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The study of stochastic queueing networks is quite important due to the many applications including transportation, telecommunication, and manufacturing industries. Since there is often no explicit solution to these types of control problems, numerical methods are needed. Following the method of Boué-Dupuis, we use a Dynamic Programming approach of optimization on a controlled Markov Chain that simulates the behavior of a fluid limit of the original process. The search for an optimal control in this case involves a Skorokhod problem to describe the dynamics on the boundary of closed, convex domain. Using relaxed stochastic controls we show that the approximating numerical solution converges to the actual solution as the size of the mesh in the discretized state space goes to zero, and illustrate with an example. / Ph. D.

Stochasticity is a ubiquitous feature of cellular processes such as gene expression that can give rise to phenotypic differences for genetically identical cells. Understanding how the underlying biochemical reactions give rise to variations in mRNA/protein levels is thus of fundamental importance to diverse cellular processes. Recent technological developments have enabled single-cell measurements of cellular macromolecules which can shed new light on processes underlying gene expression. Correspondingly, there is a need for the development of theoretical tools to quantitatively model stochastic gene expression and its consequences for cellular processes. In this dissertation, we address this need by developing general stochastic models of gene expression. By mapping the system to models analyzed in queueing theory, we derive analytical expressions for the noise in steady-state protein distributions. Furthermore, given that the underlying processes are intrinsically stochastic, cellular regulation must be designed to control the`noise' in order to adapt and respond to changing environments. Another focus of this dissertation is to develop and analyze stochastic models of post-transcription regulation. The analytical solutions of the models proposed provide insight into the effects of different mechanisms of regulation and the role of small RNAs in fine-tunning the noise in gene expression. The results derived can serve as building blocks for future studies focusing on regulation of stochastic gene expression. / Ph. D.

This research considers the transmission of real-time data within a wireless local area network (WLAN). Exact and approximate analytic network evaluation techniques are examined. The suitability of using a given technique in a particular situation is discussed. Simulation models are developed to study the performance of our protocol RT-MAC (real-time medium access control). RT-MAC is a novel, simple, and elegant MAC protocol for use in transmitting real-time data in point to point ad hoc WLAN. Our enhancement of IEEE 802.11, RT-MAC, achieves dramatic reductions in mean delay, missed deadlines, and packet collisions by selectively discarding packets and sharing station state information. For example, in a 50 station network with a normalized offered load of 0.7, mean delay is reduced from more than 14 seconds to less than 45 ms, late packets are reduced from 76% to less than 1%, and packet collisions are reduced from 36% to less than 1%. Stations using RT-MAC are interoperable with stations using IEEE 802.11. In networks with both RT-MAC and IEEE 802.11 stations, significant performance improvements were seen even when more than half of the stations in the network were not RT-MAC stations. The effect of the wireless channel and its impact on the ability of a WLAN to meet packet deadlines is evaluated. It is found that, in some cases, other factors such as the number of stations in the network and the offered load are more significant than the condition of the wireless channel. Regression models are developed from simulation data to predict network behavior in terms of throughput, mean delay, missed deadline ratio, and collision ratio. Telemetry, avionics, and packetized voice traffic models are considered. The applicability of this research is not limited to real-time wireless networks. Indeed, the collision reduction algorithm of RT-MAC is independent of the data being transported. Furthermore, RT-MAC would perform equally well in wired networks. Incorporating the results of this research into existing protocols will result in immediate and dramatic improvements in network performance. / Ph. D.

Transportation Engineers have recently begun to incorporate statistical and machine learning approaches to solving difficult problems, mainly due to the vast quantities of data collected that is stochastic (sensors, video, and human collected). In transportation engineering, a transportation system is often denoted by jurisdiction boundaries and evaluated as such. However, it is ultimately defined by the consideration of the analyst in trying to answer the question of interest. In this dissertation, a transportation system located in Jackson, Wyoming under the jurisdiction of the Grand Teton National Park and recognized as the Moose-Wilson Corridor is evaluated to identify transportation-related factors that influence its operational performance. The evaluation considers its unique prevalent conditions and takes into account future management strategies. The dissertation accomplishes this by detailing four distinct aspects in individual chapters; each chapter is a standalone manuscript with detailed introduction, purpose, literature review, findings, and conclusion. Chapter 1 provides a general introduction and provides a summary of Chapters 2 – 6. Chapter 2 focuses on evaluating the operational performance of the Moose-Wilson Corridor's entrance station, where queueing performance and arrival and probability mass functions of the vehicle arrival rates are determined. Chapter 3 focuses on the evaluation of a parking system within the Moose-Wilson Corridor in a popular attraction known as the Laurance S. Rockefeller Preserve, in which the system's operational performance is evaluated, and a probability mass function under different arrival and service rates are provided. Chapter 4 provides a data science approach to predicting the probability of vehicles stopping along the Moose-Wilson Corridor. The approach is a machine learning classification methodology known as "decision tree." In this study, probabilities of stopping at attractions are predicted based on GPS tracking data that include entrance location, time of day and stopping at attractions. Chapter 5 considers many of the previous findings, discusses and presents a developed tool which utilizes a Bayesian methodology to determine the posterior distributions of observed arrival rates and service rates which serve as bounds and inputs to an Agent-Based Model. The Agent-Based Model represents the Moose-Wilson Corridor under prevailing conditions and considers some of the primary operational changes in Grand Teton National Park's comprehensive management plan for the Moose-Wilson Corridor. The implementation of an Agent-Based Model provides a flexible platform to model multiple aspects unique to a National Park, including visitor behavior and its interaction with wildlife. Lastly, Chapter 6 summarizes and concludes the dissertation. / Doctor of Philosophy / In this dissertation, a transportation system located in Jackson, Wyoming under the jurisdiction of the Grand Teton National Park and recognized as the Moose-Wilson Corridor is evaluated to identify transportation-related factors that influence its operational performance. The evaluation considers its unique prevalent conditions and takes into account future management strategies. Furthermore, emerging analytical strategies are implemented to identify and address transportation system operational concerns. Thus, in this dissertation, decision support tools for the evaluation of a unique system in a National Park are presented in four distinct manuscripts. The manuscripts cover traditional approaches that breakdown and evaluate traffic operations and identify mitigation strategies. Additionally, emerging strategies for the evaluation of data with machine learning approaches are implemented on GPS-tracks to determine vehicles stopping at park attractions. Lastly, an agent-based model is developed in a flexible platform to utilize previous findings and evaluate the Moose-Wilson corridor while considering future policy constraints and the unique natural interactions between visitors and prevalent ecological and wildlife.

Due to the rapid development of wireless communications together with the inflexibility of the current spectrum allocation policy, radio spectrum becomes more and more exhausted. One of the critical challenges of wireless communication systems is to efficiently utilize the limited frequency resources to be able to support the growing demand of high data rate wireless services. As a promising solution, cognitive radios have been suggested to deal with the scarcity and under-utilization of radio spectrum. The basic idea behind cognitive radios is to allow unlicensed users, also called secondary users (SUs), to access the licensed spectrum of primary users (PUs) which improves spectrum utilization. In order to not degrade the performance of the primary networks, SUs have to deploy interference control, interference mitigating, or interference avoidance techniques to minimize the interference incurred at the PUs. Cognitive radio networks (CRNs) have stimulated a variety of studies on improving spectrum utilization. In this context, this thesis has two main objectives. Firstly, it investigates the performance of single hop CRNs with spectrum sharing and opportunistic spectrum access. Secondly, the thesis analyzes the performance improvements of two hop cognitive radio networks when incorporating advanced radio transmission techniques. The thesis is divided into three parts consisting of an introduction part and two research parts based on peer-reviewed publications. Fundamental background on radio propagation channels, cognitive radios, and advanced radio transmission techniques are discussed in the introduction. In the first research part, the performance of single hop CRNs is analyzed. Specifically, underlay spectrum access using M/G/1/K queueing approaches is presented in Part I-A while dynamic spectrum access with prioritized traffics is studied in Part I-B. In the second research part, the performance benefits of integrating advanced radio transmission techniques into cognitive cooperative radio networks (CCRNs) are investigated. In particular, opportunistic spectrum access for amplify-and-forward CCRNs is presented in Part II-A where collaborative spectrum sensing is deployed among the SUs to enhance the accuracy of spectrum sensing. In Part II-B, the effect of channel estimation error and feedback delay on the outage probability and symbol error rate (SER) of multiple-input multiple-output CCRNs is investigated. In Part II-C, adaptive modulation and coding is employed for decode-and-forward CCRNs to improve the spectrum efficiency and to avoid buffer overflow at the relay. Finally, a hybrid interweave-underlay spectrum access scheme for a CCRN is proposed in Part II-D. In this work, the dynamic spectrum access of the PUs and SUs is modeled as a Markov chain which then is utilized to evaluate the outage probability, SER, and outage capacity of the CCRN.

<p>In this project we illustrate how queueing simulation may be used to find the optimal interval for checkpointing problems and compare results with theoretical computations for simple systems that may be treated analytically.</p><p>We consider a relatively simple model for an internet banking facility. From time to time, the application server breaks down. The information at the time of the breakdown has to be passed onto the back up server before service may be resumed. To make the change over as efficient as possible, information of the state of user’s accounts is saved at regular intervals. This is known as checkpointing.</p><p>Firstly, we use GPSS (a queueing simulation tool) to find, by simulation, an optimal checkpointing interval, which maximises the efficiency of the server. Two measures of efficiency are considered; the availability of the server and the average time a customer spends in the system. Secondly, we investigate how far the queueing theory can go to providing an analytic solution to the problem and see whether or not this is in line with the results obtained through simulation.</p><p>The analysis shows that checkpointing is not necessary if breakdowns occur frequently and log reading after failure does not take much time. Otherwise, checkpointing is necessary and the analysis shows how GPSS may be used to obtain the optimal checkpointing interval. Relatively complicated systems may be simulated, where there are no analytic tools available. In simple cases, where theoretical methods may be used, the results from our simulations correspond with the theoretical calculations.</p>

In this project we illustrate how queueing simulation may be used to find the optimal interval for checkpointing problems and compare results with theoretical computations for simple systems that may be treated analytically. We consider a relatively simple model for an internet banking facility. From time to time, the application server breaks down. The information at the time of the breakdown has to be passed onto the back up server before service may be resumed. To make the change over as efficient as possible, information of the state of user’s accounts is saved at regular intervals. This is known as checkpointing. Firstly, we use GPSS (a queueing simulation tool) to find, by simulation, an optimal checkpointing interval, which maximises the efficiency of the server. Two measures of efficiency are considered; the availability of the server and the average time a customer spends in the system. Secondly, we investigate how far the queueing theory can go to providing an analytic solution to the problem and see whether or not this is in line with the results obtained through simulation. The analysis shows that checkpointing is not necessary if breakdowns occur frequently and log reading after failure does not take much time. Otherwise, checkpointing is necessary and the analysis shows how GPSS may be used to obtain the optimal checkpointing interval. Relatively complicated systems may be simulated, where there are no analytic tools available. In simple cases, where theoretical methods may be used, the results from our simulations correspond with the theoretical calculations.

A distributed virtual environment (DVE) is a shared virtual environment where multiple users at their workstations interact with each other. Some of these systems may support a large number of users, e. g. , massive multi-player online games, and these users may be geographically distributed. An important performance measure in a DVE system is the delay for an update of a user's state (e. g. , his position in the virtual environment) to arrive at the workstations of those users who are affected by the update. This update delay often has a stringent requirement (e. g. , less than 100 ms) in order to ensure interactivity among users. <br /><br /> In designing a DVE system, an important issue is how well the system scales as the number of users increases. In terms of scalability, a promising system architecture is a two-level hierarchical architecture. At the lower level, multiple service facilities (or basic systems) are deployed; each basic system interacts with its assigned users. At the higher level, the various basic systems ensure that their copies of the virtual environment are as consistent as possible. Although this architecture is believed to have good properties with respect to scalability, not much is known about its performance characteristics. <br /><br /> This thesis is concerned with the performance characteristics of the two-level hierarchical architecture. We first investigate the issue of scalability. We obtain analytic results on the workload experienced by the various basic systems as a function of the number of users. Our results provide valuable insights into the scalability of the architecture. We also propose a novel technique to achieve weak consistency among copies of the virtual environment at the various basic systems. Simulation results on the consistency/scalability tradeoff are presented. <br /><br /> We next study the update delay in the two-level hierarchical architecture. The update delay has two main components, namely the delay at the basic system (or server delay) and the network delay. For the server delay, we use a network of queues model where each basic system may have one or more processors. We develop an approximation method to obtain results for the distribution of server delay. Comparisons with simulation show that our approximation method yields accurate results. We also measure the time to process an update on an existing online game server. Our approximate results are then used to characterize the 95th-percentile of the server delay, using the measurement data as input. <br /><br /> As to the network delay, we develop a general network model and obtain analytic results for the network delay distribution. Numerical examples are presented to show the conditions under which geographical distribution of basic systems will lead to an improvement in the network delay. We also develop an efficient heuristic algorithm that can be used to determine the best locations for the basic systems in a network.

A distributed virtual environment (DVE) is a shared virtual environment where multiple users at their workstations interact with each other. Some of these systems may support a large number of users, e. g. , massive multi-player online games, and these users may be geographically distributed. An important performance measure in a DVE system is the delay for an update of a user's state (e. g. , his position in the virtual environment) to arrive at the workstations of those users who are affected by the update. This update delay often has a stringent requirement (e. g. , less than 100 ms) in order to ensure interactivity among users. <br /><br /> In designing a DVE system, an important issue is how well the system scales as the number of users increases. In terms of scalability, a promising system architecture is a two-level hierarchical architecture. At the lower level, multiple service facilities (or basic systems) are deployed; each basic system interacts with its assigned users. At the higher level, the various basic systems ensure that their copies of the virtual environment are as consistent as possible. Although this architecture is believed to have good properties with respect to scalability, not much is known about its performance characteristics. <br /><br /> This thesis is concerned with the performance characteristics of the two-level hierarchical architecture. We first investigate the issue of scalability. We obtain analytic results on the workload experienced by the various basic systems as a function of the number of users. Our results provide valuable insights into the scalability of the architecture. We also propose a novel technique to achieve weak consistency among copies of the virtual environment at the various basic systems. Simulation results on the consistency/scalability tradeoff are presented. <br /><br /> We next study the update delay in the two-level hierarchical architecture. The update delay has two main components, namely the delay at the basic system (or server delay) and the network delay. For the server delay, we use a network of queues model where each basic system may have one or more processors. We develop an approximation method to obtain results for the distribution of server delay. Comparisons with simulation show that our approximation method yields accurate results. We also measure the time to process an update on an existing online game server. Our approximate results are then used to characterize the 95th-percentile of the server delay, using the measurement data as input. <br /><br /> As to the network delay, we develop a general network model and obtain analytic results for the network delay distribution. Numerical examples are presented to show the conditions under which geographical distribution of basic systems will lead to an improvement in the network delay. We also develop an efficient heuristic algorithm that can be used to determine the best locations for the basic systems in a network.