Timely Throughput of Heterogeneous Wireless Networks: Fundamental Limits   and Algorithms
  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. 
Sina Lashgari and A. Salman Avestimehr
cs.IT cs.NI math.IT