In the first half of this thesis, we extend the results of Halfin and Whitt to generally distributed service times. This is accomplished by first writing the system equations for the G/GI/N queue in a manner similar to the system equations for G/GI/Infinity queue. We next identify a key relationship between these two queues. This relationship allows us to leverage several existing results for the G/GI/Infinity queue in order to prove our main result. Our main result in the first part of this thesis is to show that the diffusion scaled queue length process for the G/GI/N queue in the Halfin-Whitt regime converges to a limiting stochastic process which is driven by a Gaussian process and satisfies a stochastic convolution equation. We also show that a similar result holds true for the fluid scaled queue length process under general initial conditions. Customer abandonment is also a common feature of many call centers. Some researchers have even gone so far as to suggest that the level of customer abandonment is the single most important metric with regards to a call center's performance. In the second half of this thesis, we improve upon a result of Ward and Glynn's concerning the GI/GI/1+GI queue in heavy traffic. Whereas Ward and Glynn obtain a diffusion limit result for the GI/GI/1+GI queue in heavy traffic which incorporates only the density the abandonment distribution at the origin, our result incorporate the entire abandonment distribution. This is accomplished by a scaling the hazard rate function of the abandonment distribution as the system moves into heavy traffic. Our main results are to obtain diffusion limits for the properly scaled workload and queue length processes in the GI/GI/1+GI queue. The limiting diffusions we obtain are reflected at the origin with a negative drift which is dependent upon the hazard rate of the abandonment distribution. Because these diffusions have an analytically tractable steady-state distribution, they can be used to provide a closed-form approximation for the steady-state distribution of the queue length and workload processes in a GI/GI/1+GI queue. We demonstrate the accuracy of these approximations through simulation.

Queueing network-based approximation models were developed to evaluate the performance of fixed-route material-handling systems supporting a multiple workcenter manufacturing facility. In this research, we develop analytical models for fixed-route material-handling systems from two different perspectives: the workcenters?? point of view and the transporters?? point of view. The state-dependent nature of the transportation time is considered here for more accurate analytical approximation models for material-handling systems. Also, an analytical methodology is developed for analytical descriptions of the impact of several different vehicledispatching policies for material-handling systems. Two different types of vehicledispatching policies are considered. Those are workcenter-initiated vehicle dispatching rules and vehicle-initiated vehicle dispatching rules. For the workcenterinitiated vehicle dispatching rule, the Closest Transporter Allocation Rule (CTAR) was used to assign empty transporters to jobs needing to be moved between various workcenters. On the other hand, four different vehicle-initiated vehicle dispatching rules, Shortest Distance Dispatching Rule (SDR), Time Limit/Shortest DistanceDispatching Rule (TL/SDR), First-Come First-Serve Dispatching Rule (FCFSR), Longest Distance Dispatching Rule (LDR), are used to select job requests from workcenters when a transporter is available. From the models with a queue space limit of one at each workcenter and one transporter, two different types of extensions are considered. First, the queue space limit at each workcenter is increased from one to two while the number of transporters remains at one. Second, the number of transporters in the system is also increased from one to two while maintaining the queue space limit of one at each workcenter. Finally, using a simulation approach, we modified the Nearest Neighbor (NN) heuristic dispatching procedure for multi-load transporters proposed by Tanchoco and Co (1994) and tested for a fixed-route material-handling system. The effects of our modified NN and the original NN transporter dispatching procedures on the system performance measures, such as WIP or Cycle Time were investigated and we demonstrated that the modified NN heuristic dispatching procedure performs better than the original NN procedure in terms of these system performance measures.

The Software Life Cycle (SLC) often comprises a complex sequence of processes, each with many subparts where various execution decisions throughout the pipeline can greatly affect the success or failure of a given project. Some of the most important decisions involve the allocation of scarce resources throughout the SLC, which are often based on estimations about future market demand and various extraneous factors of high stochasticity. Despite numerous efforts in standardization, many projects are still highly dependent on the subjective aptitude of individual managers, who may in turn rely on ad hoc techniques rather than standardized and repeatable ones. The results can be unpredictability and undue reliance on specific individuals. This paper considers imposing a mathematical framework on two of the key aspects of SLC: Deciding how to dynamically allocate available resources throughout the development pipeline, and when to stop further work on a given task in light of the associated Return On Investment (ROI) metrics. In so doing, the software development process is modeled as a problem in New Product Development (NPD) Management, which can be approached using control theory and stochastic combinatorial optimization techniques. The paper begins by summarizing some of the previous developments in these fields, and proposes some future research directions for solving complex resource allocation problems under stochastic settings. The outcome is a formal framework that when combined with competent Configuration Management techniques, can rapidly achieve near-optimal solutions at each stage of the SLC in a standardized manner. / text

We consider the problem of staffing large-scale service centers with multiple customer classes and agent types operating under quality-of-service (QoS) constraints. We introduce formulations for a class of staffing problems, minimizing the cost of staffing while requiring that the long-run average QoS achieves a certain pre-specified level. The queueing models we use to define such service center staffing problems have random inter-arrival times and random service times. The models we study differ with respect to whether the arrival rates are deterministic or stochastic. In the deterministic version of the service center staffing problem, we assume that the customer arrival rates are known deterministically. It is computationally challenging to solve our service center staffing problem with deterministic arrival rates. Thus, we provide an approximation and prove that the solution of our approximation is asymptotically optimal in the sense that the gap between the optimal value of the exact model and the objective function value of the approximate solution shrinks to zero as the size of the system grows large. In our work, we also focus on doubly stochastic service center systems; that is, we focus on solving large-scale service center staffing problems when the arrival rates are uncertain in addition to the inherent randomness of the system's inter-arrival times and service times. This brings the modeling closer to reality. In solving the service center staffing problems with deterministic arrival rates, we provide a solution procedure for solving staffing problems for doubly stochastic service center systems. We consider a decision making scheme in which we must select staffing levels before observing the arrival rates. We assume that the decision maker has distributional information about the arrival rates at the time of decision making. In the presence of arrival-rate uncertainty, the decision maker's goal is to minimize the staffing cost, while ensuring the QoS achieves a given level. We show that as the system scales large in size, there is at most one key scenario under which the probability of waiting converges to a non-trivial value, i.e., a value strictly between 0 and 1. That is, the system is either over- or under-loaded in any other scenario as the size of the system grows to infinity. Exploiting this result, we propose a two-step solution procedure for the staffing problem with random arrival rates. In the first step, we use the desired QoS level to identify the key scenario corresponding to the optimal staffing level. After finding the key scenario, the random arrival-rate model reduces to a deterministic arrival-rate model. In the second step, we solve the resulting model, with deterministic arrival rate, by using the approximation model we point to above. The approximate optimal staffing level obtained in this procedure asymptotically converges to the true optimal staffing level for the random arrival-rate problem. The decision making scheme we sketch above, assumes that the distribution of the random arrival rates is known at the time of decision making. In reality this distribution must be estimated based on historical data and experience, and needs to be updated as new observations arrive. Another important issue that arises in service center management is that in the daily operation in service centers, the daily operational period is split into small decision time periods, for example, hourly periods, and then the staffing decisions need to be made for all such time periods. Thus, to achieve an overall optimal daily staffing policy, one must deal with the interaction among staffing decisions over adjacent time periods. In our work, we also build a model that handles the above two issues. We build a two-stage stochastic model with recourse that provides the staffing decisions over two adjacent decision time periods, i.e., two adjacent decision stages. The model minimizes the first stage staffing cost and the expected second stage staffing cost while satisfying a service quality constraint on the second stage operation. A Bayesian update is used to obtain the second-stage arrival-rate distribution based on the first-stage arrival-rate distribution and the arrival observations in the first stage. The second-stage distribution is used in the constraint on the second stage service quality. After reformulation, we show that our two-stage model can be expressed as a newsvendor model, albeit with a demand that is derived from the first stage decision. We provide an algorithm that can solve the two-stage staffing problem under the most commonly used QoS constraints. This work uses stochastic programming methods to solve problems arising in queueing networks. We hope that the ideas that we put forward in this dissertation lead to other attempts to deal with decision making under uncertainty for queueing systems that combine techniques from stochastic programming and analysis tools from queueing theory. / text

The average cost of operating a queueing network depends on several factors such as the complexity of the network and the service policy used. Approximate linear programming (ALP) is a method that can be used to compute an accurate lower bound on the optimal average cost as well as generate policies to be used in operating the network. These average cost solutions and policies are dependent on the type of basis function used in the ALP. In this paper, the ALP average cost solutions and policies are analyzed for twelve networks with four different types of basis functions (quadratic, linear, pure exponential, and mixed exponential). An approximate bound on the optimality gap between the ALP average cost solution and the optimal average cost solution is computed for each system, and the size of this bound is determined relative to the ALP average cost solution. Using the same set of networks, the performance of ALP generated policies are compared to the performance of the heuristic policies first-buffer-first-served (FBFS), last-buffer-first-served (LBFS), highest-queue-first-served (HQFS), and random-queue-first-served (RQFS). In general, ALP generated average cost solutions are considerably smaller than the simulated average cost under the corresponding policy, and therefore the approximate bounds on the optimality gaps are quite large. This bound increases with the complexity of the queueing network. Some ALP generated policies are not stabilizing policies for their corresponding networks, especially those produced using pure exponential and mixed exponential basis functions. For almost all systems, at least one of the heuristic policies results in mean average cost less than or nearly equal to the smallest mean average cost of all ALP generated policies in simulation runs. This means that generally there exists a heuristic policy which can perform as well as or better than any ALP generated policy. In conclusion, a useful bound on the optimality gap between the ALP average cost solution and the optimal average cost solution cannot be computed with this method. Further, heuristic policies, which are more computationally tractable than ALP generated policies, can generally match or exceed the performance of ALP generated policies, and thus computing such policies is often unnecessary for realizing cost benefits in queueing networks. / text

A Generalized Cambridge Ring is a queueing system that can be used as an approximate model of some material handling systems used in modern factories. It consists of one or more vehicles that carry cargo from origins to destinations around a loop, with queues forming when cargo temporarily exceeds the capacity of the system. For some Generalized Cambridge Rings that satisfy the usual traffic conditions for stability, it is demonstrated that some nonidling scheduling polices are unstable. A good scheduling policy will increase the efficiency of these systems by reducing waiting times and by therefore also reducing work in process (WIP). Simple heuristic policies are developed which provide substantial improvements over the commonly used first-in-first-out (FIFO) policy. Variances are incorporated into previously developed fluid models that used only means to produce a more accurate partially discrete fluid mean-variance model, which is used to further reduce waiting times. Optimal policies are obtained for some simple special cases, and simulations are used to compare policies in more general cases. The methods developed may be applicable to other queueing systems. / text

This dissertation is concerned with travel time uncertainty in transportation networks due to ephemeral phenomena such as incidents or poor weather. Such events play a major role in nonrecurring congestion, which is estimated to comprise between one-third and one-half of all delay on freeways. Although past research has considered many individual aspects of this problem, this dissertation is unique in bringing a comprehensive approach, beginning with study of its causes, moving to discussion of its effects on traveler behavior, and then demonstrating how these models can be applied to mitigate the effects of this uncertainty. In particular, two distinctive effects of uncertainty are incorporated into all aspects of these models: nonlinear traveler behavior, encompassing risk aversion, schedule delay, on-time arrival, and other user objectives that explicitly recognize travel time uncertainty; and information and adaptive routing, where travelers can adjust their routes through the network as they acquire information on its condition. In order to accurately represent uncertain events in a mathematical model, some quantitative description of these events and their impacts must be available. On freeways, a large amount of travel data is collected through intelligent transportation systems (ITS), although coverage is far from universal, and very little data is collected on arterial streets. This dissertation develops a statistical procedure for estimating probability distributions on speed, capacity, and other operational metrics by applying regression to locations where such data is available. On arterials, queueing theory is used to develop novel expressions for expected delay conditional on the signal indication. The effects of this uncertainty are considered next, both at the individual (route choice) and collective (equilibrium) levels. For individuals, the optimal strategy is no longer a path, but an adaptive policy which allows for flexible re-routing as information is acquired. Dynamic programming provides an efficient solution to this problem. Issues related to cycling in optimal policies are examined in some depth. While primarily a technical concern, the presence of cycling can be discomforting and needs to be addressed. When considering collective behavior, the simultaneous choices of many self-optimizing users (who need not share the same behavioral objective) can be expressed as the solution to a variational inequality problem, leading to existence and uniqueness results under certain regularity conditions. An improved policy loading algorithm is also provided for the case of linear traveler behavior. Finally, three network improvement strategies are considered: locating information-providing devices; adaptive congestion pricing; and network design. Each of these demonstrates how the routing and equilibrium models can be applied, using small networks as testbed locations. In particular, the information provision and adaptive congestion pricing strategies are extremely difficult to represent without an adaptive equilibrium model such as the one provided in this dissertation. / text

ITC/USA 2013 Conference Proceedings / The Forty-Ninth Annual International Telemetering Conference and Technical Exhibition / October 21-24, 2013 / Bally's Hotel & Convention Center, Las Vegas, NV / The University of Arizona's Aerial Robotics Club (ARC) sponsors the development of an unmanned aerial vehicle (UAV) able to compete in the annual Association for Unmanned Vehicle Systems International (AUVSI) Seafarer Chapter Student Unmanned Aerial Systems competition. Modern programming frameworks are utilized to develop a robust distributed imagery and telemetry pipeline as a backend for a mission operator user interface. This paper discusses the design changes made for the 2013 AUVSI competition including integrating low-latency first-person view, updates to the distributed task backend, and incremental and asynchronous updates the operator's user interface for real-time data analysis.

Server farms are popular architectures for computing infrastructures such as supercomputing centers, data centers and web server farms. As server farms become larger and their workloads more complex, designing efficient policies for managing the resources in server farms via trial-and error becomes intractable. In this thesis, we employ stochastic modeling and analysis techniques to understand the performance of such complex systems and to guide design of policies to optimize the performance. There is a rich literature on applying stochastic modeling to diverse application areas such as telecommunication networks, inventory management, production systems, and call centers, but there are numerous disconnects between the workloads and architectures of these traditional applications of stochastic modeling and how compute server farms operate, necessitating new analytical tools. To cite a few: (i) Unlike call durations, supercomputing jobs and file sizes have high variance in service requirements and this critically affects the optimality and performance of scheduling policies. (ii) Most existing analysis of server farms focuses on the First-Come- First-Served (FCFS) scheduling discipline, while time sharing servers (e.g., web and database servers) are better modeled by the Processor- Sharing (PS) scheduling discipline. (in) Time sharing systems typically exhibit thrashing (resource contention) which limits the achievable concurrency level, but traditional models of time sharing systems ignore this fundamental phenomenon. (iv) Recently, minimizing energy consumption has become an important metric in managing server farms. State-of-the-art servers come with multiple knobs to control energy consumption, but traditional queueing models don’t take the metric of energy consumption into account. In this thesis we attempt to bridge some of these disconnects by bringing the stochastic modeling and analysis literature closer to the realities of today’s compute server farms. We introduce new queueing models for computing server farms, develop new stochastic analysis techniques to evaluate and understand these queueing models, and use the analysis to propose resource management algorithms to optimize their performance.

Most used security mechanisms in high-speed networks have been adopted without adequate quantification of their impact on performance degradation. Appropriate quantitative network models may be employed for the evaluation and prediction of 'optimal' performance vs. security trade-offs. Several quantitative models introduced in the literature are based on queueing networks (QNs) and generalised stochastic Petri nets (GSPNs). However, these models do not take into consideration Performance Engineering Principles (PEPs) and the adverse impact of traffic burstiness and security protocols on performance. The contributions of this thesis are based on the development of an effective quantitative methodology for the analysis of arbitrary QN models and GSPNs through discrete-event simulation (DES) and extended applications into performance vs. security trade-offs involving infrastructure and infrastructure-less high-speed networks under bursty traffic conditions. Specifically, investigations are carried out focusing, for illustration purposes, on high-speed network routers subject to Access Control List (ACL) and also Robotic Ad Hoc Networks (RANETs) with Wired Equivalent Privacy (WEP) and Selective Security (SS) protocols, respectively. The Generalised Exponential (GE) distribution is used to model inter-arrival and service times at each node in order to capture the traffic burstiness of the network and predict pessimistic 'upper bounds' of network performance. In the context of a router with ACL mechanism representing an infrastructure network node, performance degradation is caused due to high-speed incoming traffic in conjunction with ACL security computations making the router a bottleneck in the network. To quantify and predict the trade-off of this degradation, the proposed quantitative methodology employs a suitable QN model consisting of two queues connected in a tandem configuration. These queues have single or quad-core CPUs with multiple-classes and correspond to a security processing node and a transmission forwarding node. First-Come-First-Served (FCFS) and Head-of-the-Line (HoL) are the adopted service disciplines together with Complete Buffer Sharing (CBS) and Partial Buffer Sharing (PBS) buffer management schemes. The mean response time and packet loss probability at each queue are employed as typical performance metrics. Numerical experiments are carried out, based on DES, in order to establish a balanced trade-off between security and performance towards the design and development of efficient router architectures under bursty traffic conditions. The proposed methodology is also applied into the evaluation of performance vs. security trade-offs of robotic ad hoc networks (RANETs) with mobility subject to Wired Equivalent Privacy (WEP) and Selective Security (SS) protocols. WEP protocol is engaged to provide confidentiality and integrity to exchanged data amongst robotic nodes of a RANET and thus, to prevent data capturing by unauthorised users. WEP security mechanisms in RANETs, as infrastructure-less networks, are performed at each individual robotic node subject to traffic burstiness as well as nodal mobility. In this context, the proposed quantitative methodology is extended to incorporate an open QN model of a RANET with Gated queues (G-Queues), arbitrary topology and multiple classes of data packets with FCFS and HoL disciplines under bursty arrival traffic flows characterised by an Interrupted Compound Poisson Process (ICPP). SS is included in the Gated-QN (G-QN) model in order to establish an 'optimal' performance vs. security trade-off. For this purpose, PEPs, such as the provision of multiple classes with HoL priorities and the availability of dual CPUs, are complemented by the inclusion of robot's mobility, enabling realistic decisions in mitigating the performance of mobile robotic nodes in the presence of security. The mean marginal end-to-end delay was adopted as the performance metric that gives indication on the security improvement. The proposed quantitative methodology is further enhanced by formulating an advanced hybrid framework for capturing 'optimal' performance vs. security trade-offs for each node of a RANET by taking more explicitly into consideration security control and battery life. Specifically, each robotic node is represented by a hybrid Gated GSPN (G-GSPN) and a QN model. In this context, the G-GSPN incorporates bursty multiple class traffic flows, nodal mobility, security processing and control whilst the QN model has, generally, an arbitrary configuration with finite capacity channel queues reflecting 'intra'-robot (component-to-component) communication and 'inter'-robot transmissions. Two theoretical case studies from the literature are adapted to illustrate the utility of the QN towards modelling 'intra' and 'inter' robot communications. Extensions of the combined performance and security metrics (CPSMs) proposed in the literature are suggested to facilitate investigating and optimising RANET's performance vs. security trade-offs. This framework has a promising potential modelling more meaningfully and explicitly the behaviour of security processing and control mechanisms as well as capturing the robot's heterogeneity (in terms of the robot architecture and application/task context) in the near future (c.f. [1]. Moreover, this framework should enable testing robot's configurations during design and development stages of RANETs as well as modifying and tuning existing configurations of RANETs towards enhanced 'optimal' performance and security trade-offs.