A Constraint Programming Approach for Non-Preemptive Evacuation Scheduling

Large-scale controlled evacuations require emergency services to select evacuation routes, decide departure times, and mobilize resources to issue orders, all under strict time constraints. Existing algorithms almost always allow for preemptive evacuation schedules, which are less desirable in practice. This paper proposes, for the first time, a constraint-based scheduling model that optimizes the evacuation flow rate (number of vehicles sent at regular time intervals) and evacuation phasing of widely populated areas, while ensuring a nonpreemptive evacuation for each residential zone. Two optimization objectives are considered: (1) to maximize the number of evacuees reaching safety and (2) to minimize the overall duration of the evacuation. Preliminary results on a set of real-world instances show that the approach can produce, within a few seconds, a non-preemptive evacuation schedule which is either optimal or at most 6% away of the optimal preemptive solution.Comment: Submitted to the 21st International Conference on Principles and Practice of Constraint Programming (CP 2015). 15 pages + 1 reference pag

Two Timescale Convergent Q-learning for Sleep--Scheduling in Wireless Sensor Networks

In this paper, we consider an intrusion detection application for Wireless Sensor Networks (WSNs). We study the problem of scheduling the sleep times of the individual sensors to maximize the network lifetime while keeping the tracking error to a minimum. We formulate this problem as a partially-observable Markov decision process (POMDP) with continuous state-action spaces, in a manner similar to (Fuemmeler and Veeravalli [2008]). However, unlike their formulation, we consider infinite horizon discounted and average cost objectives as performance criteria. For each criterion, we propose a convergent on-policy Q-learning algorithm that operates on two timescales, while employing function approximation to handle the curse of dimensionality associated with the underlying POMDP. Our proposed algorithm incorporates a policy gradient update using a one-simulation simultaneous perturbation stochastic approximation (SPSA) estimate on the faster timescale, while the Q-value parameter (arising from a linear function approximation for the Q-values) is updated in an on-policy temporal difference (TD) algorithm-like fashion on the slower timescale. The feature selection scheme employed in each of our algorithms manages the energy and tracking components in a manner that assists the search for the optimal sleep-scheduling policy. For the sake of comparison, in both discounted and average settings, we also develop a function approximation analogue of the Q-learning algorithm. This algorithm, unlike the two-timescale variant, does not possess theoretical convergence guarantees. Finally, we also adapt our algorithms to include a stochastic iterative estimation scheme for the intruder's mobility model. Our simulation results on a 2-dimensional network setting suggest that our algorithms result in better tracking accuracy at the cost of only a few additional sensors, in comparison to a recent prior work

Randomized longest-queue-first scheduling for large-scale buffered systems

We develop diffusion approximations for parallel-queueing systems with the randomized longest-queue-first scheduling algorithm by establishing new mean-field limit theorems as the number of buffers $n\to\infty$. We achieve this by allowing the number of sampled buffers $d=d(n)$ to depend on the number of buffers $n$, which yields an asymptotic `decoupling' of the queue length processes. We show through simulation experiments that the resulting approximation is accurate even for moderate values of $n$ and $d(n)$. To our knowledge, we are the first to derive diffusion approximations for a queueing system in the large-buffer mean-field regime. Another noteworthy feature of our scaling idea is that the randomized longest-queue-first algorithm emulates the longest-queue-first algorithm, yet is computationally more attractive. The analysis of the system performance as a function of $d(n)$ is facilitated by the multi-scale nature in our limit theorems: the various processes we study have different space scalings. This allows us to show the trade-off between performance and complexity of the randomized longest-queue-first scheduling algorithm

Realization Theory for LPV State-Space Representations with Affine Dependence

In this paper we present a Kalman-style realization theory for linear parameter-varying state-space representations whose matrices depend on the scheduling variables in an affine way (abbreviated as LPV-SSA representations). We deal both with the discrete-time and the continuous-time cases. We show that such a LPV-SSA representation is a minimal (in the sense of having the least number of state-variables) representation of its input-output function, if and only if it is observable and span-reachable. We show that any two minimal LPV-SSA representations of the same input-output function are related by a linear isomorphism, and the isomorphism does not depend on the scheduling variable.We show that an input-output function can be represented by a LPV-SSA representation if and only if the Hankel-matrix of the input-output function has a finite rank. In fact, the rank of the Hankel-matrix gives the dimension of a minimal LPV-SSA representation. Moreover, we can formulate a counterpart of partial realization theory for LPV-SSA representation and prove correctness of the Kalman-Ho algorithm. These results thus represent the basis of systems theory for LPV-SSA representation.Comment: The main difference with respect to the previous version is as follows: typos have been fixe