We propose a simple and energy efficient distributed Change Detection scheme for sensor networks based on Page's parametric CUSUM algorithm. The sensor observations are IID over time and across the sensors conditioned on the change variable. Each sensor run CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a Multiple Access Channel (MAC) corrupted with IID noise. The fusion center which is the global decision maker, performs another CUSUM to detect the change. We provide the analysis and simulation results for our scheme and compare the performance with an existing scheme which ensures energy efficiency via optimal power selection.

We propose an energy efficient distributed cooperative Change Detection scheme called DualCUSUM based on Page's CUSUM algorithm. In the algorithm, each sensor runs a CUSUM and transmits only when the CUSUM is above some threshold. The transmissions from the sensors are fused at the physical layer. The channel is modeled as a Multiple Access Channel (MAC) corrupted with noise. The fusion center performs another CUSUM to detect the change. The algorithm performs better than several existing schemes when energy is at a premium. We generalize the algorithm to also include nonparametric CUSUM and provide a unified analysis. Our results show that while the false alarm probability is smaller for observation distribution with a lighter tail, the detection delay is asymptotically the same for any distribution. Consequently, we provide a new viewpoint on why parametric CUSUM performs better than nonparametric CUSUM. In the process, we also develop new results on a reflected random walk which can be of independent interest.

In this paper we focus on a class of polling systems encountered while modeling the ferry based wireless local area network (FWLAN). A moving ferry, while walking in a predetermined cyclic path, communicates with the static nodes (or users) of the network via a wireless link. The ferry is assumed to stop and communicate with a node that has a packet to send or to receive, when it is closest to that node. The location distribution of the node to which or from which a packet arrives is assumed to have a support of positive Lebesgue measure. These features imply that polling models with finite number of queues cannot be used to model the system. We study in this paper the continuous polling systems with service disciplines that model the use of the FWLAN (and that are more complex than the classical exhaustive or gated services). Our approach is based on discretization of the continuous polling model. We propose a special way of discretizing the continuous system such that: 1) the known Pseudo conservation laws can be applied to obtain the stationary expected workload of the discrete systems; 2) the limit, of these 'discretized' expected workloads, equals the stationary expected workload of the continuous system. Our results rely heavily on fixed point analysis of infinite dimensional operators.

We consider vector fixed point (FP) equations in large dimensional spaces involving random variables, and study their realization-wise solutions. We have an underlying directed random graph, that defines the connections between various components of the FP equations. Existence of an edge between nodes i, j implies the i-th FP equation depends on the j-th component. We consider a special case where any component of the FP equation depends upon an appropriate aggregate of that of the random 'neighbour' components. We obtain finite dimensional limit FP equations (in a much smaller dimensional space), whose solutions approximate the solution of the random FP equations for almost all realizations, in the asymptotic limit (number of components increase). Our techniques are different from the traditional mean-field methods, which deal with stochastic FP equations in the space of distributions to describe the stationary distributions of the systems. In contrast our focus is on realization-wise FP solutions. We apply the results to study systemic risk in a large financial heterogeneous network with many small institutions and one big institution, and demonstrate some interesting phenomenon. 1 Note that i Wj,i + W j,b = 1 for all j.