OPS.10.1:5.3 - An aggregate curve and a completed job

A controller represents remaining workload q in job-equivalents, starting at one with no new arrivals. Its assumed output rate is k*q, with k = 1 per hour. The balance gives q(t) = exp(-t): after one hour, about 0.368 job-equivalents remain. This model can support an aggregate regulation question where that outflow law fits.

A different operating account says one indivisible job takes exactly one uninterrupted hour on the available resource. Its completion event occurs at hour one. A constant-rate fluid balance, stopped at zero, also gives q(t) = max(1-t,0) in job-equivalents, but its intermediate fractions do not make the actual job partially delivered.

Even the exponential curve permits another interpretation under different premises. For one exponentially distributed service duration with mean one hour, it is the expected number of unfinished jobs; completion by one hour then has probability about 0.632. It is not a deterministic promise.

The practitioner chooses the account by the receiving question and the operating service law, not by whether the display uses a curve or discrete events. For the fixed one-hour deadline, use the completion event. For aggregate feedback, establish the outflow relation and how a commanded rate change can be realized. A new capacity setting without a corresponding operating mechanism leaves the proposed intervention unsupported.