Large deviations sum-queue optimality of a radial sum-rate monotone opportunistic scheduler

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff "maximizing current service rate" (being opportunistic) versus "balancing unequal queues" (enhancing user-diversity to enable future high service rate opportunities). By contrast with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sum-rate monotone (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a two-queue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.Comment: Revised version. Major changes include addition of details/intermediate steps in various proofs, a summary of technical steps in Table 1, and correction of typos

Feedback control of 2-product server with setups and bounded buffers

A manufacturing machine processing two product types arriving at constant rate and setup times involved is considered in this study. An optimal process cycle is derived with respect to minimal weighted time averaged work in process (wip) level. In addition, a feedback law is proposed that steers the system to this optimal process cycle from arbitrary start point. The analysis has been done for both unbounded and bounded buffer capacity. Although the analysis is done for continuous models, the feedback law has been implemented successfully in a discrete event simulation

State feedback control of switching servers with setups

In this paper we study the control of switching servers, which can for example be found in manufacturing industry. In general, these systems are discrete event systems. A server processes multiple job types. Switching between the job types takes time and during that time, no jobs can be processed, so capacity is lost. How should a server switch between the job types in an efficient way? In this paper we derive the optimal process cycle with respect to work in process levels for a server with two job types and finite buffer capacities. The analysis is performed using a hybrid fluid model approximation. After the optimal process cycle has been defined, a state feedback controller is proposed that steers the trajectory of the system to this optimal cycle. Workstations are often placed in series to form a flowline of servers. Our goal is to control flowlines of switching servers in a way that the work in process level is minimized. In a flowline, only the most downstream workstation influences the work in process level of the system, since upstream workstations simply move jobs from one server to the other. If it is possible to have the most downstream workstation process in its optimal cycle and the other workstations can make this happen, then optimal work in process levels are achieved. This paper investigates under which conditions the upstream workstations can make the most downstream workstation work optimally. Conditions on the upstream workstations are derived and the class of flowlines is characterized for which the optimal process cycle of an isolated downstream workstation can become the optimal process cycle for the flowline. For a flowline consisting of two workstations, a state feedback controller is proposed and convergence to the optimal process cycle is proved mathematically. An extensive case study demonstrates how the controller performs, for both the hybrid fluid model and in a discrete event implementation with stochastic inter-arrival and process times

Utilizing prediction analytics in the optimal design and control of healthcare systems

In recent years, increasing availability of data and advances in predictive analytics present new opportunities and challenges to healthcare management. Predictive models are developed to evaluate various aspects of healthcare systems, such as patient demand, patient pathways, and patient outcomes. While these predictions potentially provide valuable information to improve healthcare delivery, there are still many open questions considering how to integrate these forecasts into operational decisions. In this context, this dissertation develops methodologies to combine predictive analytics with the design of healthcare delivery systems. The first part of dissertation considers how to schedule proactive care in the presence of patient deterioration. Healthcare systems are typically limited resource environments where scarce capacity is reserved for the most urgent patients. However, there has been a growing interest in the use of proactive care when a less urgent patient is predicted to become urgent while waiting. On one hand, providing care for patients when they are less critical could mean that fewer resources are needed to fulfill their treatment requirement. On the other hand, due to prediction errors, the moderate patients who are predicted to deteriorate in the future may self cure on their own and never need the treatment. Hence, allocating limited resource for these patients takes the capacity away from other more urgent ones who need it now. To understand this tension, we propose a multi-server queueing model with two patient classes: moderate and urgent. We allow patients to transition classes while waiting. In this setting, we characterize how moderate and urgent patients should be prioritized for treatment when proactive care for moderate patients is an option. The second part of the dissertation focuses on the nurse staffing decisions in the emergency departments (ED). Optimizing ED nurse staffing decisions to balance the quality of service and staffing cost can be extremely challenging, especially when there is a high level of uncertainty in patient demand. Increasing data availability and continuing advancements in predictive analytics provide an opportunity to mitigate demand uncertainty by utilizing demand forecasts. In the second part of the dissertation, we study a two-stage prediction-driven staffing framework where the prediction models are integrated with the base (made weeks in advance) and surge (made nearly real-time) staffing decisions in the ED. We quantify the benefit of having the ability to use the more expensive surge staffing. We also propose a near-optimal two-stage staffing policy that is straightforward to interpret and implement. Lastly, we develop a unified framework that combines parameter estimation, real-time demand forecasts, and capacity sizing in the ED. High-fidelity simulation experiments for the ED demonstrate that the proposed framework can reduce annual staffing costs by 11%-16% ($2 M-$3 M) while guaranteeing timely access to care

Self-Control of Traffic Lights and Vehicle Flows in Urban Road Networks

Based on fluid-dynamic and many-particle (car-following) simulations of traffic flows in (urban) networks, we study the problem of coordinating incompatible traffic flows at intersections. Inspired by the observation of self-organized oscillations of pedestrian flows at bottlenecks [D. Helbing and P. Moln\'ar, Phys. Eev. E 51 (1995) 4282--4286], we propose a self-organization approach to traffic light control. The problem can be treated as multi-agent problem with interactions between vehicles and traffic lights. Specifically, our approach assumes a priority-based control of traffic lights by the vehicle flows themselves, taking into account short-sighted anticipation of vehicle flows and platoons. The considered local interactions lead to emergent coordination patterns such as ``green waves'' and achieve an efficient, decentralized traffic light control. While the proposed self-control adapts flexibly to local flow conditions and often leads to non-cyclical switching patterns with changing service sequences of different traffic flows, an almost periodic service may evolve under certain conditions and suggests the existence of a spontaneous synchronization of traffic lights despite the varying delays due to variable vehicle queues and travel times. The self-organized traffic light control is based on an optimization and a stabilization rule, each of which performs poorly at high utilizations of the road network, while their proper combination reaches a superior performance. The result is a considerable reduction not only in the average travel times, but also of their variation. Similar control approaches could be applied to the coordination of logistic and production processes

Autonomous optimal rendezvous of underwater vehicles

The capability of an autonomous underwater vehicle (AUV) to rendezvous with other AUVs was implemented and demonstrated in the Naval Postgraduate School ARIES AUV; providing a method of overcoming the severe range limitations of high-bandwidth underwater data transfer methods in order to enable accelerated access to data collected by a network of data-gathering survey AUVs. Rendezvous was implemented by autonomous reconfiguration of ARIES' operations, using a mission planning module to combine acousticallytransmitted rendezvous requests from survey AUVs with pre-stored survey AUV mission data to generate rendezvous missions based either on time-optimal or energy-optimal trajectories. The planning module efficiently generates rendezvous trajectories based on solutions derived using optimal control theory. A new third layer of control, based on a finite state machine, was added above ARIES' autopilot and mission execution functions in order to initiate mission planning and replanning, activate missions, sequence vehicle operations through seven defined states, control acoustic communications, and handle perturbations and missed rendezvous.http://archive.org/details/autonomousoptima109459956Captain, United States NavyApproved for public release; distribution is unlimited

Convergence Analysis of Mixed Timescale Cross-Layer Stochastic Optimization

This paper considers a cross-layer optimization problem driven by multi-timescale stochastic exogenous processes in wireless communication networks. Due to the hierarchical information structure in a wireless network, a mixed timescale stochastic iterative algorithm is proposed to track the time-varying optimal solution of the cross-layer optimization problem, where the variables are partitioned into short-term controls updated in a faster timescale, and long-term controls updated in a slower timescale. We focus on establishing a convergence analysis framework for such multi-timescale algorithms, which is difficult due to the timescale separation of the algorithm and the time-varying nature of the exogenous processes. To cope with this challenge, we model the algorithm dynamics using stochastic differential equations (SDEs) and show that the study of the algorithm convergence is equivalent to the study of the stochastic stability of a virtual stochastic dynamic system (VSDS). Leveraging the techniques of Lyapunov stability, we derive a sufficient condition for the algorithm stability and a tracking error bound in terms of the parameters of the multi-timescale exogenous processes. Based on these results, an adaptive compensation algorithm is proposed to enhance the tracking performance. Finally, we illustrate the framework by an application example in wireless heterogeneous network