Correct definition for statistical phenomenon

[TaPaKaH]

Suppose we have a random service time $T$ with residual service time $R$ observed at some point along the way.

What is the correct way to call $T$ (in 1-2 words, without having to introduce $R$) if:
1) For any observation time, $\mathbb{E}R\leq\mathbb{E}T$?
2) For any observation time, $R<T$ in distribution i.e. $T$ stochastically dominates $R$.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?