Distributed Rate Allocation for Inelastic Flows

Abstract

Abstract-A common assumption behind most of the recent research on network rate allocation is that traffic flows are elastic, which means that their utility functions are concave and continuous and that there is no hard limit on the rate allocated to each flow. These critical assumptions lead to the tractability of the analytic models for rate allocation based on network utility maximization, but also limit the applicability of the resulting rate allocation protocols. This paper focuses on inelastic flows and removes these restrictive and often invalid assumptions.First, we consider nonconcave utility functions, which turn utility maximization into difficult, nonconvex optimization problems. We present conditions under which the standard price-based distributed algorithm can still converge to the globally optimal rate allocation despite nonconcavity of utility functions. In particular, continuity of price-based rate allocation at all the optimal prices is a sufficient condition for global convergence of rate allocation by the standard algorithm, and continuity at at least one optimal price is a necessary condition. We then show how to provision link capacity to guarantee convergence of the standard distributed algorithm. Second, we model real-time flow utilities as discontinuous functions. We show how link capacity can be provisioned to allow admission of all real-time flows, then propose a price-based admission control heuristics when such link capacity provisioning is impossible, and finally develop an optimal distributed algorithm to allocate rates between elastic and real-time flows.

Towards a fair non-convex resource allocation in Wireless Networks

“…Fazel et al in [3] remove the restricting assumption of concave utilities and propose a centralized method based on sum-ofsquares relaxations to calculate approximations of the optimal solution along with some performance bounds to evaluate the approximation error. Moreover, [4] and [5] have extended the NUM framework to model inelastic traffic using sigmoidal utilities and have proposed distributed algorithms for wired networks, which however are not guaranteed to converge to the optimal solution in case of oscillations in the network.…”

Downlink user selection and resource allocation for semi-elastic flows in an OFDM cell

“…al. [14] show that similar algorithms may fluctuate around the optimal point if a user's allocated rate is near the tangent point. Thus, here we force the iteration for k to terminate when:…”

“…The benefits of distributed optimization are that the base station doesn't need to know the exact utility function of each user and this will reduce signalling between the base station and users. The determination of the desired rates d in (11) indicates a role for each user, while the determination of Lagrange multiplier l in (14) indicates a role for the network. These two roles must be done in coordination.…”

“…These two roles must be done in coordination. The decomposition suggests to us that there should be an intermediate power allocation module which determines the Lagrange multipliers k in (14) and determines the powers p in (15). The communication between the users, power allocation module, and network is illustrated in Fig.…”

“…The wireless resources are thus comprised of both base station transmission power and subcarriers. This makes the resource allocation problem moderately more complex than the CDMA system and other wireless systems considered in [13,15,17] or the wireline system considered in [14,16], which consider allocation of a single type of resource (power, rate, or bandwidth).…”