Mixed network calculus

We show how to combine higgsed topological vertices introduced in [7] with conventional refined topological vertices. We demonstrate that the extended formalism describes very general interacting D5-NS5-D3 brane systems. In particular, we introduce new types of intertwining operators of Ding-Iohara-Miki algebra between different types of Fock representations corresponding to the crossings of NS5 and D5 branes. As a byproduct we obtain an algebraic description of the Hanany-Witten brane creation effect, give an efficient recipe to compute the brane factors in 3d$$ \mathcal{N} $$ N = 2 and $$ \mathcal{N} $$ N = 4 quiver gauge theories and demonstrate how 3d S-duality appears in our setup.

Higgsed network calculus

We introduce a formalism for describing holomorphic blocks of 3d quiver gauge theories using networks of Ding-Iohara-Miki algebra intertwiners. Our approach is very direct and gives an explicit identification of the blocks with Dotsenko-Fateev type integrals for q-deformed quiver W-algebras. We also explain how quiver theories corresponding to Dynkin diagrams of superalgebras arise, write down the corresponding partition functions and W-algebras, and explain the connection with supersymmetric Macdonald-Ruijsenaars commuting Hamiltonians.

Non-Statistical Method for Validation the Time Characteristics of Digital Control Systems with a Cyclic Processing Algorithm

The paper discusses the problem of performance and timing parameters with respect to the validation of digital instrumentation and control systems (I&C). Statistical methods often implicitly assume that the probability distribution law of the estimated parameters is close to normal. Thus, the confidence intervals for the parameter are determined on the grounds of this assumption. However, we encountered cases when the delay distribution law in I&C is not normal. In these cases, we used the non-statistical network calculus method for time parameters estimation. The network calculus method is well elaborated for lossless digital system models with seamless processing algorithm depending only on data volume. We consider the extension of the method to the case of I&C systems with considerable changes in the data flow and content-dependent processing disciplines. The model is restricted to systems with cyclic processing algorithms and fast network connections. Network calculus describes the data flow and system parameters in terms of flow envelopes and service curves that are generally unknown in advance. In this paper, we define equations that allow the calculation of these characteristics from experimental data. The correspondence of the Network Calculus and classical statistical estimation methods is discussed. Additionally, we give an example of model application to a real I&C system.

QoS-aware Resource Allocation for Live Streaming in Edge-Clouds Aided HetNets Using Stochastic Network Calculus

Mobile edge computing (MEC) is a key feature of next generation mobile networks aimed at providing a variety of services for different applications by performing related processing tasks closer to the user equipment. Edge clouds can be installed as an interface between the cellular networks and the core to provide the required services based on the known concept of the MEC networks. Nonetheless, the problem of green networking will be of great importance in such networks. This paper presents an energy-efficient stochastic network calculus (SNC) framework to control MEC data flows. In accordance with the entrance processes of different QoS-class data flows, closed-form problems were formulated to determine the correlation between resource utilization and the violation probability of each data flow. Also, in the access layer, this paper proposes a dynamic user association and resource allocation approach which maximizes the overall energy efficiency of cache-enabled cellular networks in addition to provide the superior fairness level for UEs. In this energy-cooperative approach, the power can be shared among the cells using a grid network. This model also performs routing in the multi-hop backhaul to efficiently use the existing infrastructure of small cell networks for simultaneous dual-hop transmissions. The simulation results exhibit that the proposed approach can effectively increase the user throughput and the total power efficiency while guaranteeing the acceptable fairness level for uniform and hotspot UE distribution models. It also proved that the energy utilization index and the system data rate can be significantly improved.

Modeling Data Flows with Network Calculus in Cyber-Physical Systems: Enabling Feature Analysis for Anomaly Detection Applications

The electric grid is becoming increasingly cyber-physical with the addition of smart technologies, new communication interfaces, and automated grid-support functions. Because of this, it is no longer sufficient to only study the physical system dynamics, but the cyber system must also be monitored as well to examine cyber-physical interactions and effects on the overall system. To address this gap for both operational and security needs, cyber-physical situational awareness is needed to monitor the system to detect any faults or malicious activity. Techniques and models to understand the physical system (the power system operation) exist, but methods to study the cyber system are needed, which can assist in understanding how the network traffic and changes to network conditions affect applications such as data analysis, intrusion detection systems (IDS), and anomaly detection. In this paper, we examine and develop models of data flows in communication networks of cyber-physical systems (CPSs) and explore how network calculus can be utilized to develop those models for CPSs, with a focus on anomaly and intrusion detection. This provides a foundation for methods to examine how changes to behavior in the CPS can be modeled and for investigating cyber effects in CPSs in anomaly detection applications.