## Journal of Applied Probability

### Matchmaking and testing for exponentiality in the M/G/∞ queue

#### 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.

#### Article information

Source
J. Appl. Probab., Volume 48, Number 1 (2011), 131-144.

Dates
First available in Project Euclid: 15 March 2011

https://projecteuclid.org/euclid.jap/1300198140

Digital Object Identifier
doi:10.1239/jap/1300198140

Mathematical Reviews number (MathSciNet)
MR2809891

Zentralblatt MATH identifier
1217.60081

#### Citation

Grübel, Rudolf; Wegener, Hendrik. Matchmaking and testing for exponentiality in the M/G/∞ queue. J. Appl. Probab. 48 (2011), no. 1, 131--144. doi:10.1239/jap/1300198140. https://projecteuclid.org/euclid.jap/1300198140

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