Optimisation Problems in Wireless Sensor Networks : Local Algorithms and Local Graphs

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

Optimisation problems in wireless sensor networks

This thesis studies optimisation problems related to modern large-scale distributed systems, such as wireless sensor networks and wireless ad-hoc networks. The concrete tasks that we use as motivating examples are the following: (i) maximising the lifetime of a battery-powered wireless sensor network, (ii) maximising the capacity of a wireless communication network, and (iii) minimising the number of sensors in a surveillance application. A sensor node consumes energy both when it is transmitting or forwarding data, and when it is performing measurements. Hence task (i), lifetime maximisation, can be approached from two different perspectives. First, we can seek for optimal data flows that make the most out of the energy resources available in the network; such optimisation problems are examples of so-called max-min linear programs. Second, we can conserve energy by putting redundant sensors into sleep mode; we arrive at the sleep scheduling problem, in which the objective is to find an optimal schedule that determines when each sensor node is asleep and when it is awake. In a wireless network simultaneous radio transmissions may interfere with each other. Task (ii), capacity maximisation, therefore gives rise to another scheduling problem, the activity scheduling problem, in which the objective is to find a minimum-length conflict-free schedule that satisfies the data transmission requirements of all wireless communication links. Task (iii), minimising the number of sensors, is related to the classical graph problem of finding a minimum dominating set. However, if we are not only interested in detecting an intruder but also locating the intruder, it is not sufficient to solve the dominating set problem; formulations such as minimum-size identifying codes and locating–dominating codes are more appropriate. This thesis presents approximation algorithms for each of these optimisation problems, i.e., for max-min linear programs, sleep scheduling, activity scheduling, identifying codes, and locating–dominating codes. Two complementary approaches are taken. The main focus is on local algorithms, which are constant-time distributed algorithms. The contributions include local approximation algorithms for max-min linear programs, sleep scheduling, and activity scheduling. In the case of max-min linear programs, tight upper and lower bounds are proved for the best possible approximation ratio that can be achieved by any local algorithm. The second approach is the study of centralised polynomial-time algorithms in local graphs – these are geometric graphs whose structure exhibits spatial locality. Among other contributions, it is shown that while identifying codes and locating–dominating codes are hard to approximate in general graphs, they admit a polynomial-time approximation scheme in local graphs.

IP Mobility in Wireless Operator Networks

Wireless network access is gaining increased heterogeneity in terms of the types of IP capable access technologies. The access network heterogeneity is an outcome of incremental and evolutionary approach of building new infrastructure. The recent success of multi-radio terminals drives both building a new infrastructure and implicit deployment of heterogeneous access networks. Typically there is no economical reason to replace the existing infrastructure when building a new one. The gradual migration phase usually takes several years. IP-based mobility across different access networks may involve both horizontal and vertical handovers. Depending on the networking environment, the mobile terminal may be attached to the network through multiple access technologies. Consequently, the terminal may send and receive packets through multiple networks simultaneously. This dissertation addresses the introduction of IP Mobility paradigm into the existing mobile operator network infrastructure that have not originally been designed for multi-access and IP Mobility. We propose a model for the future wireless networking and roaming architecture that does not require revolutionary technology changes and can be deployed without unnecessary complexity. The model proposes a clear separation of operator roles: (i) access operator, (ii) service operator, and (iii) inter-connection and roaming provider. The separation allows each type of an operator to have their own development path and business models without artificial bindings with each other. We also propose minimum requirements for the new model. We present the state of the art of IP Mobility. We also present results of standardization efforts in IP-based wireless architectures. Finally, we present experimentation results of IP-level mobility in various wireless operator deployments.

TCP Performance in Heterogeneous Wireless Networks

The TCP protocol is used by most Internet applications today, including the recent mobile wireless terminals that use TCP for their World-Wide Web, E-mail and other traffic. The recent wireless network technologies, such as GPRS, are known to cause delay spikes in packet transfer. This causes unnecessary TCP retransmission timeouts. This dissertation proposes a mechanism, Forward RTO-Recovery (F-RTO) for detecting the unnecessary TCP retransmission timeouts and thus allow TCP to take appropriate follow-up actions. We analyze a Linux F-RTO implementation in various network scenarios and investigate different alternatives to the basic algorithm. The second part of this dissertation is focused on quickly adapting the TCP's transmission rate when the underlying link characteristics change suddenly. This can happen, for example, due to vertical hand-offs between GPRS and WLAN wireless technologies. We investigate the Quick-Start algorithm that, in collaboration with the network routers, aims to quickly probe the available bandwidth on a network path, and allow TCP's congestion control algorithms to use that information. By extensive simulations we study the different router algorithms and parameters for Quick-Start, and discuss the challenges Quick-Start faces in the current Internet. We also study the performance of Quick-Start when applied to vertical hand-offs between different wireless link technologies.

Analysis of Heterogeneous IP Traffic in Wireless Environment

Wireless access is expected to play a crucial role in the future of the Internet. The demands of the wireless environment are not always compatible with the assumptions that were made on the era of the wired links. At the same time, new services that take advantage of the advances in many areas of technology are invented. These services include delivery of mass media like television and radio, Internet phone calls, and video conferencing. The network must be able to deliver these services with acceptable performance and quality to the end user. This thesis presents an experimental study to measure the performance of bulk data TCP transfers, streaming audio flows, and HTTP transfers which compete the limited bandwidth of the GPRS/UMTS-like wireless link. The wireless link characteristics are modeled with a wireless network emulator. We analyze how different competing workload types behave with regular TPC and how the active queue management, the Differentiated services (DiffServ), and a combination of TCP enhancements affect the performance and the quality of service. We test on four link types including an error-free link and the links with different Automatic Repeat reQuest (ARQ) persistency. The analysis consists of comparing the resulting performance in different configurations based on defined metrics. We observed that DiffServ and Random Early Detection (RED) with Explicit Congestion Notification (ECN) are useful, and in some conditions necessary, for quality of service and fairness because a long queuing delay and congestion related packet losses cause problems without DiffServ and RED. However, we observed situations, where there is still room for significant improvements if the link-level is aware of the quality of service. Only very error-prone link diminishes the benefits to nil. The combination of TCP enhancements improves performance. These include initial window of four, Control Block Interdependence (CBI) and Forward RTO recovery (F-RTO). The initial window of four helps a later starting TCP flow to start faster but generates congestion under some conditions. CBI prevents slow-start overshoot and balances slow start in the presence of error drops, and F-RTO reduces unnecessary retransmissions successfully.