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This work introduces a decentralized mechanism for the fair and efficient allocation of limited renewable energy sources among consumers in an energy community. In the proposed non-cooperative game, the self-interested community members independently decide whether to compete or not for access to RESs during peak hours and shift their loads analogously. In the peak hours, a proportional allocation (PA) policy is used to allocate the limited RESs among the competitors. The existence of a Nash equilibrium (NE) or dominant strategies in this non-cooperative game is shown, and closed-form expressions of the renewable energy demand and social cost are derived. Moreover, a decentralized algorithm for choosing consumers' strategies that lie on NE states is designed. The work shows that the risk attitude of the consumers can have a significant impact on the deviation of the induced social cost from the optimal. Besides, the proposed decentralized mechanism with the PA policy is shown to attain a much lower social cost than one using the naive equal sharing policy.

In time-sensitive networks, bounds on worst-case delays are typically obtained by using network calculus and assuming that flows are constrained by bit-level arrival curves. However, in IEEE TSN or IETF DetNet, source flows are constrained on the number of packets rather than bits. A common approach to obtain a delay bound is to derive a bit-level arrival curve from a packet-level arrival curve. However, such a method is not tight: we show that better bounds can be obtained by directly exploiting the arrival curves expressed at the packet level. Our analysis method also obtains better bounds when flows are constrained with g-regulation, such as the recently proposed Length-Rate Quotient rule. It can also be used to generalize some recently proposed network-calculus delay-bounds for a service curve element with known transmission rate., Comment: 19 pages, 6 figures, submitted

This work studies the decentralized and uncoordinated energy source selection problem for smart-grid consumers with heterogeneous energy profiles and risk attitudes: they compete for a limited amount of renewable energy in their local community, at the risk of paying a higher cost if that energy is not enough to supply all such demand. We model this problem as a non-cooperative game and study the existence of mixed-strategy Nash equilibria (NE) under the proportional allocation policy employed when the total demand for renewable energy exceeds the available one. We derive under NE closed-form expressions for the resulting total renewable energy demand and social cost under varying consumer profiles, energy costs and availability. The analysis also provides useful guidelines as to what consumers should do (compete or not) based on their risk attitude or if they should be more risk-taking, under certain conditions. Finally, we study numerically the efficiency of this decentralized scheme compared to a centralized one via the price-of-anarchy metric.

In Time-Sensitive Networking (TSN), it is important to formally prove per flow latency and backlog bounds. To this end, recent works apply network calculus and obtain latency bounds from service curves. The latency component of such service curves is directly derived from upper bounds on the values of the credit counters used by the Credit-Based Shaper (CBS), an essential building-block of TSN. In this paper, we derive and formally prove credit upper bounds for CBS, which improve on existing bounds., Comment: 4 pages, 0 figures, submitted

We study the admissibility of power injections in single-phase microgrids, where the electrical state is represented by complex nodal voltages and controlled by nodal power injections. Assume that (i) there is an initial electrical state that satisfies security constraints and the non-singularity of load-flow Jacobian, and (ii) power injections reside in some uncertainty set. We say that the uncertainty set is admissible for the initial electrical state if any continuous trajectory of the electrical state is ensured to be secured and non-singular as long as power injections remain in the uncertainty set. We use the recently proposed V-control and show two new results. First, if a complex nodal voltage set V is convex and every element in V is nonsingular, then V is a domain of uniqueness. Second, we give sufficient conditions to guarantee that every element in some power injection set S has a load-flow solution in V, based on impossibility of obtaining load-flow solutions at the boundary of V. By these results, we develop a framework for the admissibility-test method; this framework is extensible to multi-phase grids. Within the framework, we establish a polynomial-time method, using the infeasibility check of convex optimizations. The method is evaluated numerically., Comment: 12 pages, 6 figures

We compute bounds on end-to-end worst-case latency and on nodal backlog size for a per-class deterministic network that implements Credit Based Shaper (CBS) and Asynchronous Traffic Shaping (ATS), as proposed by the Time-Sensitive Networking (TSN) standardization group. ATS is an implementation of the Interleaved Regulator, which reshapes traffic in the network before admitting it into a CBS buffer, thus avoiding burstiness cascades. Due to the interleaved regulator, traffic is reshaped at every switch, which allows for the computation of explicit delay and backlog bounds. Furthermore, we obtain a novel, tight per-flow bound for the response time of CBS, when the input is regulated, which is smaller than existing network calculus bounds. We also compute a per-flow bound on the response time of the interleaved regulator. Based on all the above results, we compute bounds on the per-class backlogs. Then, we use the newly computed delay bounds along with recent results on interleaved regulators from literature to derive tight end-to-end latency bounds and show that these are less than the sums of per-switch delay bounds.

Network Utility Maximization (NUM) is often applied for the cross-layer design of wireless networks considering known wireless channels. However, realistic wireless channel capacities are stochastic bearing time-varying statistics, necessitating the redesign and solution of NUM problems to capture such effects. Based on NUM theory we develop a framework for scheduling, routing, congestion and power control in wireless multihop networks that considers stochastic Long or Short Term Fading wireless channels. Specifically, the wireless channel is modeled via stochastic differential equations alleviating several assumptions that exist in state-of-the-art channel modeling within the NUM framework such as the finite number of states or the stationarity. Our consideration of wireless channel modeling leads to a NUM problem formulation that accommodates non-convex and time-varying utilities. We consider both cases of non orthogonal and orthogonal access of users to the medium. In the first case, scheduling is performed via power control, while the latter separates scheduling and power control and the role of power control is to further increase users' optimal utility by exploiting random reductions of the stochastic channel power loss while also considering energy efficiency. Finally, numerical results evaluate the performance and operation of the proposed approach and study the impact of several involved parameters on convergence.