Bivariate Distributions of Maximum Remaining Service Times in Fork-Join Infinite-Server Queues

We study the maximum remaining service time in M (2) ∣ G 2 ∣∞ 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-indepe...

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Bibliographic Details
Published in:Problems of information transmission 2020, Vol.56 (1), p.73-90
Main Authors: Gorbunova, A. V., Lebedev, A. V.
Format: Article
Language:English
Subjects:
Bivariate analysis
Communication Network Theory
Communications Engineering
Control
Electrical Engineering
Engineering
Information Storage and Retrieval
Markov analysis
Networks
Queues
Queuing theory
Stochastic processes
Subsystems
Systems Theory
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Summary:We study the maximum remaining service time in M (2) ∣ G 2 ∣∞ 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.
ISSN:0032-9460
1608-3253
DOI:10.1134/S003294602001007X