In this paper, we study an N server fork-join queueing network with nearly deterministic arrivals and service times. Specifically, we aim to approximate the length of the largest of the N queues in the network. From a practical point of view, this has interesting applications, such as modeling the delays in a large supply chain. We present a fluid limit and a steady-state result for the maximum queue length , as N\to\infty. These results have remarkable differences. The steady-state result depends on two model parameters, while the fluid limit only depends on one model parameter. In addition, the fluid limit requires a different spatial scaling than the backlog in steady state . In order to prove these results, we use extreme value theory and diffusion approximations for the queue lengths.
In this paper, we study an N server fork-join queue with nearly deterministic arrival and service times. Specifically, we present a fluid limit for the maximum queue length as N\to\infty. This fluid limit depends on the initial number of tasks . In order to prove these results, we develop extreme value theory and diffusion approximations for the queue lengths.
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queueing network
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arrivals
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aim to approximate the length of the largest of the N queues in the network. From a practical point of view, this has interesting applications, such as modeling the delays in a large supply chain. We
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and a steady-state result
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These results have remarkable differences. The steady-state result depends on two model parameters, while the fluid limit only depends on one model parameter. In addition, the fluid limit requires a different spatial scaling than the backlog in steady state
This fluid limit depends on the initial number of tasks
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