Approximating the timely throughput of heterogeneous wireless networks

Abstract

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(T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ), 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 <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">det</sub> , and C(T <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ) is bounded by 2√(N(C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">det</sub> + N/4)), which is asymptotically negligible compared to C <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">det</sub> , 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.