  This paper addresses a Gaussian interference channel with two
transmitter-receiver~(Tx-Rx) pairs under stochastic data arrival~(GIC-SDA).
Information bits arrive at the transmitters according to independent and
asynchronous Bernoulli processes~(Tx-Tx~asynchrony). Each information source
turns off after generating a given total number of bits. The transmissions are
\textit{asynchronous} (Tx-Rx~asynchrony) in the sense that each Tx sends a
codeword to its Rx immediately after there are enough bits available in its
buffer. Such asynchronous style of transmission is shown to significantly
reduce the transmission delay in comparison with the existing Tx-Rx synchronous
transmission schemes. The receivers learn the activity frames of both
transmitters by employing sequential joint-typicality detection. As a
consequence, the GIC-SDA under Tx-Rx asynchrony is represented by a standard
GIC with state known at the receivers. The cardinality of the state space is
$\binom{2N_1+2N_2}{2N_2}$ in which $N_1, N_2$ are the numbers of transmitted
codewords by the two transmitters. Each realization of the state imposes two
sets of constraints on $N_1, N_2$ referred to as the geometric and reliability
constraints. In a scenario where the transmitters are only aware of the
statistics of Tx-Tx~asynchrony, it is shown how one designs $N_1,N_2$ to
achieve target transmission rates for both users and minimize the probability
of unsuccessful decoding.
