Approximating the timely throughput of heterogeneous wireless networks

In this paper we consider the down link of a heterogeneous 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(T³), which is the maximum average number of packets delivered successfully before their deadline. We propose 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(T³) is bounded by 2√(N(C_det + N/4)), which is asymptotically negligible compared to C_det, when the network is operating at high-throughput regime. Moreover, using LP rounding methods we prove that the relaxed problem can be approximated in polynomial time with additive gap of N.