C.32.LCA:4.7 - Derive useful timing from the action window

Start from the last time at which an action can still obtain the required consequence. Work backward through the necessary detection, communication, decision and execution. Include waiting for an available processor, person, authorization or resource, not only active processing time.

For a serial path with applicable upper duration bounds, a sufficient timing condition is

[ t_{\mathrm{change}}+ L_{\mathrm{detect}}+ L_{\mathrm{deliver}}+ L_{\mathrm{decide}}+ L_{\mathrm{execute}} \leq t_{\mathrm{needed}}. ]

Each bound must cover its whole contribution under the compared conditions. Periodic observation contributes the worst wait until the next observation as well as the observation work. A computation bound must include the resource arrangement under which it can be achieved. A decision bound must include the availability of a participant with the required authority.

This sum applies to the stated serial path. For parallel or returning work, construct the timing from its dependencies and resource occupations. Identify when each required input and permission can be available, which resource each action occupies, and when it releases that resource. Reconcile different names for the same person, device or capacity before assigning intervals. A machine may continue a cycle after its operator is free; an allocation must reflect that actual occupation rather than charging both for the whole elapsed cycle.

Construct a candidate schedule by placing each action after its required inputs and authorizations, in intervals where all the resources it needs are jointly available. Preserve any required uninterrupted duration, overlap, synchronization and recurring demand. At a join requiring all outputs, the receiving action can start only after the latest required output is available; its own duration still contributes to final completion. Use C.32.MWA.PP:4.7 for the joint workload and commitment construction. A failed placement rejects that schedule; it does not prove that a different order or allocation is impossible. A necessary bound can establish a stronger rejection: required occupation exceeding the available qualified capacity in the same window cannot be repaired by rescheduling within that window.

For example, two otherwise parallel branches each require ten minutes from the same editor before their outputs can be used together. With one continuously available editor and no other required work, serializing the two edits gives a twenty-minute completion. A deadline fifteen minutes after both edits become available is impossible under those conditions, although either branch alone fits. A second qualified and authorized editor, a changed operation or a later deadline changes a different premise of the construction.

Retain a timing summary only when the receiving answer follows from what it keeps. Total free time can conceal incompatible windows; an average rate can conceal a late individual response. Derive the response time or useful bound from the retained dependencies, availability and occupation conditions. If two allowed arrangements share the proposed summary but give different answers, retain the distinguishing condition, derive a bound that covers both, or restrict the claim. Failure to find such a pair does not establish sufficiency. This specializes the information question in :4.3 to the time and capacity needed by the control decision. An average duration does not establish a worst-case deadline.

Choose an observation or decision rhythm from how rapidly a consequential difference can develop and how long a useful response takes. Periodic checking, event-triggered messages and prediction of an approaching limit are alternatives. An event trigger needs an obtainable detector and a response route; otherwise “notify on exception” supplies no timing result.

Separate update period, end-to-end latency and prediction horizon. A planner can update slowly while predicting far ahead; a fast controller can use a delayed estimate. Changing one quantity may change model error, computation, communication load or the available response. Recompute the affected dependence rather than assuming that more frequent updates are better.

Before the next update, specify what the current action may do and why that continuation remains acceptable. If a premise can fail sooner than a response can arrive, obtain a local protective action, shorten the exposure, change the observation or reduce the promised operating region. A monitoring arrangement cannot protect a condition it notices only after the last useful action.