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Gain an in-depth understanding of the issues that cause cycle time problems and learn how to solve them.

M/M/1 Queue with Loading and Unloading

Consider a single machine and single lot class, but where process time consists of three parts: loading the lot, servicing the lot, and unloading the lot. The dispatch rule is FIFO. We can use the formula given before for the M/G/1 queue to calculate the limiting expected system cycle time, where the process time has three parts,

  • λ E[S02] (2 (1-ρ) )-1 + μ-1,
  • Suppose λ = 0.05, and the three parts of the process time are distributed exponentially with means 1/μ1 = 1.0, 1/μ2 = 4.0, and 1/μ3 = 2.0. Then
  • μ-1 = μ1 + μ2+ μ3 + = 7.0.
  • Now the second moment of the process time,
  • E[S02] = Var[S0] + E[S0]2 = μ1-2 + μ2-2 + μ3-2 + μ-2 = 70.0,
  • since the process time is the sum of three independent exponential random variables. The traffic intensity ρ = 0.35. Hence the limiting expected system cycle time should be
  • (0.05 * 70.0)(2*(1-0.35))-1 + 7.0 » 9.7.

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