caa a22 4500 445839716 CHVBK 20180317145340.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s00186-010-0337-y doi (NATIONALLICENCE)springer-10.1007/s00186-010-0337-y The age of the arrival process in the G/M/1 and M/G/1 queues [Elektronische Daten] [Moshe Haviv, Yoav Kerner] This paper shows that in the G/M/1 queueing model, conditioning on a busy server, the age of the inter-arrival time and the number of customers in the queue are independent. The same is the case when the age is replaced by the residual inter-arrival time or by its total value. Explicit expressions for the conditional density functions, as well as some stochastic orders, in all three cases are given. Moreover, we show that this independence property, which we prove by elementary arguments, also leads to an alternative proof for the fact that given a busy server, the number of customers in the queue follows a geometric distribution. We conclude with a derivation for the Laplace Stieltjes Transform (LST) of the age of the inter-arrival time in the M/G/1 queue. Springer-Verlag, 2010 G/M/1 queue nationallicence M/G/1 queue nationallicence Age of inter arrival time nationallicence Haviv Moshe Department of Statistics, The Hebrew University of Jerusalem, 91905, Jerusalem, Israel aut Kerner Yoav Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel aut Mathematical Methods of Operations Research Springer-Verlag 73/1(2011-02-01), 139-152 1432-2994 73:1<139 2011 73 186 https://doi.org/10.1007/s00186-010-0337-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00186-010-0337-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Haviv Moshe Department of Statistics, The Hebrew University of Jerusalem, 91905, Jerusalem, Israel aut NATIONALLICENCE 700 1- Kerner Yoav Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, Beer Sheva, Israel aut NATIONALLICENCE 773 0- Mathematical Methods of Operations Research Springer-Verlag 73/1(2011-02-01), 139-152 1432-2994 73:1<139 2011 73 186 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer