The M/M/s queue has exponentially distributed interarrival and process times, and s servers. In a wafer fab, this might correspond to a workstation with highly variable arrivals and highly variable process times, with multiple identical tools in the workstation. We should note that processing times in a wafer fab are not usually variable enough to follow an exponential distribution. However, the M/M/s formulas are a good place to start, and can apply in some cases.
Let λ be the arrival rate, μ the service rate, and ρ = λ/(s μ) the traffic intensity (server loading). For either first-in-first-out (FIFO), or last-in-first-out (LIFO) dispatch rules, the mean of the long-term workstation cycle time distribution is given by
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