[ot] [wrong] DistractionBot Goes To Work

Karl gmkarl at gmail.com
Sat Jun 5 11:26:32 PDT 2021


>
> X(t) ~= (number of people who have arrived between 0 and t) - (number of
>>>>>> people who have been fully served between 0 and t)
>>>>>>
>>>>>
>>>>> Both of these values are calculable.
>>>>>
>>>>
>>>> S_n is the number of minutes that pass after person (n-1) arrives,
>>>> before person n arrives.
>>>>
>>>
>>> We can likely write both of these in abstract parts, as X(t) is written
>>> above.
>>>
>>
>> Number of people who have arrived = sum of 1 for each person whose
>> arrival time is less than or equal to t
>>
>> Number of people who have been fully served = sum of 1 for each person
>> whose serving conditions have been met
>>
>
> Serving conditions.  The time at which a person is completely served is
> the maximum of one minute after they arrive, and two minutes after the
> previous person arrived.
>

The time at which a person arrives, assuming person 0 arrives at time 0, is
likely Sum[j=1...infinity, S_j * I{j <= n}]

>
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