  The proliferation of different wireless access technologies, together with
the growing number of multi-radio wireless devices suggest that the
opportunistic utilization of multiple connections at the users can be an
effective solution to the phenomenal growth of traffic demand in wireless
networks. In this paper we consider the downlink of a wireless network with $N$
Access Points (AP's) and $M$ clients, where each client is connected to several
out-of-band AP's, and requests delay-sensitive traffic (e.g., real-time video).
We adopt the framework of Hou, Borkar, and Kumar, and study the maximum total
timely throughput of the network, denoted by $C_{T^3}$, which is the maximum
average number of packets delivered successfully before their deadline. Solving
this problem is challenging since even the number of different ways of
assigning packets to the AP's is $N^M$. We overcome the challenge by proposing
a deterministic relaxation of the problem, which converts the problem to a
network with deterministic delays in each link. We show that the additive gap
between the capacity of the relaxed problem, denoted by $C_{det}$, and
$C_{T^3}$ is bounded by $2\sqrt{N(C_{det}+N/4)}$, which is asymptotically
negligible compared to $C_{det}$, when the network is operating at
high-throughput regime.
  In addition, our numerical results show that the actual gap between $C_{T^3}$
and $C_{det}$ is in most cases much less than the worst-case gap proven
analytically. Moreover, using LP rounding methods we prove that the relaxed
problem can be approximated within additive gap of $N$. We extend the
analytical results to the case of time-varying channel states, real-time
traffic, prioritized traffic, and optimal online policies. Finally, we
generalize the model for deterministic relaxation to consider fading, rate
adaptation, and multiple simultaneous transmissions.
