Count reusable preparation stations from fixed occupancy intervals

A resource can serve several activities when their occupied intervals do not overlap. Count simultaneous occupancy before assuming every activity needs its own preparation station. Then construct a station schedule: a peak count alone should not replace an inspectable assignment.

Define the interval convention

Fictional practice example: activity A occupies turns zero to two, B occupies one to three, and C occupies two to four. All starts and ends use the same invented clock. The stations are interchangeable, and each activity needs exactly one station throughout its interval.

For this exercise, occupancy includes the start and excludes the end. A station released at turn two is immediately available to another activity starting at two. No cleanup, setup, transfer delay, or eligibility restriction is present. These are model assumptions, not statements about actual rooms, conferencing limits, or Kiguri reservations.

Count occupants between the endpoints

Make an endpoint register for zero, one, two, three, and four. From zero up to one, only A occupies a station. From one up to two, A and B are both present. From two up to three, B and C are present. From three up to four, only C remains.

The peak is two simultaneous activities. One station cannot serve A and B during the interval from one to two. This gives a lower bound of two stations. Do not count the number of named activities as the required number of stations; that would ignore the opportunity to reuse one after its occupant leaves.

Construct an assignment that meets the bound

Assign A to station one from zero to two, then C to station one from two to four. Assign B to station two from one to three. Within either station, no occupied intervals overlap under the stated convention.

This explicit arrangement shows that two stations are sufficient for the fixture, while the overlap already showed that fewer cannot work. Keep both reasons. A lower bound without a valid assignment would leave feasibility unproven; an assignment using three stations would work but would not establish that three are necessary.

Check equal-time changes and omitted buffers

At turn two, record A's release before C's admission. Treating A as still occupying its station at that instant would contradict the start-inclusive, end-exclusive rule and could create a false three-activity peak. Conversely, ignoring B during either overlap would falsely allow one station.

If a real activity requires cleanup, represent that additional occupancy explicitly. An A station unavailable until after turn two cannot immediately accept C. Likewise, different station capabilities can prevent the illustrated reuse even when intervals do not overlap. Establish those conditions with their owners rather than assuming the simplified schedule proves a real arrangement is available.

Verify the timelines and the remaining limits

Retain each activity's fixed interval, the occupancy convention, endpoint counts, and station assignment together. Ask a second reader to name both overlapping pairs and locate the station reused by A and C. They should also explain why the shared endpoint is permitted in this model.

If start or end times are uncertain, preserve that uncertainty rather than forcing them into exact intervals. These are known occupied durations, not ranges bounding unknown event instants. The finish is a replayable resource-count argument for the declared fixture, with omissions attached. Actual access, availability, reservations, and preparation commitments remain separate checks through the team's established process.