Journal of Applied Probability

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

Rudolf Grübel and Hendrik Wegener

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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

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

First available in Project Euclid: 15 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 62M07: Non-Markovian processes: hypothesis testing 62M20: Prediction [See also 60G25]; filtering [See also 60G35, 93E10, 93E11]

Asymptotics Kendall's tau log-concave density log-convex density queue prediction permutation


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.

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