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 λ be the arrival rate, μ the service rate, and ρ = λ/μ be the traffic intensity (server loading). From Equation 6.25 of Prabhu, the mean of the long-term cycle time distribution is given by

  • λ E[S02] (2 (1-ρ) )-1 + μ-1,
  • or, if we substitute in the variance plus the squared mean for the second moment of the service time distribution,
  • λ ( Var[S0] + μ-2) (2(1-ρ))-1 + μ-1.