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— Workstation Queue Time (Kingman / VUT)

Approximate queue time and WIP at a single production workstation using the Kingman (VUT) equation for a G/G/m queue: CT_q ≈ ((c_a²+c_e²)/2)·(u^{√(2(m+1))−1}/(m(1−u)))·t_e.

Solution

History

Sources:
[1] J. F. C. Kingman, "The single server queue in heavy traffic," Math. Proc. Cambridge Philos. Soc., vol. 57, no. 4, pp. 902–904, 1961.
[2] H. Sakasegawa, "An approximation formula L_q ≈ αρ^β/(1−ρ)," Ann. Inst. Stat. Math., vol. 29, no. 1, pp. 67–75, 1977.
[3] W. J. Hopp and M. L. Spearman, Factory Physics, 3rd ed. Long Grove, IL, USA: Waveland Press, 2011.

Reference content only — not a substitute for professional engineering judgment. Verify all values, tolerances, and specifications against current official standards before use in production or safety-critical work. Provided without warranty of accuracy or fitness for any purpose.