Stationary Distribution
In general the stationary distribution of the number of jobs at each queue is intractable. Flatto considered the case of two servers (N=2) and derived the stationary distribution for the number of jobs at each queue via uniformization techniques. Pinotsi and Zazanis show that a product form solution exists when arrivals are deterministic as the queue lengths are then independent D/M/1 queues.
Read more about this topic: Fork-join Queue
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