caa a22 4500 386350469 CHVBK 20180307111827.0 cr unu---uuuuu 161130e198910 xx s 000 0 eng 10.1017/S0269964800001376 doi S0269964800001376 pii (NATIONALLICENCE)cambridge-10.1017/S0269964800001376 Flatto Leopold AT&T Bell Laboratories Murray Hill, New Jersey 07974 The Longer Queue Model [Elektronische Daten] [Leopold Flatto] Two queues forming two independent Poisson processes are served by one server with exponential service time. The server always works on the longer queue and, in case that they are of equal length, chooses either one with probability ½. Let πij be the probability that the two queue lengths equal i andj at equilibrium and π(z, w) = ∑πi j Ziwj. We determine π(z, w) and derive from this asymptotic formulas forπij as i, j → ∞. These asymptotic formulas are used to study the interdependence of the queue lengths. In particular, we obtain limit laws for the queue lengths conditioned on each other. Copyright © Cambridge University Press 1989 Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 537-559 0269-9648 3:4<537 1989 3 PES https://doi.org/10.1017/S0269964800001376 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1017/S0269964800001376 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Flatto Leopold AT&T Bell Laboratories Murray Hill, New Jersey 07974 NATIONALLICENCE 773 0- Probability in the Engineering and Informational Sciences Cambridge University Press 3/4(1989-10), 537-559 0269-9648 3:4<537 1989 3 PES CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge