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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,… Click to show full abstract
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.
Journal Title: Problems of Information Transmission
Year Published: 2020
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