We discuss joint spatial-temporal scaling limits of sums
A
λ
,
γ
A_{\lambda ,\gamma }
(indexed by
(
x
,
y
)
∈
R
+
2
(x,y) \in \mathbb {R}^2_+
) of large number
O
(
λ
γ
)
O(\lambda ^{\gamma })
of independent copies of integrated input process
X
=
{
X
(
t
)
,
t
∈
R
}
X = \{X(t), t \in \mathbb {R}\}
at time scale
λ
\lambda
, for any given
γ
>
0
\gamma >0
. We consider two classes of inputs
X
X
: (I) Poisson shot-noise with (random) pulse process, and (II) regenerative process with random pulse process and regeneration times following a heavy-tailed stationary renewal process. The above classes include several queueing and network traffic models for which joint spatial-temporal limits were previously discussed in the literature. In both cases (I) and (II) we find simple conditions on the input process in order that the normalized random fields
A
λ
,
γ
A_{\lambda ,\gamma }
tend to an
α
\alpha
-stable Lévy sheet
(
1
>
α
>
2
)
(1> \alpha >2)
if
γ
>
γ
0
\gamma > \gamma _0
, and to a fractional Brownian sheet if
γ
>
γ
0
\gamma > \gamma _0
, for some
γ
0
>
0
\gamma _0>0
. We also prove an ‘intermediate’ limit for
γ
=
γ
0
\gamma = \gamma _0
. Our results extend the previous works of R. Gaigalas and I. Kaj [Bernoulli 9 (2003), no. 4, 671–703] and T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman [Ann. Appl. Probab. 12 (2002), no. 1, 23–68] and other papers to more general and new input processes.