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Bridges and networks: exact asymptotics. (English) Zbl 1085.60068
Extending the Markov additive methodology developed by the second author [Ann. Appl. Probab. 9, No. 1, 110–145 (1999; Zbl 0937.60091)] and the authors [ibid. 11, No. 3, 569–607 (2001; Zbl 1016.60078)], it is applied, amongst other things, to a modified, stable, two-node Jackson network where the second server helps the first one whenever he is free. For the network referred to, the sharp asymptotics of the steady state distribution of the number of customers queued at each node as the number of customers queued at the first server grows large, are arrived at. The paper also contains some other relevant findings.

MSC:
60K25 Queueing theory (aspects of probability theory)
60K20 Applications of Markov renewal processes (reliability, queueing networks, etc.)
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