Mean Field Interactions in Heterogeneous Networks

In the context of complex networks, we often encounter systems in which the constituent entities randomly interact with each other as they evolve with time. Such random interactions can be described by Markov processes, constructed on suitable state spaces. For many practical systems (e.g. server farms, cloud data centers, social networks), the Markov processes, describing the time-evolution of their constituent entities, become analytically intractable as a result of the complex interdependence among the interacting entities. However, if the `strength' of these interactions converges to a constant as the size of the system is increased, then in the large system limit the underlying Markov process converges to a deterministic process, known as the mean field limit of the corresponding system. Thus, the mean field limit provides a deterministic approximation of the randomly evolving system. Such approximations are accurate for large system sizes. Most prior works on mean field techniques have analyzed systems in which the constituent entities are identical or homogeneous. In this dissertation, we use mean field techniques to analyze large complex systems composed of heterogeneous entities. First, we consider a class of large multi-server systems, that arise in the context of web-server farms and cloud data centers. In such systems, servers with heterogeneous capacities work in parallel to process incoming jobs or requests. We study schemes to assign the incoming jobs to the servers with the goal of achieving optimal performance in terms of certain metrics of interest while requiring the state information of only a small number of servers in the system. To this end, we consider randomized dynamic job assignment schemes which sample a small random subset of servers at every job arrival instant and assign the incoming job to one of the sampled servers based on their instantaneous states. We show that for heterogeneous systems, naive sampling of the servers may result in an `unstable' system. We propose schemes which maintain stability by suitably sampling the servers. The performances of these schemes are studied via the corresponding mean field limits, that are shown to exist. The existence and uniqueness of an asymptotically stable equilibrium point of the mean field is established in every case. Furthermore, it is shown that, in the large system limit, the servers become independent of each other and the stationary distribution of occupancy of each server can be obtained from the unique equilibrium point of the mean field. The stationary tail distribution of server occupancies is shown to have a fast decay rate which suggests significantly improved performance for the appropriate metrics relevant to the application. Numerical studies are presented which show that the proposed randomized dynamic schemes significantly outperform randomized static schemes where job assignments are made independently of the server states. In certain scenarios, the randomized dynamic schemes are observed to be nearly optimal in terms of their performances. Next, using mean field techniques, we study a different class of models that arise in the context of social networks. More specifically, we study the impact of social interactions on the dynamics of opinion formation in a social network consisting of a large number of interacting social agents. The agents are assumed to be mobile and hence do not have any fixed set of neighbors. Opinion of each agent is treated as a binary random variable, taking values in the set {0,1}. This represents scenarios, where the agents have to choose from two available options. The interactions between the agents are modeled using 1) the `voter' rule and 2) the `majority' based rule. Under each rule, we consider two scenarios, (1) where the agents are biased towards a specific opinion and (2) where the agents have different propensities to change their past opinions. For each of these scenarios, we characterize the equilibrium distribution of opinions in the network and the convergence rate to the equilibrium by analyzing the corresponding mean field limit. Our results show that the presence of biased agents can significantly reduce the rate of convergence to the equilibrium. It is also observed that, under the dynamics of the majority rule, the presence of `stubborn' agents (those who do not update their opinions) may result in a metastable network, where the opinion distribution of the non-stubborn agents fluctuates among multiple stable configurations

Scheduling for today’s computer systems: bridging theory and practice

Scheduling is a fundamental technique for improving performance in computer systems. From web servers to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers. In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems. The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time and provide results characterizing the distribution of response time and the fairness of scheduling policies. These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs

Management of Cloud systems applied to eHealth

This thesis explores techniques, models and algorithms for an efficient management of Cloud systems and how to apply them to the healthcare sector in order to improve current treatments. It presents two Cloud-based eHealth applications to telemonitor and control smoke-quitting and hypertensive patients. Different Cloud-based models were obtained and used to develop a Cloudbased infrastructure where these applications are deployed. The results show that these applications improve current treatments and that can be scaled as computing requirements grow. Multiple Cloud architectures and models were analyzed and then implemented using different techniques and scenarios. The Smoking Patient Control (S-PC) tool was deployed and tested in a real environment, showing a 28.4% increase in long-term abstinence. The Hypertension Patient Control (H-PC) tool, was successfully designed and implemented, and the computing boundaries were measuredAquesta tesi explora tèniques, models i algorismes per una gestió eficient en sistemes al Núvol i com aplicar-ho en el sector de la salut per tal de millorar els tractaments actuals. Presenta dues aplicacions de salut electrònica basades en el Núvol per telemonitoritzar i controlar pacients fumadors i hipertensos. S'ha obtingut diferents models basats en el Núvol i s'han utilitzat per a desenvolupar una infraestructura on desplegar aquestes aplicacions. Els resultats mostren que aquestes aplicacions milloren els tractaments actuals així com escalen a mesura que els requeriments computacionals augmenten. Múltiples arquitectures i models han estat analitzats i implementats utilitzant diferents tècniques i escenaris. L'aplicació Smoking Patient Control (S-PC) ha estat desplegada i provada en un entorn real, aconseguint un augment del 28,4% en l'absistinència a llarg termini de pacients fumadors. L'aplicació Hypertension Patient Control (H-PC) ha estat dissenyada i implementada amb èxit, i els seus límits computacionals han estat mesurats.Esta tesis explora ténicas, modelos y algoritmos para una gestión eficiente de sistemas en la Nube y como aplicarlo en el sector de la salud con el fin de mejorar los tratamientos actuales. Presenta dos aplicaciones de salud electrónica basadas en la Nube para telemonitorizar y controlar pacientes fumadores e hipertensos. Se han obtenido diferentes modelos basados en la Nube y se han utilizado para desarrollar una infraestructura donde desplegar estas aplicaciones. Los resultados muestran que estas aplicaciones mejoran los tratamientos actuales así como escalan a medida que los requerimientos computacionales aumentan. Múltiples arquitecturas y modelos han sido analizados e implementados utilizando diferentes técnicas y escenarios. La aplicación Smoking Patient Control (S-PC) se ha desplegado y provado en un entorno real, consiguiendo un aumento del 28,4% en la abstinencia a largo plazo de pacientes fumadores. La aplicación Hypertension Patient Control (H-PC) ha sido diseñada e implementada con éxito, y sus límites computacionales han sido medidos

Soft real-time scheduling on multiprocessors

The design of real-time systems is being impacted by two trends. First, tightly-coupled multiprocessor platforms are becoming quite common. This is evidenced by the availability of affordable symmetric shared-memory multiprocessors and the emergence of multicore architectures. Second, there is an increase in the number of real-time systems that require only soft real-time guarantees and have workloads that necessitate a multiprocessor. Examples of such systems include some tracking, signal-processing, and multimedia systems. Due to the above trends, cost-effective multiprocessor-based soft real-time system designs are of growing importance. Most prior research on real-time scheduling on multiprocessors has focused only on hard real-time systems. In a hard real-time system, no deadline may ever be missed. To meet such stringent timing requirements, all known theoretically optimal scheduling algorithms tend to preempt process threads and migrate them across processors frequently, and also impose certain other restrictions. Hence, the overheads of such algorithms can significantly reduce the amount of useful work that is accomplished and limit their practical implementation. On the other hand, non-optimal algorithms that are more practical suffer from the drawback that their validation tests require workload restrictions that can approach roughly 50% of the available processing capacity. Thus, for soft real-time systems, which can tolerate occasional or bounded deadline misses, and hence, allow for a tradeoff between timeliness and improved processor utilization, the existing scheduling algorithms or their validation tests can be overkill. The thesis of this dissertation is: Processor utilization can be improved on multiprocessors while providing non-trivial soft real-time guarantees for different soft real-time applications, whose preemption and migration overheads can span different ranges and whose tolerances to tardiness are different, by designing new algorithms, simplifying optimal algorithms, and developing new validation tests. The above thesis is established by developing validation tests that are sufficient to provide soft real-time guarantees under non-optimal (but more practical) algorithms, designing and analyzing a new restricted-migration scheduling algorithm, determining the guarantees on timeliness that can be provided when some limiting restrictions of known optimal algorithms are relaxed, and quantifying the benefits of the proposed mechanisms through simulations. First, we show that both preemptive and non-preemptive global earliest-deadline-first(EDF) scheduling can guarantee bounded tardiness (that is, lateness) to every recurrent real-time task system while requiring no restriction on the workload (except that it not exceed the available processing capacity). The tardiness bounds that we derive can be used to devise validation tests for soft real-time systems that are EDF-scheduled. Though overheads due to migrations and other factors are lower under EDF (than under known optimal algorithms), task migrations are still unrestricted. This may be unappealing for some applications, but if migrations are forbidden entirely, then bounded tardiness cannot always be guaranteed. Hence, we consider providing an acceptable middle path between unrestricted-migration and no-migration algorithms, and as a second result, present a new algorithm that restricts, but does not eliminate, migrations. We also determine bounds on tardiness that can be guaranteed under this algorithm. Finally, we consider a more efficient but non-optimal variant of an optimal class of algorithms called Pfair scheduling algorithms. We show that under this variant, called earliest- pseudo-deadline-first (EPDF) scheduling, significantly more liberal restrictions on workloads than previously known are sufficient for ensuring a specified tardiness bound. We also show that bounded tardiness can be guaranteed if some limiting restrictions of optimal Pfair algorithms are relaxed. The algorithms considered in this dissertation differ in the tardiness bounds guaranteed and overheads imposed. Simulation studies show that these algorithms can guarantee bounded tardiness for a significant percentage of task sets that are not schedulable in a hard real-time sense. Furthermore, for each algorithm, conditions exist in which it may be the preferred choice

Stochastic Dynamic Programming and Stochastic Fluid-Flow Models in the Design and Analysis of Web-Server Farms

A Web-server farm is a specialized facility designed specifically for housing Web servers catering to one or more Internet facing Web sites. In this dissertation, stochastic dynamic programming technique is used to obtain the optimal admission control policy with different classes of customers, and stochastic uid- ow models are used to compute the performance measures in the network. The two types of network traffic considered in this research are streaming (guaranteed bandwidth per connection) and elastic (shares available bandwidth equally among connections). We first obtain the optimal admission control policy using stochastic dynamic programming, in which, based on the number of requests of each type being served, a decision is made whether to allow or deny service to an incoming request. In this subproblem, we consider a xed bandwidth capacity server, which allocates the requested bandwidth to the streaming requests and divides all of the remaining bandwidth equally among all of the elastic requests. The performance metric of interest in this case will be the blocking probability of streaming traffic, which will be computed in order to be able to provide Quality of Service (QoS) guarantees. Next, we obtain bounds on the expected waiting time in the system for elastic requests that enter the system. This will be done at the server level in such a way that the total available bandwidth for the requests is constant. Trace data will be converted to an ON-OFF source and fluid- flow models will be used for this analysis. The results are compared with both the mean waiting time obtained by simulating real data, and the expected waiting time obtained using traditional queueing models. Finally, we consider the network of servers and routers within the Web farm where data from servers flows and merges before getting transmitted to the requesting users via the Internet. We compute the waiting time of the elastic requests at intermediate and edge nodes by obtaining the distribution of the out ow of the upstream node. This out ow distribution is obtained by using a methodology based on minimizing the deviations from the constituent in flows. This analysis also helps us to compute waiting times at different bandwidth capacities, and hence obtain a suitable bandwidth to promise or satisfy the QoS guarantees. This research helps in obtaining performance measures for different traffic classes at a Web-server farm so as to be able to promise or provide QoS guarantees; while at the same time helping in utilizing the resources of the server farms efficiently, thereby reducing the operational costs and increasing energy savings