Details
| Original language | English |
|---|---|
| Pages (from-to) | 131-144 |
| Number of pages | 14 |
| Journal | Journal of applied probability |
| Volume | 48 |
| Issue number | 1 |
| Publication status | Published - Mar 2011 |
Abstract
Customers arrive sequentially at times x1 < x2 <... < xn and stay for independent random times Z1,. . ., Zn > 0. The Z-variables all have the same distribution Q. We are interested in situations where the data are incomplete in the sense that only the order statistics associated with the departure times xi +Zi are known, or that the only available information is the order in which the customers arrive and depart. In the former case we explore possibilities for the reconstruction of the correct matching of arrival and departure times. In the latter case we propose a test for exponentiality.
Keywords
- Asymptotics, Kendall's τ, Log-concave density, Log-convex density, Permutation, Prediction, Queue
ASJC Scopus subject areas
- Mathematics(all)
- Statistics and Probability
- Mathematics(all)
- General Mathematics
- Decision Sciences(all)
- Statistics, Probability and Uncertainty
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In: Journal of applied probability, Vol. 48, No. 1, 03.2011, p. 131-144.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Matchmaking and testing for exponentiality in the M/G/ ∞ queue
AU - Grübel, Rudolf
AU - Wegener, Hendrik
PY - 2011/3
Y1 - 2011/3
N2 - Customers arrive sequentially at times x1 < x2 <... < xn and stay for independent random times Z1,. . ., Zn > 0. The Z-variables all have the same distribution Q. We are interested in situations where the data are incomplete in the sense that only the order statistics associated with the departure times xi +Zi are known, or that the only available information is the order in which the customers arrive and depart. In the former case we explore possibilities for the reconstruction of the correct matching of arrival and departure times. In the latter case we propose a test for exponentiality.
AB - Customers arrive sequentially at times x1 < x2 <... < xn and stay for independent random times Z1,. . ., Zn > 0. The Z-variables all have the same distribution Q. We are interested in situations where the data are incomplete in the sense that only the order statistics associated with the departure times xi +Zi are known, or that the only available information is the order in which the customers arrive and depart. In the former case we explore possibilities for the reconstruction of the correct matching of arrival and departure times. In the latter case we propose a test for exponentiality.
KW - Asymptotics
KW - Kendall's τ
KW - Log-concave density
KW - Log-convex density
KW - Permutation
KW - Prediction
KW - Queue
UR - http://www.scopus.com/inward/record.url?scp=80054765333&partnerID=8YFLogxK
U2 - 10.1239/jap/1300198140
DO - 10.1239/jap/1300198140
M3 - Article
AN - SCOPUS:80054765333
VL - 48
SP - 131
EP - 144
JO - Journal of applied probability
JF - Journal of applied probability
SN - 0021-9002
IS - 1
ER -