دانلود مقاله ترجمه شده کاربرد نظریه فیلد میانگین در مطالعه محاسبات ابری – مجله IEEE

بخشی از ترجمه:

امروزه تکنیک های محاسباتی ای که بر مبنای کلاینت/سرور وجود دارد، در حال تغییر رویکرد و موضع خود به سمت رایانش های ابری هستند.گرایشی که به سمت زیر ساختار های ابری وجود دار، فقط محدود به دنیای تجارت و شغل نیست، بلکه حتی ریشه در آژانس های دولتی نیز دارد. مدیران هر دو بخش باید یک دیدگاه شفافی از این حوزه داشته باشند تا بتوانند واکنش مناسبی به یک اقتصاد متغیر و محیط تکنولوژیک، نشان دهند. در این مطالعه قصد داریم  یک موازنه یا تعامل پویایی را در بکار گیری سرویس رایانش ابری، به وسیله ی کاربرد نظریه  فیلد میانگین ارائه دهیم. در فرمولاسیون ما، هر عامل (مثلاٌ هر شرکت یا آژانس دولتی)  در بین دو  مسئله ی ” پیاده سازی برنامه ی رایانش سنتی” و ” انتقال  به برنامه های رایانش ابری” قرار گرفته است. به منظور تصمیم گیری در خصوص اینکه سطح انتقال به رایانش ابری چطور باید باشد، هر عامل باید هزینه ی کلی ای که شامل دو مؤلفه میباشد را بهینه سازی کند: هزینه ی کاری مربوط به جابجایی به سرویس رایانش ابری و هزینه ی پیاده سازی رایانش ابری. در این فرمولاسیون،  هزینه ی بکار گیری برای پیاده سازی رایانش ابری ، متکی به تصمیم گیری در خصوص بکار گیری این سرویس ها میباشد. بنابراین یک سطح بهینه ی عامل در خصوص  بکار گیری این سرویس های ابری، نه تنها بسته به تلاش خودش و هزینه های بکار گیری دارد، بلکه متأثیر از تصمیم های بکای گیری این رویس ها نیز میشود. این مسئله ی تصمیم گیری، به وسیله ی سیستمی از معادلات دیفرانسیل جرئی (PDE) هال حال شده است، که در آن، PDE های بازی های فیلد میانگین، از یک PDE رو به عقب، معادله ی جاکوبی همیلتون برای یک مسئله ی کنترل شده و یک معادله ی Fokker-Planc تشکیل شده است. بنابراین، راه حلی که توسط معادله ی Fokker-planck فراهم میشود به ما اجازه داده تا تکامل پویایی چگالی را در بکار گیری رایانش ابری مورد مطالعه قرار دهیم. بنابراین این روش به ما اجازه داده تا تأثیر تصمیم گیری های بکار گیری تکنولوژی را بر روی تصیمم گیری بهینه ی شرکت مورد ارزیابی و بررسی قرار دهیم.

بخشی از مقاله انگلیسی:

Abstract— Computing is undergoing a substantial shift from client/server to the cloud. The enthusiasm for cloud infrastructures is not only present in the business world, but also extends to government agencies. Managers of both segments thus need to have a clear view of how this new era will evolve in the coming years, in order to appropriately react to a changing economic and technological environment. In this study, we explore the dynamic equilibrium of cloud computing adoption through the application of Mean Field Games. In our formulation, each agent (i.e., each firm or government agency) arbitrates between “continuing to implement the traditional on-site computing paradigm” and “moving to adopt the cloud computing paradigm”. To decide on his level of moving to the cloud computing paradigm, each agent will optimize a total cost that consists of two components: the effort cost of moving to the cloud computing paradigm and the adoption cost of implementing the cloud computing paradigm. In the formulation, the adoption cost is linked to the general trend of decisions on the computing paradigm adoption. Thus, an agent’s optimal level of transition to the cloud computing paradigm is not only dependent on his own effort and adoption costs but also affected by the general trend of adoption decisions. The problem is solved by a system of partial differential equations (PDEs), that is, mean field games PDEs, which consists of a backward PDE, the Hamilton Jacobi Bellman equation for a controlled problem, and a forward Fokker-Planck equation transported by the optimal control from the backward HJB equation. Thus, the solution to the forward Fokker-Planck equation enables us to study the dynamic evolution of the density of the cloud computing adoption. It therefore allows us to investigate the impact of the general trend of technology adoption decisions on a firm’s optimal decision of technology transition. I. INTRODUCTION Computing is undergoing a significant shift from client/server to the cloud, a shift similar in importance and impact to the transition from mainframe to client/server. Speculation abounds on how this new era will evolve in the coming years, and managers in business, industry and government have a critical need for a clear vision of where the industry is heading. To answer the question of “How will the computing paradigm transition evolve in the coming years?”, we believe that the general trend of decision has a big impact on individual decisions, as it is often the case in the evolution of information technology (IT). The objective of this work is to model and analyze this aspect. Economics aspects are naturally essential in shaping industry transformations. Accordingly, the emergence of cloud services is fundamentally shifting the economics of IT in several economics aspects. First, cloud technology standardizes and pools IT resources and automates many of the maintenance tasks done manually today. Second, cloud architectures facilitate elastic consumption, self-service, and pay-as-yougo pricing. Third, cloud allows core IT infrastructure to be brought into large data centers that take advantage of significant economies of scale in three areas, supply-side savings, demand-side aggregation and multi-tenancy efficiency. It can thus be seen that a firm, shifting from the traditional on-site paradigm to the cloud computing paradigm, may benefit from cost advantages through either shifting fixed costs to variable costs or through paying lower unit operation costs as a result of the positive economy of scales that cloud service providers experience. Consequently, it is reasonable to analyze a firm’s use of cloud computing as a cost minimization problem. However, individual costs of cloud computing adoption are also hinged on the general trend of adoption decisions of other entities as seen from the lower unit operation costs thanks to the positive economy of scales mentioned above. Focusing on such an economics perspective, we study the transition dynamics from the traditional on-site computing paradigm to the cloud computing paradigm as the dynamic equilibrium of decision on the technology upgrade through studying mean field games (MFG), introduced by JeanMichel Lasry and Pierre- Louis Lions ([2]). MFG is well adapted to economic modeling and is devoted to the analysis of differential games with a large number of “small” players who have very little influence on the overall system. Recent studies related to economics of cloud computing include Tak et. al. [6] and Kantarcioglu et. al. [5]. Tak et.al. [6] identify a comprehensive set of factors affecting the costs of a deployment choice, including in-house, cloud, and combination, and use “NPV (Net Present Value)-based” cost analysis for cloud computing adoption recommendations. They do not include the risk factor in their current version of analysis due to the complexity of quantifying associated security risk encountered with deployment choices. Kantarcioglu et. al. [5] use “Real Options Theory” to find the optimal time of shifting from the traditional on- 220 Fiftieth Annual Allerton Conference Allerton House, UIUC, Illinois, USA October 1 – 5, 2012 978-1-4673-4539-2/12/$31.00 ©۲۰۱۲ IEEE site computing paradigm to the cloud computing paradigm. Different from Tak et. al. [6], Kantarcioglu et. al. [5] model the benefit arising from the computing paradigm adoption decision as a jump diffusion process, which captures both uncertainty and security impacts on the optimal decision of transition to the cloud computing paradigm. The optimal decision is determined by a threshold level. Depending on the specification of the model, the threshold level may be either identified as a single benefit value or identified as a relative benefit ratio from the adoption of two distinct computing paradigms. In Kantarcioglu et. al. [5], the recommendation of computing paradigm adoption is a binary rule, either moving to the cloud computing paradigm or remaining the use of the traditional on-site computing paradigm. The current study, through studying MFG, focuses on the impact of the general trend of decision on the choice of computing paradigm transition times. The result is a dynamic equilibrium of the level of cloud computing adoption, replacing the stopping time decision (i.e., a binary decision) provided in Kantarcioglu et. al. [5]. That is, through the current study, we arrive at a firm’s optimal level of use of cloud computing, which can be any level between zero adoption of the cloud computing paradigm and complete adoption of the cloud computing paradigm, considering the general trend of adoption decisions. The remainder of the paper is organized as follows. In Section II, we first provide a general framework of modeling such computing technology transition problems, followed by giving a specific formulation of the problem. The existence of solution of the specific model formulation proposed is also studies. In Section III, we discuss the challenges in implementing the proposed model. We present concluding remarks in Section IV. II. THE MODEL We aim at characterizing the dynamic equilibrium of the computing paradigm shift between the choice of the traditional on-site computing paradigm and the cloud computing paradigm. We look at a large economy in a continuous time setting so that there is a sufficiently large number of firms, allowing an averaging effect. A. General Framework The formulation focuses on the impact of the general trend of decisions on the choice of technology transition times. In such a setting, a continuum of agents having homogenous preferences, pay a cost to move from one point to another point in the state space, X, where X(t) ∈ [۰, ۱] represents the level of use of cloud computing technology. Agents have the common cost function f(t, α, x, m(·),) representing what an agent pays to have the characteristics x (i.e., the level of cloud computing adoption) at time t. m(t, ·) is the density of the population for a given level of x and α(t) is a control variable modeling the effort of the firm in increasing its use of cloud computing technology. The evolution of X(t) is described as a random process with a drift term `(x, α) and a diffusion term σ(x); some specific formulation is given below in subsection II-B.