This is a follow-up question of the question "Aggregate arrivals from a Poisson Process".

The inter-arrival time of a renewal process, t, conforms to a general distribution, denoted by PDF $f(t)$.

Next we aggregate the requests according to the following pattern: from the first arrival, within the fixed-length time interval $T$, the requests in this interval are aggregated to the first arrival. In other words, the requests in this interval are removed except the first one. This procedure repeats for the rest arrivals. The following figure illustrates this aggregation pattern.

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My question is, what is the distribution of the inter-arrival times after the request aggregation?


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