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6G networks will be highly dynamic, re-configurable, and resilient. To enable and support such features, employing AI has been suggested. Integrating AIin networks will likely require distributed AI deployments with resilient connectivity, e.g., for communication between RL agents and environment. Such approaches need to be validated in realistic network environments. In this demo, we use ContainerNet to emulate AI-capable and autonomic networks that employ the routing protocol KIRA to provide resilient connectivity and service discovery. As an example AI application, we train and infer deep RL agents learning medium access control (MAC) policies for a wireless network environment in the emulated network., Comment: Accepted for presentation in the Demo Session at the IEEE International Conference on Network Protocols (ICNP), 2024

Finding efficient routes for data packets is an essential task in computer networking. The optimal routes depend greatly on the current network topology, state and traffic demand, and they can change within milliseconds. Reinforcement Learning can help to learn network representations that provide routing decisions for possibly novel situations. So far, this has commonly been done using fluid network models. We investigate their suitability for millisecond-scale adaptations with a range of traffic mixes and find that packet-level network models are necessary to capture true dynamics, in particular in the presence of TCP traffic. To this end, we present $\textit{PackeRL}$, the first packet-level Reinforcement Learning environment for routing in generic network topologies. Our experiments confirm that learning-based strategies that have been trained in fluid environments do not generalize well to this more realistic, but more challenging setup. Hence, we also introduce two new algorithms for learning sub-second Routing Optimization. We present $\textit{M-Slim}$, a dynamic shortest-path algorithm that excels at high traffic volumes but is computationally hard to scale to large network topologies, and $\textit{FieldLines}$, a novel next-hop policy design that re-optimizes routing for any network topology within milliseconds without requiring any re-training. Both algorithms outperform current learning-based approaches as well as commonly used static baseline protocols in scenarios with high-traffic volumes. All findings are backed by extensive experiments in realistic network conditions in our fast and versatile training and evaluation framework., Comment: Accepted at Transactions of Machine Learning Research (TMLR) 2024

The Intelligent Transportation System (ITS) environment is known to be dynamic and distributed, where participants (vehicle users, operators, etc.) have multiple, changing and possibly conflicting objectives. Although Reinforcement Learning (RL) algorithms are commonly applied to optimize ITS applications such as resource management and offloading, most RL algorithms focus on single objectives. In many situations, converting a multi-objective problem into a single-objective one is impossible, intractable or insufficient, making such RL algorithms inapplicable. We propose a multi-objective, multi-agent reinforcement learning (MARL) algorithm with high learning efficiency and low computational requirements, which automatically triggers adaptive few-shot learning in a dynamic, distributed and noisy environment with sparse and delayed reward. We test our algorithm in an ITS environment with edge cloud computing. Empirical results show that the algorithm is quick to adapt to new environments and performs better in all individual and system metrics compared to the state-of-the-art benchmark. Our algorithm also addresses various practical concerns with its modularized and asynchronous online training method. In addition to the cloud simulation, we test our algorithm on a single-board computer and show that it can make inference in 6 milliseconds.

Operators of reconfigurable wavelength-division multiplexed (WDM) optical networks adapt the lightpath topology to balance load and reduce transmission delays. Such an adaption generally depends on a known or estimated traffic matrix. Network function virtualization (NFV) allows to implicitly change this traffic matrix. However, these two degrees of freedom have largely been considered separately, using resources suboptimally. Especially for delay-sensitive services, an optimal use of resources can be crucial. We aim to jointly optimize the embedding of virtualized network function (VNF) forwarding graphs with delay constraints and the lightpath topology of WDM optical networks. Unlike previous work, we consider all three types of delays: propagation, processing and forwarding-induced queuing delay. We model the latter two as M/M/1 queues. We formulate and analyze a mixed-integer nonlinear program (MINLP), reformulate it as a mixed-integer quadratic constrained program (MIQCP) and approximate it by a mixed-integer linear program (MILP). We evaluate our approach for small-scale examples of a multicast service.

We generalize the Borkar-Meyn stability Theorem (BMT) to distributed stochastic approximations (SAs) with information delays that possess an arbitrary moment bound. To model the delays, we introduce Age of Information Processes (AoIPs): stochastic processes on the non-negative integers with a unit growth property. We show that AoIPs with an arbitrary moment bound cannot exceed any fraction of time infinitely often. In combination with a suitably chosen stepsize, this property turns out to be sufficient for the stability of distributed SAs. Compared to the BMT, our analysis requires crucial modifications and a new line of argument to handle the SA errors caused by AoI. In our analysis, we show that these SA errors satisfy a recursive inequality. To evaluate this recursion, we propose a new Gronwall-type inequality for time-varying lower limits of summations. As applications to our distributed BMT, we discuss distributed gradient-based optimization and a new approach to analyzing SAs with momentum.

We formulate offloading of computational tasks from a dynamic group of mobile agents (e.g., cars) as decentralized decision making among autonomous agents. We design an interaction mechanism that incentivizes such agents to align private and system goals by balancing between competition and cooperation. In the static case, the mechanism provably has Nash equilibria with optimal resource allocation. In a dynamic environment, this mechanism's requirement of complete information is impossible to achieve. For such environments, we propose a novel multi-agent online learning algorithm that learns with partial, delayed and noisy state information, thus greatly reducing information need. Our algorithm is also capable of learning from long-term and sparse reward signals with varying delay. Empirical results from the simulation of a V2X application confirm that through learning, agents with the learning algorithm significantly improve both system and individual performance, reducing up to 30% of offloading failure rate, communication overhead and load variation, increasing computation resource utilization and fairness. Results also confirm the algorithm's good convergence and generalization property in different environments., Comment: arXiv admin note: substantial text overlap with arXiv:2204.02267

We propose a multi-agent distributed reinforcement learning algorithm that balances between potentially conflicting short-term reward and sparse, delayed long-term reward, and learns with partial information in a dynamic environment. We compare different long-term rewards to incentivize the algorithm to maximize individual payoff and overall social welfare. We test the algorithm in two simulated auction games, and demonstrate that 1) our algorithm outperforms two benchmark algorithms in a direct competition, with cost to social welfare, and 2) our algorithm's aggressive competitive behavior can be guided with the long-term reward signal to maximize both individual payoff and overall social welfare.

We formulate computation offloading as a decentralized decision-making problem with autonomous agents. We design an interaction mechanism that incentivizes agents to align private and system goals by balancing between competition and cooperation. The mechanism provably has Nash equilibria with optimal resource allocation in the static case. For a dynamic environment, we propose a novel multi-agent online learning algorithm that learns with partial, delayed and noisy state information, and a reward signal that reduces information need to a great extent. Empirical results confirm that through learning, agents significantly improve both system and individual performance, e.g., 40% offloading failure rate reduction, 32% communication overhead reduction, up to 38% computation resource savings in low contention, 18% utilization increase with reduced load variation in high contention, and improvement in fairness. Results also confirm the algorithm's good convergence and generalization property in significantly different environments.

Iterative distributed optimization algorithms involve multiple agents that communicate with each other, over time, in order to minimize/maximize a global objective. In the presence of unreliable communication networks, the Age-of-Information (AoI), which measures the freshness of data received, may be large and hence hinder algorithmic convergence. In this paper, we study the convergence of general distributed gradient-based optimization algorithms in the presence of communication that neither happens periodically nor at stochastically independent points in time. We show that convergence is guaranteed provided the random variables associated with the AoI processes are stochastically dominated by a random variable with finite first moment. This improves on previous requirements of boundedness of more than the first moment. We then introduce stochastically strongly connected (SSC) networks, a new stochastic form of strong connectedness for time-varying networks. We show: If for any $p \ge0$ the processes that describe the success of communication between agents in a SSC network are $\alpha$-mixing with $n^{p-1}\alpha(n)$ summable, then the associated AoI processes are stochastically dominated by a random variable with finite $p$-th moment. In combination with our first contribution, this implies that distributed stochastic gradient descend converges in the presence of AoI, if $\alpha(n)$ is summable.

We present Distributed Deep Deterministic Policy Gradient (3DPG), a multi-agent actor-critic (MAAC) algorithm for Markov games. Unlike previous MAAC algorithms, 3DPG is fully distributed during both training and deployment. 3DPG agents calculate local policy gradients based on the most recently available local data (states, actions) and local policies of other agents. During training, this information is exchanged using a potentially lossy and delaying communication network. The network therefore induces Age of Information (AoI) for data and policies. We prove the asymptotic convergence of 3DPG even in the presence of potentially unbounded Age of Information (AoI). This provides an important step towards practical online and distributed multi-agent learning since 3DPG does not assume information to be available deterministically. We analyze 3DPG in the presence of policy and data transfer under mild practical assumptions. Our analysis shows that 3DPG agents converge to a local Nash equilibrium of Markov games in terms of utility functions expressed as the expected value of the agents local approximate action-value functions (Q-functions). The expectations of the local Q-functions are with respect to limiting distributions over the global state-action space shaped by the agents' accumulated local experiences. Our results also shed light on the policies obtained by general MAAC algorithms. We show through a heuristic argument and numerical experiments that 3DPG improves convergence over previous MAAC algorithms that use old actions instead of old policies during training. Further, we show that 3DPG is robust to AoI; it learns competitive policies even with large AoI and low data availability.

Using Service Function Chaining (SFC) in wireless networks became popular in many domains like networking and multimedia. It relies on allocating network resources to incoming SFCs requests, via a Virtual Network Embedding (VNE) algorithm, so that it optimizes the performance of the SFC. When the load of incoming requests -- competing for the limited network resources - increases, it becomes challenging to decide which requests should be admitted and which one should be rejected. In this work, we propose a deep Reinforcement learning (RL) solution that can learn the admission policy for different dependencies, such as the service lifetime and the priority of incoming requests. We compare the deep RL solution to a first-come-first-serve baseline that admits a request whenever there are available resources. We show that deep RL outperforms the baseline and provides higher acceptance rate with low rejections even when there are enough resources.

As we move from 5G to 6G, edge computing is one of the concepts that needs revisiting. Its core idea is still intriguing: instead of sending all data and tasks from an end user's device to the cloud, possibly covering thousands of kilometers and introducing delays that are just owed to limited propagation speed, edge servers deployed in close proximity to the user, e.g., at some 5G gNB, serve as proxy for the cloud. Yet this promising idea is hampered by the limited availability of such edge servers. In this paper, we discuss a way forward, namely the virtual edge computing (V-Edge) concept. V-Edge bridges the gap between cloud, edge, and fog by virtualizing all available resources including the end users' devices and making these resources widely available using well-defined interfaces. V-Edge also acts as an enabler for novel microservices as well as cooperative computing solutions. We introduce the general V-Edge architecture and we characterize some of the key research challenges to overcome, in order to enable wide-spread and even more powerful edge services.

Information exchange over networks can be affected by various forms of delay. This causes challenges for using the network by a multi-agent system to solve a distributed optimisation problem. Distributed optimisation schemes, however, typically do not assume network models that are representative for real-world communication networks, since communication links are most of the time abstracted as lossless. Our objective is therefore to formulate a representative network model and provide practically verifiable network conditions that ensure convergence of distributed algorithms in the presence of interference and possibly unbounded delay. Our network is modelled by a sequence of directed-graphs, where to each network link we associate a process for the instantaneous signal-to-interference-plus-noise ratio. We then formulate practical conditions that can be verified locally and show that the age of information (AoI) associated with data communicated over the network is in $\mathcal{O}(\sqrt{n})$. Under these conditions we show that a penalty-based gradient descent algorithm can be used to solve a rich class of stochastic, constrained, distributed optimisation problems. The strength of our result lies in the bridge between practical verifiable network conditions and an abstract optimisation theory. We illustrate numerically that our algorithm converges in an extreme scenario where the average AoI diverges.

More and more management and orchestration approaches for (software) networks are based on machine learning paradigms and solutions. These approaches depend not only on their program code to operate properly, but also require enough input data to train their internal models. However, such training data is barely available for the software networking domain and most presented solutions rely on their own, sometimes not even published, data sets. This makes it hard, or even infeasible, to reproduce and compare many of the existing solutions. As a result, it ultimately slows down the adoption of machine learning approaches in softwarised networks. To this end, we introduce the "softwarised network data zoo" (SNDZoo), an open collection of software networking data sets aiming to streamline and ease machine learning research in the software networking domain. We present a general methodology to collect, archive, and publish those data sets for use by other researches and, as an example, eight initial data sets, focusing on the performance of virtualised network functions., Comment: IEEE/IFIP 15th International Conference on Network and Service Management (CNSM), Halifax, Canada. 2019

In many Cyber-Physical Systems, we encounter the problem of remote state estimation of geographically distributed and remote physical processes. This paper studies the scheduling of sensor transmissions to estimate the states of multiple remote, dynamic processes. Information from the different sensors have to be transmitted to a central gateway over a wireless network for monitoring purposes, where typically fewer wireless channels are available than there are processes to be monitored. For effective estimation at the gateway, the sensors need to be scheduled appropriately, i.e., at each time instant one needs to decide which sensors have network access and which ones do not. To address this scheduling problem, we formulate an associated Markov decision process (MDP). This MDP is then solved using a Deep Q-Network, a recent deep reinforcement learning algorithm that is at once scalable and model-free. We compare our scheduling algorithm to popular scheduling algorithms such as round-robin and reduced-waiting-time, among others. Our algorithm is shown to significantly outperform these algorithms for many example scenarios.

For optimal placement and orchestration of network services, it is crucial that their structure and semantics are specified clearly and comprehensively and are available to an orchestrator. Existing specification approaches are either ambiguous or miss important aspects regarding the behavior of virtual network functions (VNFs) forming a service. We propose to formally and unambiguously specify the behavior of these functions and services using Queuing Petri Nets (QPNs). QPNs are an established method that allows to express queuing, synchronization, stochastically distributed processing delays, and changing traffic volume and characteristics at each VNF. With QPNs, multiple VNFs can be connected to complete network services in any structure, even specifying bidirectional network services containing loops. We propose a tool-based workflow that supports the specification of network services and the automatic generation of corresponding simulation code to enable an in-depth analysis of their behavior and performance. In a case study, we show how developers can benefit from analysis insights, e.g., to anticipate the impact of different service configurations. We also discuss how management and orchestration systems can benefit from our clear and comprehensive specification approach and its extensive analysis possibilities, leading to better placement of VNFs and improved Quality of Service., Comment: 9 pages

We consider networked control systems consisting of multiple independent controlled subsystems, operating over a shared communication network. Such systems are ubiquitous in cyber-physical systems, Internet of Things, and large-scale industrial systems. In many large-scale settings, the size of the communication network is smaller than the size of the system. In consequence, scheduling issues arise. The main contribution of this paper is to develop a deep reinforcement learning-based \emph{control-aware} scheduling (\textsc{DeepCAS}) algorithm to tackle these issues. We use the following (optimal) design strategy: First, we synthesize an optimal controller for each subsystem; next, we design a learning algorithm that adapts to the chosen subsystems (plants) and controllers. As a consequence of this adaptation, our algorithm finds a schedule that minimizes the \emph{control loss}. We present empirical results to show that \textsc{DeepCAS} finds schedules with better performance than periodic ones.

Recent studies show the increasing popularity of distributed cloud applications, which are composed of multiple microservices. Besides their known benefits, microservice architecture also enables to mix and match cloud applications and Network Function Virtualization (NFV) services (service chains), which are composed of Virtual Network Functions (VNFs). Provisioning complex services containing VNFs and microservices in a combined NFV/cloud platform can enhance service quality and optimise cost. Such a platform can be based on the multi-cloud concept. However, current multi-cloud solutions do not support NFV requirements, making them inadequate to support complex services. In this paper, we investigate these challenges and propose a solution for jointly managing and orchestrating microservices and virtual network functions., Comment: Accepted in The Ninth International Conferences on Cloud Computing, GRIDs, and Virtualization

When deploying resource-intensive signal processing applications in wireless sensor or mesh networks, distributing processing blocks over multiple nodes becomes promising. Such distributed applications need to solve the placement problem (which block to run on which node), the routing problem (which link between blocks to map on which path between nodes), and the scheduling problem (which transmission is active when). We investigate a variant where the application graph may contain feedback loops and we exploit wireless networks? inherent multicast advantage. Thus, we propose Multicast-Aware Routing for Virtual network Embedding with Loops in Overlays (MARVELO) to find efficient solutions for scheduling and routing under a detailed interference model. We cast this as a mixed integer quadratically constrained optimisation problem and provide an efficient heuristic. Simulations show that our approach handles complex scenarios quickly., Comment: 6 pages

To adapt to continuously changing workloads in networks, components of the running network services may need to be replicated (scaling the network service) and allocated to physical resources (placement) dynamically, also necessitating dynamic re-routing of flows between service components. In this paper, we propose JASPER, a fully automated approach to jointly optimizing scaling, placement, and routing for complex network services, consisting of multiple (virtualized) components. JASPER handles multiple network services that share the same substrate network; services can be dynamically added or removed and dynamic workload changes are handled. Our approach lets service designers specify their services on a high level of abstraction using service templates. From the service templates and a description of the substrate network, JASPER automatically makes scaling, placement and routing decisions, enabling quick reaction to changes. We formalize the problem, analyze its complexity, and develop two algorithms to solve it. Extensive empirical results show the applicability and effectiveness of the proposed approach.

Allocating resources to virtualized network functions and services to meet service level agreements is a challenging task for NFV management and orchestration systems. This becomes even more challenging when agile development methodologies, like DevOps, are applied. In such scenarios, management and orchestration systems are continuously facing new versions of functions and services which makes it hard to decide how much resources have to be allocated to them to provide the expected service performance. One solution for this problem is to support resource allocation decisions with performance behavior information obtained by profiling techniques applied to such network functions and services. In this position paper, we analyze and discuss the components needed to generate such performance behavior information within the NFV DevOps workflow. We also outline research questions that identify open issues and missing pieces for a fully integrated NFV profiling solution. Further, we introduce a novel profiling mechanism that is able to profile virtualized network functions and entire network service chains under different resource constraints before they are deployed on production infrastructure., Comment: Submitted to and accepted by the European Workshop on Software Defined Networks (EWSDN) 2016

Virtualized network services consisting of multiple individual network functions are already today deployed across multiple sites, so called multi-PoP (points of presence) environ- ments. This allows to improve service performance by optimizing its placement in the network. But prototyping and testing of these complex distributed software systems becomes extremely challenging. The reason is that not only the network service as such has to be tested but also its integration with management and orchestration systems. Existing solutions, like simulators, basic network emulators, or local cloud testbeds, do not support all aspects of these tasks. To this end, we introduce MeDICINE, a novel NFV prototyping platform that is able to execute production-ready network func- tions, provided as software containers, in an emulated multi-PoP environment. These network functions can be controlled by any third-party management and orchestration system that connects to our platform through standard interfaces. Based on this, a developer can use our platform to prototype and test complex network services in a realistic environment running on his laptop., Comment: 6 pages, pre-print

In conventional large-scale networks, creation and management of network services are costly and complex tasks that often consume a lot of resources, including time and manpower. Network softwarization and network function virtualization have been introduced to tackle these problems. They replace the hardware-based network service components and network control mechanisms with software components running on general-purpose hardware, aiming at decreasing costs and complexity of implementing new services, maintaining the implemented services, and managing available resources in service provisioning platforms and underlying infrastructures. To experience the full potential of these approaches, innovative development support tools and service provisioning environments are needed. To answer these needs, we introduce the SONATA architecture, a service programming, orchestration, and management framework. We present a development toolchain for virtualized network services, fully integrated with a service platform and orchestration system. We motivate the modular and flexible architecture of our system and discuss its main components and features, such as function- and service-specific managers that allow fine- grained service management, slicing support to facilitate multi-tenancy, recursiveness for improved scalability, and full-featured DevOps support.

A current trend in networking and cloud computing is to provide compute resources over widely dispersed places exemplified by initiatives like Network Function Virtualisation. This paves the way for a widespread service deployment and can improve service quality; a nearby server can reduce the user-perceived response times. But always using the nearest server is a bad decision if that server is already highly utilized. This paper investigates the optimal assignment of users to widespread resources -- a convex capacitated facility location problem with integrated queuing systems. We determine the response times depending on the number of used resources. This enables service providers to balance between resource costs and the corresponding service quality. We also present a linear problem reformulation showing small optimality gaps and faster solving times; this speed-up enables a swift reaction to demand changes. Finally, we compare solutions by either considering or ignoring queuing systems and discuss the response time reduction by using the more complex model. Our investigations are backed by large-scale numerical evaluations.

A current trend in networking and cloud computing is to provide compute resources at widely dispersed places; this is exemplified by developments such as Network Function Virtualisation. This paves the way for wide-area service deployments with improved service quality: e.g, a nearby server can reduce the user-perceived response times. But always using the nearest server can be a bad decision if that server is already highly utilised. This paper formalises the two related problems of allocating resources at different locations and assigning users to them with the goal of minimising the response times for a given number of resources to use -- a non-linear capacitated facility location problem with integrated queuing systems. To efficiently handle the non-linearity, we introduce five linear problem approximations and adapt the currently best heuristic for a similar problem to our scenario. All six approaches are compared in experiments for solution quality and solving time. Surprisingly, our best optimisation formulation outperforms the heuristic in both time and quality. Additionally, we evaluate the influence ot resource distributions in the network on the response time: Cut by half for some configurations. The presented formulations are applicable to a broader optimisation domain.

The size of modern data centers is constantly increasing. As it is not economic to interconnect all machines in the data center using a full-bisection-bandwidth network, techniques have to be developed to increase the efficiency of data-center networks. The Software-Defined Network paradigm opened the door for centralized traffic engineering (TE) in such environments. Up to now, there were already a number of TE proposals for SDN-controlled data centers that all work very well. However, these techniques either use a high amount of flow table entries or a high flow installation rate that overwhelms available switching hardware, or they require custom or very expensive end-of-line equipment to be usable in practice. We present HybridTE, a TE technique that uses (uncertain) information about large flows. Using this extra information, our technique has very low hardware requirements while maintaining better performance than existing TE techniques. This enables us to build very low-cost, high performance data-center networks.

The coordination of base stations in mobile access networks is an important approach to reduce harmful interference and to deliver high data rates to the users. Such coordination mechanisms, like Coordinated Multi-Point (CoMP) where multiple BSs transmit data to a user equipment, can be easily implemented when centralizing the data processing of the base stations, known as Cloud RAN. This centralization also imposes significant requirements on the backhaul network for high capacities and low latencies for the connections to the base stations. These requirements can be mitigated by (a) a flexible placement of the base station data processing functionality and by (b) dynamically assigning backhaul network resources. We show how these two techniques increase the feasibility of base station coordination in dense mobile access networks by using a heuristic algorithm. We furthermore present a prototype implementation of our approach based on software defined networking (SDN) with OpenDaylight and Maxinet.

While services benefit from distributed cloud centers running in isolation, allowing multiple centers to cooperate on implementing services unlocks the full power of distributed cloud computing. Distributed cloud services are typically set up by chaining together a number of functions that are specified with an implicit order. They can incorporate complex structures, e.g., include functions that classify and forward flows over distinct branches and functions that are traversed by certain types of flows but skipped by others. These requirements need specification techniques more powerful than existing graph-based ones. We present a context-free grammar for abstract description of service function chaining structures and a concrete syntax based on the YANG data modeling language that can easily be translated into an explicit configuration of service functions. Finally, we present examples of using our models for complex services within common use cases of service function chaining.

To study large-scale effects on the Internet various mod- els have been introduced to generate Internet-like autono- mous system (AS) topologies. The models for large-scale AS topologies have been focused on replicating structural graph properties. One of the most promising model is the Positive Feedback Model model (PFP). These models how- ever lack the ability to generate routing path and realistic latency. We present a model to enrich the AS peering graph with peering points. Our new model allows to calculate path for the connections between end hosts and to infer the latency from these paths. We introduce a new notion for the genera- tion of AS topologies: the compactness of an AS. We introduce an algorithm based on the PFP algorithm which generates instances for our model. Verifying the gen- erated model instances shows that the resulting latencies as well as the geographic properties match measured data sets.

Only little is publicly known about traffic in non-educational data centers. Recent studies made some knowledge available, which gives us the opportunity to create more realistic traffic models for data center research. We used this knowledge to create the first publicly available traffic generator that produces realistic traffic between hosts in data centers of arbitrary size. We characterize traffic by using six probability distribution functions and concentrate on the generation of traffic on flow-level. The distribution functions are described as step functions, which makes our generator highly configurable to generate traffic for different kinds of data centers. Moreover, in data centers, traffic between hosts in the same rack and hosts in different racks have different properties. We model this phenomenon, making our generated traffic very realistic. We carefully evaluated our approach and conclude that it reproduces these characteristics with high accuracy.

Network appliances perform different functions on network flows and constitute an important part of an operator's network. Normally, a set of chained network functions process network flows. Following the trend of virtualization of networks, virtualization of the network functions has also become a topic of interest. We define a model for formalizing the chaining of network functions using a context-free language. We process deployment requests and construct virtual network function graphs that can be mapped to the network. We describe the mapping as a Mixed Integer Quadratically Constrained Program (MIQCP) for finding the placement of the network functions and chaining them together considering the limited network resources and requirements of the functions. We have performed a Pareto set analysis to investigate the possible trade-offs between different optimization objectives.

Video streaming is in high demand by mobile users, as recent studies indicate. In cellular networks, however, the unreliable wireless channel leads to two major problems. Poor channel states degrade video quality and interrupt the playback when a user cannot sufficiently fill its local playout buffer: buffer underruns occur. In contrast to that, good channel conditions cause common greedy buffering schemes to pile up very long buffers. Such over-buffering wastes expensive wireless channel capacity. To keep buffering in balance, we employ a novel approach. Assuming that we can predict data rates, we plan the quality and download time of the video segments ahead. This anticipatory scheduling avoids buffer underruns by downloading a large number of segments before a channel outage occurs, without wasting wireless capacity by excessive buffering. We formalize this approach as an optimization problem and derive practical heuristics for segmented video streaming protocols (e.g., HLS or MPEG DASH). Simulation results and testbed measurements show that our solution essentially eliminates playback interruptions without significantly decreasing video quality.