Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Network virtualization is enabling infrastructure providers (InPs) to offer new services to service providers (SPs). InPs are usually bound by service level agreements to ensure various levels of resource availability for different SPs’ virtual networks (VNs). They provision redundant backup resources while embedding an SP’s VN request to conform to the SLAs during physical failures in the infrastructure. An extreme backup resource provisioning is to reserve a mutually exclusive backup of each element in an SP’s VN request. Such dedicated protection scheme can enable an InP to ensure fast VN recovery, thus, providing high uptime guarantee to the SPs. In this paper, we study the 1 + 1-Protected Virtual Network Embedding (1 + 1-ProViNE) problem. We propose Dedicated Protection for Virtual Network Embedding ( DRONE ), a suite of solutions to the 1 + 1-ProViNE problem. DRONE includes an integer linear programming formulation for optimal solution ( OPT-DRONE ) and a heuristic ( FAST-DRONE ) to tackle the computational complexity of the optimal solution. Trace driven simulations show that FAST-DRONE allocates only 14.3% extra backup resources on average compared to the optimal solution, while executing 200–1200 times faster. Simulation results also show that FAST-DRONE can accept four times more VN requests on average compared to the state-of-the-art solution for providing dedicated protection to VNs.

Dedicated Protection for Survivable Virtual Network Embedding

Network Virtualization (NV) has recently been considered as a key feature of the Future Internet because it allows easy transition from existing IPv4 based Internet to new mechanisms and protocols, and a more efficient usage of infrastructure by sharing it with different virtual network operators while deploying new services. However, Network Virtualization also raises new challenges for network operators [1]. One of the main challenges is the efficient resource allocation, known as virtual network mapping problem, in which virtual nodes and links are embedded to specific substrate nodes and paths. In this paper, we study this problem for the online scenario, where virtual network requests come and leave dynamically while considering the ability to reconfigure (re-arrange) the currently mapped virtual networks. All the recent research on this topic just focuses on the acceptance ratio of the virtual networks but do not address the possible service disruption during the reconfiguration. This paper proposes a so-called reactive reconfiguration mechanism, which reacts to any rejection of new coming virtual network requests. If a virtual network is rejected due to the lack of physical resources, the mechanism is triggered to reconfigure the currently-mapped networks so that the new request can be embedded. At the same time, it minimizes the number of necessary changes to reduce the service disruption. The mechanism is mathematically formulated as Integer Linear Programming (ILP) problem and solved by CPLEX [2]. Its performance is then evaluated through extensive simulations and compared with the case of no reconfiguration. A heuristic is then proposed to speed up the solving time of the ILP problem while maintaining its performance.

Optimal mapping of virtual networks considering reactive reconfiguration

The problem of ensuring virtual network (VN) connectivity in presence of multiple link failures in the substrate network (SN) is not well investigated in Network Virtualization (NV) literature. We name this problem as Connectivity-aware Virtual Network Embedding (CoViNE). Solving CoViNE will enable a VN operator to perform failure recovery without depending on the SN provider, similar to the IP restoration mechanisms in IP-over-WDM networks. There are two steps in solving CoViNE: i) finding the virtual links that should be embedded disjointly, and ii) finding a substrate resource efficient embedding that ensures the virtual link disjointness constraint. We present two solutions to the CoViNE problem. The first solution uses a heuristic to compute the disjointness constraint, while an optimization model is used for VN embedding. The second solution, in contrast, uses heuristic for both the steps, and thus can solve larger instances of the problem. We compare our solutions with a cut set based approach that ensures VN connectivity for a single substrate link failure. Evaluation results show that our heuristics allocate ∼15% extra resources on average compared to the cut set based optimal solution, and executes two to three orders of magnitude faster on the same problem instances.

Connectivity-aware virtual network embedding

Adaptive multi-objective artificial immune system based virtual network embedding

Network Virtualization is claimed to be a key component of the Future Internet by enabling the coexistence of heterogeneous (virtual) networks on the same physical infrastructure, providing the dynamic creation and support of different networks with different paradigms and mechanisms in the same physical network. A major challenge in the dynamic provision of virtual networks resides on the efficient embedding of virtual resources into physical ones. Since this problem is known to be \(\mathcal{NP}\)-hard, previous research focused on designing heuristic-based algorithms; most of them do not consider a simultaneous optimization of the node and the link mapping, leading to non-optimal solutions. This paper proposes an integer linear programming formulation to solve the virtual network embedding problem, as a simultaneous optimization of virtual nodes and links placement, providing the optimal boundary for each virtual network mapping. A link − node formulation is used and the multi-commodity flow constrain is applied. In addition, a heuristic algorithm for virtual network embedding is also proposed and compared against the optimal formulation. The performance of the integer linear programming formulation and of the heuristic is evaluated by means of simulation. Simulation experiments show significant improvements of the virtual network acceptance ratio, in average additional 10% of the virtual network requests are accepted when using the integer linear programming formulation, which corresponds, in average, to more 7 virtual networks accommodated on the physical network.

Virtual Network Mapping – An Optimization Problem

/pdf/virtual-network-mapping-an-optimization-problem-27wl00qp2j.pdf

Enabling integration of Wireless Sensor Networks (WSN) and smart objects with the Internet is an important milestone towards the so called Internet of Things. Providing these networks with QoS capabilities is crucial for emerging applications that have end-to-end requirements on the border wireless network domain. Impairments such as delays and losses are heavily influenced by the quality of the communication channels, the routing, the MAC protocol and the interactions of these influential factors. In this work we report on a hierarchical routing scheme for sensor networks with multi-channel radios aiming at improving QoS. The scheme decouples the aforementioned influences: The MAC-protocol is responsible for a scheduling in a set of nodes called a cluster. Neighboring clusters use different frequencies. The routing is done at the level of clusters. The (distributed) algorithms executed by the network nodes to support this architecture are evaluated against optimal solutions for clustering, frequency allocation and routing derived from Integer Linear Programming.

QoS Impact of Hierarchical Routing in Multi-channel Sensor Networks

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Virtual Network Mapping – An Optimization Problem

Virtual Network Mapping – An Optimization Problem

QoS Impact of Hierarchical Routing in Multi-channel Sensor Networks