Nonparametric estimation of the service time distribution in the M/G/∞ queue
The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and a...
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| Published in | Advances in applied probability Vol. 48; no. 4; pp. 1117 - 1138 |
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| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Cambridge, UK
Cambridge University Press
01.12.2016
Applied Probability Trust |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0001-8678 1475-6064 |
| DOI | 10.1017/apr.2016.67 |
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| Abstract | The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well. |
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| AbstractList | The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well. The subject of this paper is the problem of estimating the service time distribution of the M/G/∞ queue from incomplete data on the queue. The goal is to estimate G from observations of the queue-length process at the points of the regular grid on a fixed time interval. We propose an estimator and analyze its accuracy over a family of target service time distributions. An upper bound on the maximal risk is derived. The problem of estimating the arrival rate is considered as well. |
| Author | Goldenshluger, Alexander |
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| CitedBy_id | crossref_primary_10_1016_j_cam_2021_113693 crossref_primary_10_1016_j_spa_2020_01_011 crossref_primary_10_1016_j_ejor_2019_06_055 crossref_primary_10_1287_opre_2022_0091 crossref_primary_10_1007_s11134_024_09921_2 crossref_primary_10_1007_s11134_021_09688_w crossref_primary_10_1016_j_csda_2021_107405 crossref_primary_10_1287_stsy_2018_0026 crossref_primary_10_1093_imaman_dpaf002 crossref_primary_10_1016_j_spl_2024_110250 crossref_primary_10_1214_23_AOS2290 crossref_primary_10_1016_j_eswa_2024_124076 crossref_primary_10_3150_17_BEJ936 crossref_primary_10_1214_23_AAP1990 |
| Cites_doi | 10.3150/07-BEJ5184 10.1214/aoms/1177697107 10.1017/S0021900200013784 10.1016/j.spa.2014.09.003 10.1007/b13794 10.1007/978-1-4419-0320-4 10.1023/A:1003214209227 10.1017/S0021900200029089 10.1017/S0001867800039434 10.1017/S0021900200007671 10.1214/aop/1176996550 10.1111/j.1467-9868.2004.B5725.x 10.1002/j.1538-7305.1957.tb01497.x 10.1007/BF00534916 10.1023/A:1003831118254 10.1007/BF01040651 10.1007/978-3-642-80838-8_15 10.2307/1426082 10.1093/biomet/84.2.295 |
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| Keywords | Primary 62G05 Secondary 60K25 stationary process nonparametric estimation minimax risk 62M09 M/G/∞ queue covariance function rates of convergence |
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| References | S0001867816000677_ref1 Lindley (S0001867816000677_ref15) 1956 Goldenshluger (S0001867816000677_ref10) 1997; 6 Nemirovski (S0001867816000677_ref18) 2000; 1738 S0001867816000677_ref24 S0001867816000677_ref25 S0001867816000677_ref26 S0001867816000677_ref20 S0001867816000677_ref23 Kingman (S0001867816000677_ref14) 1993 Parzen (S0001867816000677_ref19) 1962 S0001867816000677_ref13 S0001867816000677_ref16 S0001867816000677_ref11 S0001867816000677_ref12 S0001867816000677_ref9 Reynolds (S0001867816000677_ref21) 1975; 7 S0001867816000677_ref8 S0001867816000677_ref7 S0001867816000677_ref6 S0001867816000677_ref5 S0001867816000677_ref17 S0001867816000677_ref4 Ross (S0001867816000677_ref22) 1970 S0001867816000677_ref3 S0001867816000677_ref2 |
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| SubjectTerms | Estimation Markov analysis Nonparametric statistics Probability Queues Queuing theory Upper bounds |
| Title | Nonparametric estimation of the service time distribution in the M/G/∞ queue |
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