What are the roles that ideas and mathematics play in research of engineering subjects? This article tries to answer this question with the author’s own research experience. In the past 30 years, the author’s research started from perturbation analysis (PA) of queueing networks, to PA of Markov systems, to Markov decision processes (MDP), and to stochastic control; and based on these research, the author has successfully developed a sensitivity-based optimization approach to the area of learning and optimization of stochastic systems, leading to a simple and unified framework for the area, new research directions, and new results in the area. This paper reviews the above research topics and the history of their development with an emphasis on what the roles that ideas and mathematics play in each of the advances along the path.

Buildings worldwide account for nearly 40% of global energy consumption. The biggest energy consumer in buildings is the heating, ventilation and air conditioning (HVAC) systems. In HVAC systems, chillers account for a major portion of the energy consumption. Maintaining chillers in good conditions through early fault detection and diagnosis is thus a critical issue.

In this paper, the fault detection and diagnosis for an air-cooled chiller with air coming from outside in variable flow rates is studied. The problem is difficult since the air-cooled chiller is operating under major uncertainties including the cooling load, and the air temperature and flow rate. A potential method to overcome the difficulty caused by the uncertainties is to perform fault detection and diagnosis based on a gray-box model with parameters regarded as constants. The method is developed and verified by us in another paper for a water-cooled chiller with the uncertainty of cooling load. The verification used a Kalman filter to predict parameters of a gray-box model and statistical process control (SPC) for measuring and analyzing their variations for fault detection and diagnosis. The gray-box model in the method, however, requires that the air temperature and flow rate be nearly constant. By introducing two new parameters and deleting data points with low air flow rate, the requirement can be satisfied and the method can then be applicable for an air-cooled chiller. The simulation results show that the method with the revised model and some data points dropped improved the fault detection and diagnosis (FDD) performance greatly. It can detect both sudden and gradual air-cooled chiller capacity degradation and sensor faults as well as their recoveries.

The ever increasing complexity of the Internet has made it impossible to effectively manage the Internet infrastructure. In this paper, we argue that the increased complexity was due to the “random accidents” introduced throughout the evolution of the Internet, such as ad-hoc based routing, cross-layer optimizations. These ad-hoc events increased the vulnerability and degraded the manageability of Internet. We also propose a new framework for network design and deployment, termed “assurable communication networks (ACNs)” that places the manageability in the center in network architecture. We suggest that rigorous mathematical model be developed for the measurement on the impact of manageability and accountability.

Based on the recognition that customers are both price and lead-time sensitive, sellers nowadays often pursue a delivery-time based market segmentation strategy. In this paper, we consider an inventory model where the seller provides two delivery options with possible delivery upgrade. The inventory is replenished in cycles and within each cycle, the seller employs commitment control to allocate its on-hand inventory between two classes of customers. We develop the optimal inventory allocation and replenishment policies, and demonstrate that the optimal control can be characterized by a switching curve. In the further analysis, we subsume dynamic pricing as an effective means to balance the two demand streams. Finally, we investigate similarities and differences between the pricing and delivery upgrade strategies.

Resource planning for a remanufacturing system is in general extremely difficult in terms of problem size, uncertainties, complicated constraints, etc. In this paper, we present a new method based on constrained ordinal optimization (COO) for remanufacturing planning. The key idea of our method is to estimate the feasibility of plans by machine learning and to select a subset with the estimated feasibility based on the procedure of horse racing with feasibility model (HRFM). Numerical testing shows that our method is efficient and effective for selecting good plans with high probability. It is thus a scalable optimization method for large scale remanufacturing planning problems with complicated stochastic constraints.

We provide an overview of the recently developed general infinitesimal perturbation analysis (IPA) framework for stochastic hybrid systems (SHSs), and establish some conditions under which this framework can be used to obtain unbiased performance gradient estimates in a particularly simple and efficient manner. We also propose a general scheme for systematically deriving an abstraction of a discrete event system (DES) in the form of an SHS. Then, as an application of the general IPA framework, we study a class of stochastic non-cooperative games termed “resource contention games” modeled through stochastic flow models (SFMs), where two or more players (users) compete for the use of a sharable resource. Simulation results are provided for a simple version of such games to illustrate and contrast system-centric and user-centric optimization.

With the advance of new computational technology, stochastic systems simulation and optimization has become increasingly a popular subject in both academic research and industrial applications. This paper presents some of recent developments about the problem of optimizing a performance function from a simulation model.We begin by classifying different types of problems and then provide an overview of the major approaches, followed by a more in-depth presentation of two specific areas: optimal computing budget allocation and the nested partitions method.

In this paper, a probabilistic scheme is presented for directed data transmission without maintaining route tables. In the model, each message is required to reach the base station (BS) successfully with a certain probability. We analyze the relationship between the number of the intermediate nodes, link reliability and relay probability. We obtain the condition for relay probability which can guarantee the performance of the networks. This scheme is robust and adaptable to the change of topology of the sensor networks. Simulation with Ns-2 helps to illustrate the main results of the analysis.