Katerina Papadaki

Patrolling Games

A key operational problem for those charged with the security of vulnerable facilities (such as airports or art galleries) is the scheduling and deployment of patrols. Motivated by the problem of optimizing randomized, and thus unpredictable, patrols, we present a class of patrolling games. The facility to be patrolled can be thought of as a network or graph Q of interconnected nodes (e.g., rooms, terminals), and the Attacker can choose to attack any node of Q within a given time T. He requires m consecutive periods there, uninterrupted by the Patroller, to commit his nefarious act (and win). The Patroller can follow any path on the graph. Thus, the patrolling game is a win-lose game, where the Value is the probability that the Patroller successfully intercepts an attack, given best play on both sides. We determine analytically either the Value of the game, or bounds on the Value, for various classes of graphs, and we discuss possible extensions and generalizations.

Approximate dynamic programming for link scheduling in wireless mesh networks

In this paper a novel interference-based formulation and solution methodology for the problem of link scheduling in wireless mesh networks is proposed. Traditionally, this problem has been formulated as a deterministic integer program, which has been shown to be NP-hard. The proposed formulation is based on dynamic programming and allows greater flexibility since dynamic and stochastic components of the problem can be embedded into the optimization framework. By temporal decomposition we reduce the size of the integer program and using approximate dynamic programming (ADP) methods we tackle the curse of dimensionality. The numerical results reveal that the proposed algorithm outperforms well-known heuristics under different network topologies. Finally, the proposed ADP methodology can be used not only as an upper bound but also as a generic framework where different heuristics can be integrated.

Future Wireless Mobile Networks

In this article, the authors outline some key benefits that stem from the use of mechanical relaying within or across the cells in future wireless mobile networks. The authors have argued that, when information messages that can be stored are elastic enough and subsequently carried by mobile nodes, before relayed to other terminals or the BS at a later time, interference and energy consumption levels can be dramatically decreased during network operation due to the locality of the transmissions. In addition, mechanical relaying allows for innovative resource-management techniques to be deployed in the network, such as providing load balancing or switching-off BSs with low levels of utilization. To fully understand the issues regarding mechanical relaying, it is necessary to examine in a more detailed manner the required architectural changes together with the implementation aspects of integrating the mechanical relaying paradigm with the current and emerging mobile networks such as LTE advanced. This will be part of our future line of enquiry.

Exploiting structure in adaptive dynamic programming algorithms for a stochastic batch service problem

Abstract The purpose of this paper is to illustrate the importance of using structural results in dynamic programming algorithms. We consider the problem of approximating optimal strategies for the batch service of customers at a service station. Customers stochastically arrive at the station and wait to be served, incurring a waiting cost and a service cost. Service of customers is performed in groups of a fixed service capacity. We investigate the structure of cost functions and establish some theoretical results including monotonicity of the value functions. Then, we use our adaptive dynamic programming monotone algorithm that uses structure to preserve monotonicity of the estimates at each iterations to approximate the value functions. Since the problem with homogeneous customers can be solved optimally, we have a means of comparison to evaluate our heuristic. Finally, we compare our algorithm to classical forward dynamic programming methods.

Energy-Efficient Relaying via Store-Carry and Forward within the Cell

In this paper, store-carry and forward (SCF) decision policies for relaying within the cell are developed. The key motivation of SCF relaying stems from the fact that energy consumption levels can be dramatically reduced by capitalizing on the inherent mobility of nodes and the elasticity of Internet applications. More specifically, we show how the actual mobility of relay nodes can be incorporated as an additional resource in the system to achieve savings in the required communication energy levels. To this end, we provide a mathematical programming formulation on the aforementioned problem and find optimal routing and scheduling policies to achieve maximum energy savings. By investigating structural properties of the proposed mathematical program we show that optimal solutions can be computed efficiently in time. The tradeoffs between energy and delay in the system are meticulously studied and Pareto efficient curves are derived. Numerical investigations show that the achievable energy gains by judiciously storing and carrying information from mobile relays can grow well above 70 percent for the macrocell scenario when compared to a baseline multihop wireless relaying scheme that uses shortest path routes to the base station.

Robust scheduling in spatial reuse TDMA wireless networks

We propose a framework that produces robust schedules in collision-free medium access schemes. We demonstrate the approach on the STDMA link scheduling problem that seeks to minimize the frame length using the physical interference model and stochastic link gains. By using conservative link gain values as opposed to average values in the SINR-target constraints, we show that the proposed approach produces shorter schedules when timeslots required for retransmission are taken into account. We derive properties on the expected frame length and provide bounds on the probability of SINR constraint violation and on the number of timeslots needed for retransmission.

Switching off low utilization base stations via store carry and forward relaying

Recent research studies on green cellular networking indicate that most of the traffic is serviced by a few cell sites while the rest of the cells remain under-utilized, contributing to significant energy consumption levels. Previous proposals suggest turning off Base Stations (BSs) during low utilization periods to save energy by allowing neighboring cells to increase their coverage to provide the necessary connectivity. In this paper, an alternative (and also complimentary) method is proposed, based on the store-carry and forward (SCF) relaying paradigm that allows BSs with low utilization levels to be switched-off. The proposed SCF relaying scheme exploits the mobility of relay nodes to migrate traffic from BSs of very low utilization to neighbour BSs, allowing in that respect these sites to be switched off. To this end, a joint routing and scheduling problem is formulated to maximize the number of cell sites that can be switched off by also taking into account the communication cost of operating the network. Numerical investigations reveal that significant energy gains can be attained using the proposed SCF relaying scheme for switching off BSs.

Gateway selection and routing in wireless mesh networks

This paper deals with issues regarding network planning and optimization in multi-hop wireless mesh networks (WMNs). The central focus is on mathematical programming formulations for both the uncapacitated and capacitated joint gateway selection and routing (U/C-GSR) problem in WMNs, which are in general NP-complete, when expressed as decision problems. We detail a reformulation using the shortest path cost matrix (SPM) and prove that it gives the optimal solution when applied to the uncapacitated case. We extend the SPM formulation to the capacitated case and show computationally, by using a lower bound on the optimal solution, that it performs within a small optimality gap. Evidence from numerical investigations shows that, the proposed formulation can dramatically improve the computation time for WMNs with realistic network sizes. Furthermore, a set of extensions to the basic formulation is detailed to allow modeling issues such as multi-rate transmission, restricting the number of hops in each routing sub-tree and declaring unreliable nodes as leaf nodes in the routing tree.

Ultra Low Energy Store-Carry and Forward Relaying within the Cell

In this paper we address the issue of store-carry and forward (SCF) relaying within a cell in a mobile network. The proposed scheme can be considered as a generalization of various multihop wireless relaying schemes, where storing and carrying an information message by a mobile relay node is not allowed. The key motivation of utilizing SCF relaying within the cell is that energy consumption levels can be dramatically reduced by capitalizing on the inherent mobility of nodes and the elasticity of Internet applications. In that respect, we consider a novel multihop cellular architecture to achieve energy savings both at the network side (i.e., Base Stations) and at the user terminals. The proposed scheme makes use of mobility information of relays (vehicles) while roaming inside the cell to device flows that could achieve maximum energy savings. We show that under SCF relaying large energy savings can be achieved by tolerating a controlled delay over the initiated service.

Load Balancing via Store-Carry and Forward Relaying in Cellular Networks

We bring to the fore a novel load balancing tech- nique based on delay tolerant message forwarding that relies on the store-carry and forward paradigm by utilizing the mobility of vehicular nodes in multi-cell wireless networks. Considerations are made not only on the achievable load balancing performance but also on the en route energy consumption. That accounts for the optimal trade-offs between load balancing, communication energy consumption and message delivery delay in the cellular network. A mathematical program is formulated for finding optimal forwarding decision policies for the proposed store-carry and forward (SCF) relaying scheme for load balancing. Furthermore, a low complexity on-line algorithm for the proposed network setup is derived and its performance is compared with the optimal solution. To sharpen the understanding of the proposed message forwarding techniques, a wide set of numerical investigations are presented revealing that by trading-off message delivery delays, the variance of the load across cells can be dramatically reduced.