  This paper focuses on the problem of modeling the correspondence pattern for
ordinary people. Suppose that letters arrive at a rate $\lambda$ and are
answered at a rate $\mu$. Furthermore, we assume that, for a constant $T$, a
letter is disregarded when its waiting time exceeds $T$, and the remains are
answered in {\it last in first out} order. Let $W_n$ be the waiting time of the
$n$-th {\it answered} letter. It is proved that $W_n$ converges weekly to
$W_T$, a non-negative random variable which possesses a density with {\it
power-law} tail when $\lambda=\mu$ and with exponential tail otherwise. Note
that this may provide a reasonable explanation to the phenomenons reported by
Oliveira and Barab\'asi in \cite{OB}.
