Advances in Applied Probability

Response times in M/M/s fork-join networks

Sung-Seok Ko and Richard F. Serfozo

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We study a fork-join processing network in which jobs arrive according to a Poisson process and each job splits into m tasks, which are simultaneously assigned to m nodes that operate like M/M/s queueing systems. When all of its tasks are finished, the job is completed. The main result is a closed-form formula for approximating the distribution of the network's response time (the time to complete a job) in equilibrium. We also present an analogous approximation for the distribution of the equilibrium queue length (the number of jobs in the system), when each node has one server. Kolmogorov-Smirnov statistical tests show that these formulae are good fits for the distributions obtained from simulations.

Article information

Adv. in Appl. Probab. Volume 36, Number 3 (2004), 854-871.

First available in Project Euclid: 31 August 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.) [See also 90Bxx]
Secondary: 60K25: Queueing theory [See also 68M20, 90B22]

Fork-join network queueing communications network assembly network parallel processing synchronization supply chain little law for distributions


Ko, Sung-Seok; Serfozo, Richard F. Response times in M/M/ s fork-join networks. Adv. in Appl. Probab. 36 (2004), no. 3, 854--871. doi:10.1239/aap/1093962238.

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