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Bivariate distributions of maximum remaining service times in fork-join infinite-server queues. (English. Russian original) Zbl 1447.60135
Probl. Inf. Transm. 56, No. 1, 73-90 (2020); translation from Probl. Peredachi Inf. 56, No. 1, 80-98 (2020).
Summary: We study the maximum remaining service time in $$M^{(2)} \vert G_2 \vert \infty$$ fork-join queueing systems where an incoming task forks on arrival for service into two subtasks, each of them being served in one of two infinite-sever subsystems. The following cases for the arrival rate are considered: (1) time-independent, (2) given by a function of time, (3) given by a stochastic process. As examples of service time distributions, we consider exponential, hyperexponential, Pareto, and uniform distributions. In a number of cases we find copula functions and the Blomqvist coefficient. We prove asymptotic independence of maximum remaining service times under high load conditions.
##### MSC:
 60K25 Queueing theory (aspects of probability theory) 68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
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