Control of Robotic Mobility-On-Demand Systems: a Queueing-Theoretical Perspective

In this paper we present and analyze a queueing-theoretical model for autonomous mobility-on-demand (MOD) systems where robotic, self-driving vehicles transport customers within an urban environment and rebalance themselves to ensure acceptable quality of service throughout the entire network. We cast an autonomous MOD system within a closed Jackson network model with passenger loss. It is shown that an optimal rebalancing algorithm minimizing the number of (autonomously) rebalancing vehicles and keeping vehicles availabilities balanced throughout the network can be found by solving a linear program. The theoretical insights are used to design a robust, real-time rebalancing algorithm, which is applied to a case study of New York City. The case study shows that the current taxi demand in Manhattan can be met with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi fleet). Finally, we extend our queueing-theoretical setup to include congestion effects, and we study the impact of autonomously rebalancing vehicles on overall congestion. Collectively, this paper provides a rigorous approach to the problem of system-wide coordination of autonomously driving vehicles, and provides one of the first characterizations of the sustainability benefits of robotic transportation networks.Comment: 10 pages, To appear at RSS 201

Coexistence of grass, saplings and trees in the Staver-Levin forest model

In this paper, we consider two attractive stochastic spatial models in which each site can be in state 0, 1 or 2: Krone's model in which 0${}={}$vacant, 1${}={}$juvenile and 2${}={}$a mature individual capable of giving birth, and the Staver-Levin forest model in which 0${}={}$grass, 1${}={}$sapling and 2${}={}$tree. Our first result shows that if $(0,0)$ is an unstable fixed point of the mean-field ODE for densities of 1's and 2's then when the range of interaction is large, there is positive probability of survival starting from a finite set and a stationary distribution in which all three types are present. The result we obtain in this way is asymptotically sharp for Krone's model. However, in the Staver-Levin forest model, if $(0,0)$ is attracting then there may also be another stable fixed point for the ODE, and in some of these cases there is a nontrivial stationary distribution.Comment: Published at http://dx.doi.org/10.1214/14-AAP1079 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Testing the Structure of a Gaussian Graphical Model with Reduced Transmissions in a Distributed Setting

Testing a covariance matrix following a Gaussian graphical model (GGM) is considered in this paper based on observations made at a set of distributed sensors grouped into clusters. Ordered transmissions are proposed to achieve the same Bayes risk as the optimum centralized energy unconstrained approach but with fewer transmissions and a completely distributed approach. In this approach, we represent the Bayes optimum test statistic as a sum of local test statistics which can be calculated by only utilizing the observations available at one cluster. We select one sensor to be the cluster head (CH) to collect and summarize the observed data in each cluster and intercluster communications are assumed to be inexpensive. The CHs with more informative observations transmit their data to the fusion center (FC) first. By halting before all transmissions have taken place, transmissions can be saved without performance loss. It is shown that this ordering approach can guarantee a lower bound on the average number of transmissions saved for any given GGM and the lower bound can approach approximately half the number of clusters when the minimum eigenvalue of the covariance matrix under the alternative hypothesis in each cluster becomes sufficiently large

Attack Detection in Sensor Network Target Localization Systems with Quantized Data

We consider a sensor network focused on target localization, where sensors measure the signal strength emitted from the target. Each measurement is quantized to one bit and sent to the fusion center. A general attack is considered at some sensors that attempts to cause the fusion center to produce an inaccurate estimation of the target location with a large mean-square-error. The attack is a combination of man-in-the-middle, hacking, and spoofing attacks that can effectively change both signals going into and coming out of the sensor nodes in a realistic manner. We show that the essential effect of attacks is to alter the estimated distance between the target and each attacked sensor to a different extent, giving rise to a geometric inconsistency among the attacked and unattacked sensors. Hence, with the help of two secure sensors, a class of detectors are proposed to detect the attacked sensors by scrutinizing the existence of the geometric inconsistency. We show that the false alarm and miss probabilities of the proposed detectors decrease exponentially as the number of measurement samples increases, which implies that for sufficiently large number of samples, the proposed detectors can identify the attacked and unattacked sensors with any required accuracy

Optimizing the MapReduce Framework on Intel Xeon Phi Coprocessor

With the ease-of-programming, flexibility and yet efficiency, MapReduce has become one of the most popular frameworks for building big-data applications. MapReduce was originally designed for distributed-computing, and has been extended to various architectures, e,g, multi-core CPUs, GPUs and FPGAs. In this work, we focus on optimizing the MapReduce framework on Xeon Phi, which is the latest product released by Intel based on the Many Integrated Core Architecture. To the best of our knowledge, this is the first work to optimize the MapReduce framework on the Xeon Phi. In our work, we utilize advanced features of the Xeon Phi to achieve high performance. In order to take advantage of the SIMD vector processing units, we propose a vectorization friendly technique for the map phase to assist the auto-vectorization as well as develop SIMD hash computation algorithms. Furthermore, we utilize MIMD hyper-threading to pipeline the map and reduce to improve the resource utilization. We also eliminate multiple local arrays but use low cost atomic operations on the global array for some applications, which can improve the thread scalability and data locality due to the coherent L2 caches. Finally, for a given application, our framework can either automatically detect suitable techniques to apply or provide guideline for users at compilation time. We conduct comprehensive experiments to benchmark the Xeon Phi and compare our optimized MapReduce framework with a state-of-the-art multi-core based MapReduce framework (Phoenix++). By evaluating six real-world applications, the experimental results show that our optimized framework is 1.2X to 38X faster than Phoenix++ for various applications on the Xeon Phi