M/G/1 Queue
The M/G/1 queue has exponentially
distributed interarrival times, general process times, and
a single server. The inclusion of general process times
makes this formula more relevant for wafer fabs, where
processing times are typically not as variable as the
exponential distribution used with M/M/1 queues. The
dispatch rule is FIFO for the equations that follow. Let l
be the arrival rate, m the
service rate, and r = l/m
be the traffic intensity (server
loading). From Equation 6.25 of Prabhu, the mean of the long-term cycle time distribution is
given by
l E[S02] (2 (1-r)
)-1 + m-1,
or, if we substitute in the
variance plus the squared mean for the second moment of
the service time distribution,
l (
Var[S0] + m-2)
(2(1-r))-1 + m-1.
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