On-demand and resource reservation pricing models, widely used in cloud computing, are currently used in Multi-Access Edge Computing (MEC). Nevertheless the edge's resources are distributed and each server has lower capacity. If too much resources were reserved in advance, on-demand users may not get their jobs served on time, jeopardizing MEC's latency benefits. Concurrently, reservation plan users may possess un-used quota. Therefore, we propose a sharing platform where reservation plan users can re-sell unused resource quota to on-demand users. To investigate the mobile network operator's (MNO‘s) incentive of allowing re-selling, we formulate a 3-stage non-cooperative Stackelberg Game and characterize the optimal strategies of buyers and re-sellers. We show that users’ actions give rise to 4 different outcomes at equilibrium, dependent on the prices and supply levels of the sharing and on-demand pools. Based on the 4 possible outcomes, we characterise the MNO's optimal prices for on-demand users. Numerical results show that having both pools gives the MNO an optimal revenue when the on-demand pool's supply is low, and unexpectedly, when the MNO's commission is low. We develop an interactive prototype, and show that users’ decision distributions in studies on our prototype are similar to that of our decision model.

In mobile edge computing (MEC) systems, users offload computationally intensive tasks to edge servers at base stations. However, with unequal demand across the network, there might be excess demand at some locations and underutilized resources at other locations. To address such load-unbalanced problem in MEC systems, in this paper we propose virtual machines (VMs) sharing across base stations. Specifically, we consider the joint VM placement and pricing problem across base stations to match demand and supply and maximize revenue at the network level. To make this problem tractable, we decompose it into master and slave problems. For the placement master problem, we propose a Markov approximation algorithm MAP on the design of a continuous time Markov chain. As for the pricing slave problem, we propose OPA - an optimal VM pricing auction, where all users are truthful. Furthermore, given users' potential untruthful behaviors, we propose an incentive compatible auction iCAT along with a partitioning mechanism PUFF, for which we prove incentive compatibility and revenue guarantees. Finally, we combine MAP and OPA or PUFF to solve the original problem, and analyze the optimality gap. Simulation results show that collaborative base stations increases revenue by up to 50%.

Multi-access Edge Computing (MEC) is an emerging paradigm which allows users to offload their computationally intensive tasks to the network edge. In this paper, we analyze resource allocation in MEC from the market and economic perspective. Due to extremely heterogeneous usage demands across users in the future IoE market, current coarse-grained pricing schemes result in partial wastage: some users would have excess un-utilized resource quota while others might have reserved insufficient resources. Therefore, we introduce a novel sharing economy-inspired business model, where a platform facilitates the sharing of resource quota among users, increasing resource efficiency. The goal is to maximize the overall welfare of users who join the sharing platform. As the platform lacks control and has imperfect knowledge of users' payoff functions and distributions, a distributed pricing mechanism is proposed. In our mechanism, the platform and users jointly arrive at an equilibrium. We prove that the equilibrium point of the mechanism is the socially optimal point. Simulations illustrate convergence, the robustness of our mechanism to changes in demand and supply, and that sharing increases the welfare of users.

Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we jointly optimize end-to-end source rates and link powers to achieve weighted max-min rate fairness for all sources in the network? This optimization problem is hard to solve as physical layer link rate functions are nonlinear, nonconvex, and coupled in the transmit powers. We show that the weighted max-min rate fairness problem can, in fact, be decoupled into separate fairness problems for flow rate and power control. For a large class of physical layer link rate functions, we characterize the optimal solution analytically by a nonlinear Perron-Frobenius theory through solving a conditional eigenvalue problem that captures the interaction of multiuser interference. We propose an iterative algorithm to compute the optimal flow rate that converges geometrically fast without any parameter configuration. Numerical results demonstrate that our iterative algorithm is computationally fast for the Shannon capacity, CDMA, and piecewise link rate functions.

Rate adaptation and power control are two key resource allocation mechanisms in multiuser wireless networks. In the presence of interference, how do we jointly optimize end-to-end source rates and link powers to achieve weighted max-min rate fairness for all sources in the network? This optimization problem is hard to solve as physical layer link rate functions are nonlinear, nonconvex, and coupled in the transmit powers. We show that the weighted max-min rate fairness problem can, in fact, be decoupled into separate fairness problems for flow rate and power control. For a large class of physical layer link rate functions, we characterize the optimal solution analytically by a nonlinear Perron-Frobenius theory (through solving a conditional eigenvalue problem) that captures the interaction of multiuser interference. We give an iterative algorithm to compute the optimal flow rate that converges geometrically fast without any parameter configuration. Numerical results show that our iterative algorithm is computationally fast for both the Shannon capacity, CDMA, and piecewise linear link rate functions.

Typical formulations of max-min weighted SIR problems involve either a total power constraint or individual power constraints. These formulations are unable to handle the complexities in multicell networks where each base station can be subject to its own sum power constraint. This paper considers the max-min weighted SIR problem subject to multiple weighted-sum power constraints, where the weights can represent relative power costs of serving different users. First, we derive the uplink-downlink duality principle by applying Lagrange duality to the single-constraint problem. Next, we apply nonlinear Perron-Frobenius theory to derive a closed-form solution for the multiple-constraint problem. Then, by exploiting the structure of the closed-form solution, we relate the multiple-constraint problem with its single-constraint subproblems and establish the dual uplink problem. Finally, we further apply nonlinear Perron-Frobenius theory to derive an algorithm which converges geometrically fast to the optimal solution.

This paper studies the optimization of a multicell multiple-input-single-output (MISO) downlink system in which each base station serves multiple users, and each user is served by only one base station. First, we consider the problem of maximizing the minimum weighted signal-to-interference-plus-noise ratio (SINR) of all users subject to a single weighted-sum power constraint, where the weights can represent relative power costs of serving different users in each cell. We apply concave Perron-Frobenius theory to propose a joint power control and linear beamforming algorithm which converges geometrically fast to the optimal solution. As a by-product, we resolve an open problem of convergence of a previously proposed algorithm by Wiesel, Eldar, and Shamai in 2006. Next, we study the max-min weighted SINR problem subject to multiple weighted-sum power constraints and we show that it can be decoupled into its associated single-constrained subproblems.

Designing fast algorithms that adapt the transmit and receive power and beamformers to optimize performance for different users is important in wireless MIMO downlink systems. This paper studies the max-min weighted SIR problem in the downlink, where multiple users are weighted according to priority and are subject to a total power constraint. The difficulty of this nonconvex problem is compounded by the coupling in the transmit and receive beamformers, thereby making it hard to optimize in a distributed fashion. We first show that this problem can be optimally and efficiently computed using a fast algorithm when the channels are rank-one. The optimal transmit and receive power and beamformers are also derived analytically. We then exploit the MIMO uplink-downlink duality to adapt our algorithm to compute a local optimal solution for channels with general rank.