OPS.10.1:11 - SoTA-Echoing

For a quick mean comparison of one continuing first-come server, adopt the service-process and two-moment construction in Hopp and Spearman, Factory Physics, third edition, §8.6.5, equations 8.25–8.26. A utilization-only calculation is cheaper but loses the action-changing service variation in section 5.1. Sections 4.2 and 4.4 retain both variance contributions, the saturation factor and their premises. The formula is a mature approximation with a useful exact Poisson-arrival special case, not a universal service law. Its low calculation cost is accepted for the mean question; a changed operating regime or a required deadline probability reopens the choice.

For dependent traffic, adapt the richer description developed by Whitt and You (2022), §§2.1–2.2: count dispersion over time retains variability a fixed two-moment description can lose. This costs additional traffic characterization. Section 4.4 selects that effort when the lost dependence matters. Their robust-queueing construction approximates mean performance in a steady regime under its stationarity and independent-service assumptions. Although the derivation uses a worst-case construction, the returned result estimates a mean; it does not guarantee an upper bound on individual waits. Changed dependence, routing or the requested result reopens that use.

For changing aggregate workload, Oliveira, Sagawa and Mušič (2025), §§3–4, supplies a current continuous feedback-control alternative. Adapt its explicit accumulation and capacity-response account for a suitable aggregate question; reject treating continuous versus discrete representation as the test for whether feedback is possible. Sections 4.3 and 5.3 retain the outflow law, completion interpretation and obtainable capacity change. An event model requires individual timing detail and is preferable when that detail decides the deadline. The paper’s simulated control response does not establish physical access or every individual completion. Reopen when a changed service law or required completion event invalidates the chosen correspondence.

The finite probability and changed-dependence case is a direct construction from its stated premises. It avoids a simulation project for four enumerable outcomes. Use a larger probabilistic construction when the joint inputs or the risk question being answered require it.