080/07474948908836173Suche in Google Scholar

[18] D. G. Kendall, Some problems in the theory of queues, J. Roy. Statist. Soc. Ser. B. 13 (1951), 151–173. 10.1111/j.2517-6161.1951.tb00080.xSuche in Google Scholar

[19] D. G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, Ann. Math. Statistics 24 (1953), 338–354. 10.1214/aoms/1177728975Suche in Google Scholar

[20] S.-H. Kim, C. Alexopoulos, K.-L. Tsui and J. R. Wilson, A distribution-free tabular CUSUM chart for autocorrelated data, IIE Trans. 39 (2007), 317–330. 10.1080/07408170600743946Suche in Google Scholar

[21] L. Kleinrock, Queueing Systems. Volume I: Theory, John Wiley & Sons, New York, 1975. Suche in Google Scholar

[22] V. G. Kulkarni, Introduction to Modeling and Analysis of Stochastic Systems, 2nd ed., Springer Texts Statist., Springer, New York, 2011. 10.1007/978-1-4419-1772-0Suche in Google Scholar

[23] D. V. Lindley, The theory of queues with a single server, Proc. Cambridge Philos. Soc. 48 (1952), 277–289. 10.1017/S0305004100027638Suche in Google Scholar

[24] M. C. Morais, Stochastic ordering in the performance analysis of quality control schemes, Ph.D. thesis, Universidade Técnica de Lisboa, 2002. Suche in Google Scholar

[25] M. C. Morais and S. Knoth, On ARL-unbiased charts to monitor the traffic intensity of a single server queue, Proceedings of the 12th. International Workshop on Intelligent Statistical Quality Control, Helmut Schmidt Universität, Hamburg (2016), 217–242. 10.1007/978-3-319-75295-2_5Suche in Google Scholar

[26] M. C. Morais and A. Pacheco, On stochastic ordering and control charts for traffic intensity, Sequential Anal. 35 (2016), no. 4, 536–559. 10.1080/07474946.2016.1238266Suche in Google Scholar

[27] S. Nadarajah and S. Kotz, On the linear combination of exponential and gamma random variables, Entropy 7 (2005), no. 2, 161–171. 10.3390/e7020161Suche in Google Scholar

[28] C. Palm, Intensitätsschwankungen im Fernsprechverkehr, Ericsson Technics 44 (1943), 1–189. Suche in Google Scholar

[29] J. J. J. Pignatiello, C. A. Acosta-Mejía and B. V. Rao, The performance of control charts for monitoring process dispersion, 4th Industrial Engineering Research Conference Proceedings, Institute of Industrial Engineers, Peachtree Corners (1995), 320–328. Suche in Google Scholar

[30] S. M. Ross, Introduction to Probability Models, 9th ed., Elsevier, Amsterdam, 2006. Suche in Google Scholar

[31] M. D. M. Santos, On control charts and the detection of increases in the traffic intensity of queueing systems, Master’s thesis, University of Lisbon, 2016. Suche in Google Scholar

[32] H. Shore, General control charts for attributes, IIE Trans. 32 (2000), 1149–1160. 10.1080/07408170008967469Suche in Google Scholar

[33] H. Shore, Control charts for the queue length in a G/G/s system, IIE Transactions 38 (2006), 1117–1130. 10.1080/07408170600737336Suche in Google Scholar

[34] S. Subba Rao, U. N. Bhat and K. Harishchandra, Control of traffic intensity in a queue—a method based on SPRT, Opsearch 21 (1984), no. 2, 63–80. Suche in Google Scholar

[35] M. C. Testik, J. K. Cochran and G. C. Runger, Adaptive server staffing in the presence of time-varying arrivals: A feed-forward control approach, J. Oper. Res. Soc. 55 (2004), 233–239. 10.1057/palgrave.jors.2601677Suche in Google Scholar

[36] M. Zobu and V. Sağlam, Control of traffic intensity in hyperexponential and mixed Erlang queueing systems with a method based on SPRT, Math. Probl. Eng. 2013 (2013), Article ID 241241. 10.1155/2013/241241Suche in Google Scholar