Network Slicing for Wireless Networks Operating in a Shared Spectrum Environment

Network slicing is a very common practice in modern computer networks. It can serve as an efficient way to distribute network resources to physical groups of users, and allows the network to provide performance guarantees in terms of the Quality of Service. Physical links are divided logically and are assigned on a per-service basis to accomplish this. Traditionally, network slicing has been done mostly in wired networks, and bringing these practices to wireless networks has only been done recently. The main contribution of this thesis is network slicing applied to wireless environments where multiple adjacent networks are forced to share the same spectrum, namely in LTE and 5G. Spectrum in the sub-6GHz range is crowded by a wide range of services, and managing interference between networks is often challenging. A modified graph coloring technique is used both as a means to identify areas of interference and overlap between two networks, as well as assign spectrum resources to each node in an efficient manner. A central entity, known as the ”Overseer”, was developed as a bridge to pass interference-related information between the two coexisting networks. Performance baselines were first gathered for network slicing in a single-network scenario, followed by the introduction of a second network and the evaluation of the efficacy of the graph coloring approach. In the cases of highest interference from the secondary network, the modified graph coloring approach provided more than 22.3% reduction in median user delay, and more than 36.0% increase in median single-user and slice-aggregate throughput across all three network slices compared to the non-graph coloring scenario

A Framework for Service Differentiation and Optimization in Multi-hop Wireless Networks

In resource-constrained networks such as multi-hop wireless networks (MHWNs), service differentiation algorithms designed to address end users' interests (e.g. user satisfaction, QoS, etc.) should also consider efficient utilization of the scarce network resources in order to maximize the network's interests (e.g. revenue). For this very reason, service differentiation in MHWNs is quite different from the wired network scenario. We propose a service differentiation tool called the ``Investment Function'', which essentially captures the network's cumulative resource investment in a given packet at a given time. This investment value can be used by the network algorithm to implement specific service differentiation principles. As proof-of-concept, we use the investment function to improve fairness among simultaneous flows that traverse varying number of hops in a MHWN (multihop flow fairness). However, to attain the optimal value of a specific service differentiation objective, optimal service differentiation and investment function parameters may need to be computed. The optimal parameters can be computed by casting the service differentiation problem as a network flow problem in MHWNs, with the goal of optimizing the service differentiation objective. The capacity constraints for these problems require knowledge of the adjacent-node interference values, and constructing these constraints could be very expensive based on the transmission scheduling scheme used. As a result, even formulating the optimization problem may take unacceptable computational effort or memory or both. Under optimal scheduling, the adjacent node interference values (and thus the capacity constraints) are not only very expensive to compute, but also cannot be expressed in polynomial form. Therefore, existing optimization techniques cannot be directly applied to solve optimization problems in MHWNs. To develop an efficient optimization framework, we first model the MHWN as a Unit Disk Graph (UDG). The optimal transmission schedule in the MHWN is related to the chromatic number of the UDG, which is very expensive to compute. However, the clique number, which is a lower bound on the chromatic number, can be computed in polynomial time in UDGs. Through an empirical study, we obtain tighter bounds on the ratio of the chromatic number to clique number in UDGs, which enables us to leverage existing polynomial time clique-discovery algorithms to compute very close approximations to the chromatic number value. This approximation not only allows us to quickly formulate the capacity constraints in polynomial form, but also allows us to significantly deviate from the traditional approach of discovering all or most of the constraints \textit{a priori}; instead, we can discover the constraints as needed. We have integrated this approach of constraint-discovery into an active-set optimization algorithm (Gradient Projection method) to solve network flow problems in multi-hop wireless networks. Our results show significant memory and computational savings when compared to existing methods

Design, Analysis and Computation in Wireless and Optical Networks

abstract: In the realm of network science, many topics can be abstracted as graph problems, such as routing, connectivity enhancement, resource/frequency allocation and so on. Though most of them are NP-hard to solve, heuristics as well as approximation algorithms are proposed to achieve reasonably good results. Accordingly, this dissertation studies graph related problems encountered in real applications. Two problems studied in this dissertation are derived from wireless network, two more problems studied are under scenarios of FIWI and optical network, one more problem is in Radio- Frequency Identification (RFID) domain and the last problem is inspired by satellite deployment. The objective of most of relay nodes placement problems, is to place the fewest number of relay nodes in the deployment area so that the network, formed by the sensors and the relay nodes, is connected. Under the fixed budget scenario, the expense involved in procuring the minimum number of relay nodes to make the network connected, may exceed the budget. In this dissertation, we study a family of problems whose goal is to design a network with “maximal connectedness” or “minimal disconnectedness”, subject to a fixed budget constraint. Apart from “connectivity”, we also study relay node problem in which degree constraint is considered. The balance of reducing the degree of the network while maximizing communication forms the basis of our d-degree minimum arrangement(d-MA) problem. In this dissertation, we look at several approaches to solving the generalized d-MA problem where we embed a graph onto a subgraph of a given degree. In recent years, considerable research has been conducted on optical and FIWI networks. Utilizing a recently proposed concept “candidate trees” in optical network, this dissertation studies counting problem on complete graphs. Closed form expressions are given for certain cases and a polynomial counting algorithm for general cases is also presented. Routing plays a major role in FiWi networks. Accordingly to a novel path length metric which emphasizes on “heaviest edge”, this dissertation proposes a polynomial algorithm on single path computation. NP-completeness proof as well as approximation algorithm are presented for multi-path routing. Radio-frequency identification (RFID) technology is extensively used at present for identification and tracking of a multitude of objects. In many configurations, simultaneous activation of two readers may cause a “reader collision” when tags are present in the intersection of the sensing ranges of both readers. This dissertation ad- dresses slotted time access for Readers and tries to provide a collision-free scheduling scheme while minimizing total reading time. Finally, this dissertation studies a monitoring problem on the surface of the earth for significant environmental, social/political and extreme events using satellites as sensors. It is assumed that the impact of a significant event spills into neighboring regions and there will be corresponding indicators. Careful deployment of sensors, utilizing “Identifying Codes”, can ensure that even though the number of deployed sensors is fewer than the number of regions, it may be possible to uniquely identify the region where the event has taken place.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Random graph models for wireless communication networks

PhDThis thesis concerns mathematical models of wireless communication networks, in particular ad-hoc networks and 802:11 WLANs. In ad-hoc mode each of these devices may function as a sender, a relay or a receiver. Each device may only communicate with other devices within its transmission range. We use graph models for the relationship between any two devices: a node stands for a device, and an edge for a communication link, or sometimes an interference relationship. The number of edges incident on a node is the degree of this node. When considering geometric graphs, the coordinates of a node give the geographical position of a node. One of the important properties of a communication graph is its connectedness | whether all nodes can reach all other nodes. We use the term connectivity, the probability of graphs being connected given the number of nodes and the transmission range to measure the connectedness of a wireless network. Connectedness is an important prerequisite for all communication networks which communication between nodes. This is especially true for wireless ad-hoc networks, where communication relies on the contact among nodes and their neighbours. Another important property of an interference graph is its chromatic number | the minimum number of colours needed so that no adjacent nodes are assigned the same colour. Here adjacent nodes share an edge; adjacent edges share at least one node; and colours are used to identify di erent frequencies. This gives the minimum number of frequencies a network needs in order to attain zero interference. This problem can be solved as an optimization problem deterministically, but is algorithmically NP-hard. Hence, nding good asymptotic approximations for this value becomes important. Random geometric graphs describe an ensemble of graphs which share common features. In this thesis, node positions follow a Poisson point process or a binomial point process. We use probability theory to study the connectedness of random graphs and random geometric graphs, which is the fraction of connected graphs among many graph samples. This probability is closely related to the property of minimum node degree being at least unity. The chromatic number is closely related to the maximum degree as n ! 1; the chromatic number converges to maximum degree when graph is sparse. We test existing theorems and improve the existing ones when possible. These motivated me to study the degree of random (geometric) graph models. We study using deterministic methods some degree-related problems for Erda}os-R enyi random graphs G(n; p) and random geometric graphs G(n; r). I provide both theoretical analysis and accurate simulation results. The results lead to a study of dependence or non-dependence in the joint distribution of the degrees of neighbouring nodes. We study the probability of no node being isolated in G(n; p), that is, minimum node degree being at least unity. By making the assumption of non-dependence of node degree, we derive two asymptotics for this probability. The probability of no node being isolated is an approximation to the probability of the graph being connected. By making an analogy to G(n; p), we study this problem for G(n; r), which is a more realistic model for wireless networks. Experiment shows that this asymptotic result also works well for small graphs. We wish to nd the relationship between these basic features the above two important problems of wireless networks: the probability of a network being connected and the minimum number of channels a network needs in order to minimize interference. Inspired by the problem of maximum degree in random graphs, we study the problem of the maximum of a set of Poisson random variables and binomial random variables, which leads to two accurate formulae for the mode of the maximum for general random geometric graphs and for sparse random graphs. To our knowledge, these are the best results for sparse random geometric graphs in the literature so far. By approximating the node degrees as independent Poisson or binomial variables, we apply the result to the problem of maximum degree in general and sparse G(n; r), and derived much more accurate results than in the existing literature. Combining the limit theorem from Penrose and our work, we provide good approximations for the mode of the clique number and chromatic number in sparse G(n; r). Again these results are much more accurate than existing ones. This has implications for the interference minimization of WLANs. Finally, we apply our asymptotic result based on Poisson distribution for the chromatic number of random geometric graph to the interference minimization problem in IEEE 802:11b/g WLAN. Experiments based on the real planned position of the APs in WLANs show that our asymptotic results estimate the minimum number of channels needed accurately. This also means that sparse random geometric graphs are good models for interference minimization problem of WLANs. We discuss the interference minimization problem in single radio and multi-radio wireless networking scenarios. We study branchand- bound algorithms for these scenarios by selecting di erent constraint functions and objective functions

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

Industry applications of neutral-atom quantum computing solving independent set problems

Architectures for quantum computing based on neutral atoms have risen to prominence as candidates for both near and long-term applications. These devices are particularly well suited to solve independent set problems, as the combinatorial constraints can be naturally encoded in the low-energy Hilbert space due to the Rydberg blockade mechanism. Here, we approach this connection with a focus on a particular device architecture and explore the ubiquity and utility of independent set problems by providing examples of real-world applications. After a pedagogical introduction of basic graph theory concepts of relevance, we briefly discuss how to encode independent set problems in Rydberg Hamiltonians. We then outline the major classes of independent set problems and include associated example applications with industry and social relevance. We determine a wide range of sectors that could benefit from efficient solutions of independent set problems -- from telecommunications and logistics to finance and strategic planning -- and display some general strategies for efficient problem encoding and implementation on neutral-atom platforms.Comment: 28 pages, 9 example application