[ot] [wrong] DistractionBot Goes To Work

[Karl]

On Sat, Jun 5, 2021, 3:44 PM Karl <gmkarl at gmail.com> wrote:

>
>
> On Sat, Jun 5, 2021, 3:42 PM Karl <gmkarl at gmail.com> wrote:
>
>> S_n and a 1 minute delay.
>>
>> St(n): time person n arrives.
>> Sts(n): time person n begins being served
>> Stf(n): time person n is done being served and leaves
>>
>> Stf(n) = Sts(n) + 1
>> Sts(n) = max(St(n), Stf(n -1))
>>
>
> Sts(n) = max(St(n), Sts(n - 1) + 1)
>
> Each iteration, the final value is either one more than the previous, or a
> newly defined value.
>

St(n) = Sum[j=1...infinity, S_j * I{j <= n}]

In the end, we want the number of people as a function of time.  How many
people have arrived by time t?

Arrived(t) = Sum[j=0...infinity, 1 I{St(j) < t}]

Using the impulse function to do everything is new to me.  Not easily
accessible.

>
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