  We revisit a classical problem in dynamic storage allocation. Items arrive in
a linear storage medium, modeled as a half-axis, at a Poisson rate $r$ and
depart after an independent exponentially distributed unit mean service time.
The arriving item sizes are assumed to be independent and identically
distributed (i.i.d.) from a common distribution $H$. A widely employed
algorithm for allocating the items is the ``first-fit'' discipline, namely,
each arriving item is placed in the the left-most vacant interval large enough
to accommodate it. In a seminal 1985 paper, Coffman, Kadota, and Shepp [6]
proved that in the special case of unit length items (i.e. degenerate $H$), the
first-fit algorithm is asymptotically optimal in the following sense: the ratio
of expected empty space to expected occupied space tends towards $0$ as the
occupied space tends towards infinity. In a sequel to [6], the authors of [5]
conjectured that the first-fit discipline is also asymptotically optimal for
non-degenerate $H$.
  In this paper we provide the first proof of first-fit asymptotic optimality
for a non-degenerate distribution $H$, namely the case when items can be of
sizes 1 and 2. Specifically, we prove that, under first-fit, the steady-state
packing configuration, scaled down by $r$, converges in distribution to the
optimal limiting packing configuration, i.e. the one with smaller items on the
left, larger items on the right, and with no gaps between.
