arXiv:1608.00944v1 [cs.DC] 2 Aug 2016 OAPA NIE YTM ORA,DI 10.1109/JSYST.2016 DOI: JOURNAL, SYSTEMS IEEE IN APPEAR TO s au tRs samauefrters flsn h value the losing of risk the uncertain the inherent in for its a measure given uncertainties a architecture, from of as distributed Additionally, migrating Risk of function parameters. at by a Value system use as lost) various changes and and (or architecture environment value gained distributed this is a how to that architecture (DARPA) value demonstration monolithic ca Agency net simplified we Projects simulation, the a the Through Research program. to of Advanced satellite modularity fractionated it Defense of the apply level of then ca the this We about how architecture. extensi explain making and an decision framework add enhance the We o to layer architecture spectrum. computational distributed architecture f and systems decision modularity five-stage conceptual unifies a and use that cost we instabilit m work paper, to this increase potential integrated In from in transition architectures. can widely-studied analogo result the are it however, of trade-off, and those as this behind system only, mechanisms the The benefits of archi Distributed provide complexity lifetime. not its uncertai during to does confront response may in it robustness sy that and a flexibility provides more architectures with monolithic from evo departure and scalability This increasing and accommoda stakeholders, becaus management, multiple uncertainty systems improving socio-technical in role and their technical complex many opttoa ytm rhtcue ope ytm,unc (MOS architecture systems, systems archi open complex modular distributed management, architecture, tainty architecture, systems systems computational satellites, ated gnyNS otatNNA11AB35C. contract Agency/NASA fTcnlg,Hbkn J 79 S.H snwwt Faceboo with now 10017. is NY He York, USA. 07093 NJ, Hoboken, Technology, of nepie,SeesIsiueo ehooy ooe,NJ Hoboken, [email protected]). 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NTRODUCTION negneigsseswhich systems engineering in itiue rMonolithic? or Distributed osnMse,KaDll,adBbkHeydari Babak and Dalili, Kia Mosleh, Mohsen 79 S (e- USA 07093 , vn Institute evens n. 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The appropriate level of system toward more decentralized scheme of architecture, in modularity is, among other factors such as technical design which subsystems are loosely coupled. For example, consider requirements, determined by the flexibility required for the a processing unit. Depending on the relative rate of change system to deal with the changes and uncertainties that the and uncertainty in the use, technology upgrade or budget, the system confronts during its lifetime. The value that modularity, CPU can be an integrated part of the system (e.g., Smart as a systems mechanism for managing uncertainty, adds to phone), becomes modular at discretion of the user (e.g., the system has a diminishing return. Although a low degree PC), transitions to client-server architecture to accommodate of modularity hampers response to environmental changes, smoother response to technology upgrade, security threads, or over-modularity increases the overall cost of the system, gives computational demand, or migrate to a fully flexible system rise to a host of potential problems at the interfaces. Hence, with dynamic resource-sharing (e.g., Cloud computing). finding the appropriate level of modularity, corresponding to In this paper, we formulate these problems under the underlying forces in the system’s environment, is a crucial step umbrella of the general concept of modularity. Modularity in decision-making under uncertainty from the perspective of has often been recognized as a general set of principles—as system architecture. opposed to a mere design technique—that enhance managing In this paper, we consider distributed architecture as a complex products and organizational systems. Modularity in part of a modular architecture spectrum and analyze the the broadest sense of word, is defined as a mechanism to trade-offs associated with migrating from a monolithic to a break up a complex system into discrete pieces that can then distributed architecture for a real, yet simplified, case of a interact with one another through standardized interfaces [10]. satellite system that was a part of a demonstration for a This broad definition of modularity requires us to think of DARPA/NASA program on fractionated satellites. We use a modularity as a continuous spectrum that includes a wide conceptual framework, developed in our previous work [9], range of architectures which covers integrated, modular yet to enhance architecture decisions according to the level of monolithic, and distributed schemes. This framework can be composition or modularity for systems under uncertainty. We used as a basis for computational methods for deciding about add an extensive computational layer to the framework, apply systems architecture and flexibility calculations related to it in the context of space systems, and analyze the value modularity. We will use this broad definition of modularity of design alternatives for various uncertainty parameters and together with the notion of a modularity spectrum to create subsystems configurations. The proposed framework helps to a framework that can be used as a basis for computational identify design alternatives based on the level of responsive- architecture decision methods and flexibility evaluation for ness to environment uncertainty achievable by various levels systems. of modularity. This provides decision makers with systemic Engineers have long held the intuition that more decen- intuition when selecting and evaluating alternatives for a given tralized schemes—i.e. higher levels of modularity—increase set of environment uncertainty parameters in the otherwise a system’s flexibility [11], [12]. They have used modularity intractable space of design alternative possibilities. In order for complexity management in many domains, such as soft- to determine the value of moving toward more decentralized ware [13], hardware architecture [14], the automotive industry schemes, we quantify the net gain in the value of the system [15], production networks [16], outsourcing [17], and mass that incorporates increased flexibility, and the associated cost customization [18]. Furthermore, modularity has widely been of adopting higher levels of modularity in the system. To studied and applied in organizational design and systems compute this value, we add a stochastic simulation layer on architecture [19]; it has been argued that a loosely coupled top of the proposed model that determines the conditions under firm, in which each unit can function autonomously and which transition toward a distributed architecture is sensible. concurrently, can benefit from increased strategic flexibility to Results of this framework are calculated in the form of proba- respond to environmental changes, due to reduced difficulty bility distributions of the net value of an architectural change, of adaptive coordination [20]. Proper use of modularity is to accommodate different decision makers with heterogeneous also argued to bring economies of scale, increase feasibility expected costs or tolerance for risk. of product/component change, increase product variety, and The organization of the rest of the paper is as follows. In enhance product diagnosis, maintenance, repair, and disposal Section II, we describe the underlying conceptual systems [21]. Finally, modularity is shown to help with increasing architecture framework [9] that is used in this paper, and systems flexibility and evolvability by reducing the cost of explain how it unifies modularity and distributed architecture change and upgrade in the system on the one hand, and on a five-stage spectrum and helps in selecting/evaluating facilitating product innovation on the other hand [14]. design alternatives. In Section III, we introduce the challenge Despite these advantages of modularity, there are studies of decision making for distributed architectures in space that show that many systems follow an opposite path toward systems. In Section IV, we add a computational layer to the more integration, which suggest thinking about its downsides conceptual framework and build a mathematical model for a and the underlying trade-offs [22], [23], [10], [24]. When simplified case of satellite systems. Finally, in Section V, we discussing such trade-offs, it is crucial to remember that mod- illustrate and compare configuration alternatives for different ularity is not a binary property but a continuum, representing values of uncertainties in the environment and various system the degree of coupling between components of a system, and parameters, and apply different measures, such as Value at describes the extent to which a system’s components can Risk (VaR), for comparison. TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 3
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M+ Operation: Decomposition Splitting Fractionation Resource sharing
• System on a chip • Smartphone • PC Mainboard • Client-server • Cloud Computing Mainboard
Fig. 1. Five-stage modularity and distributed architecture spectrum, and corresponding four M+ operations. Adaptability of the system increases as we move right. Each operation assesses the aggregate value of moving one step for a given system, subsystem or component [9].
II. MODULARITYANDDISTRIBUTEDARCHITECTURE depending on the specific problem and resolution needed, FRAMEWORK e.g., measures based on DSM for Modular (M2) systems [24] and network modularity index [34] for Dynamic-Distributed In conventional systems engineering approaches, design (M4) systems. The framework enhances systems architecture alternatives are evaluated based on meeting requirements that decisions under uncertainty by limiting the search space to are derived from a set of probable scenarios, practical and possible alternatives with various degrees of responsiveness technical limitations, and cost considerations. Requirement- to uncertainty. Selecting design alternatives from different driven approaches, by their very nature, are insufficient for defined stages in the architecture spectrum, together with assessing a system’s responsiveness to uncertainty. Unless quantifying the value of the transition from one stage to non-functional requirements are explicitly quantified [25], one another, effectively reduces the complexity of the design cannot use requirement-driven approaches to compare the decision problem and provides intuitions to systems architects. goodness of a more expensive design that exhibits smaller cost growth when it faces an undesired uncertainty, vis-a-vis The systems architecture framework [9] considers five a less expensive, yet inflexible design [4]. stages of modularity, indicated by M0 to M4. Stage M0 In this paper we use a value-centric design approach, which describes fully integrated systems, in which components are has been suggested as a way to overcome the shortcomings connected to each other in a way that neither physical nor of traditional approaches and to evaluate the flexibility of functional sub-parts can be identified, e.g., System on a Chip, design alternatives [26], [27], [28]. In this approach, the in which several electronic systems are integrated into a single focus is shifted from a requirement-centric to a value-centric chip. M0 is considered the minimum level of modularity and perspective in which the designer compares the system net is the baseline in the modularity framework. M1 represents present value for different design alternatives over the lifetime. systems with identifiable sub-parts, each responsible for a spe- The system value may encompass costs and revenue streams cific share of the overall system’s functionality. Components as well as the (real) option value of flexibility resulting from at this stage, although modular in function, cannot easily be modularity, scalablity, and evolvability [29]. customized, replaced, or upgraded during later stages of the Methods for deciding about systems architecture under system’s lifecycle. Smartphone and tablet mainboards can be uncertainty fall into two broad categories: Those that provide considered to be at this modularity stage. a set of qualitative systemic intuition to select plausible design At stage M2, similar to M1, functionalities can be broken alternatives (e.g., [30], [31]), and those that take a fixed set down and attributed to components. However, the related of alternatives as input and determine their optimality based components are connected to the rest of the system via on some exact methods (e.g., [32], [14]). In principle, one standardized interfaces. These standard interfaces allow the can combine these two methods to first find a set of design components to be replaced or upgraded without disrupting the alternatives based on systemic intuitions and then select the rest of the system. As opposed to Smartphone mainboards, most appropriate one (see [33] for an example in space personal computers mainboards are at stage M2, which allows systems). However, this two-step process is not sufficient users to customize or upgrade components such as memory for many problems where multiple iterations between these and CPUs. While M0, M1 and M2 encompass all cases of two steps are needed. Under these circumstances, a unified modularization for monolithic systems—systems comprised of framework that inherently includes both of these steps can a single physical unit—M3 and M4 cover systems with more significantly enhance the iterative process of nominating and than one unit, in which communications between units is a selecting design alternatives. possibility. As a unified framework, we employ a value-based decision At M3, certain functionalities of the otherwise monolithic making framework developed in our previous work [9]. This system are transferred to different, and often remote, physical framework is based on a systems architecture spectrum that units. Here, we refer to these units as systems fractions. A covers a wide range of modularity/distributed architecture in function can be centralized in one or more fractions, creating complex systems and classifies the degree of modularity into a client-server system in which a certain task can be delegated five stages, as shown in Fig. 1. While in this paper we only by a majority of fractions that lack a certain functionality, evaluate transitions between stages in the framework, within to a fraction with a powerful version of that module. A each stage, a continuous measure of modularity can be defined communication channel is needed for pre-processed and post- TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 4 processed resources between the client units and the server including technology evolution, demand fluctuation, launch fraction. Client-server computation systems are an example failure, funding availability, and changes in stakeholders’ of systems at stage M3. Unlike M3, in which the division requirements. Accommodating most of these uncertainties in of labor among subsystems is static, in M4, the task can be conventional monolithic designs would result in increased dynamically distributed among various fractions that have dif- cost and complexity. For example, in response to components ferent capabilities in terms of the required functionality. Cloud failure, the conventional approach either suggests extreme computing systems are an example of systems at M4. The measures of reliability or the use of redundant parts, both architecture of systems at M4 can be represented by complex of which result in higher mass, cost, and in most cases networks models where nodes represent subsystems and edges higher power. Addressing other types of uncertainties, such as represent interactions between the subsystems (subsystems’ changes in technology or stakeholder requirements, is either heterogeneous parameters can be modeled by nodes’ attributes not possible, or requires unconventional and often costly and heterogeneity of subsystems’ interactions can be modeled methods [37], [38]. by weighted links and multi-layered networks) [35], [36]. As a result of these problems, systemic flexibility is needed Moving to distributed architectures (i.e., M3 and M4) cre- to deal with the increased levels of uncertainty. New methods ates a more adaptable system, but this extra adaptability and have been suggested, based on flexible and adaptable design, flexibility come at a cost and, under certain conditions, may that enable spacecraft systems to respond to uncertainty more result in instability. The reason behind the increased chance of rapidly and at a reasonable cost. One approach is to deploy instability is that distributed architectures require complex task a constellation progressively, commencing with a small and coordination schemes to allocate resources under uncertain affordable capacity, which can be increased, as needed, in demand and there are often many paths for resource exchange stages by launching additional satellites and re-configuring the as well as multiple feedback loops between the components existing constellation in orbit [39]. Another approach is to in a system with high levels of modularity (i.e., Static- provide on-orbit servicing, which makes various options, such Distributed). Moreover, the chance of instability increases as service for life extension or upgrade, available after the further in systems with even higher levels of modularity (i.e., spacecraft has been deployed [37]. However, physical access Dynamic-Distributed), in which components have a level of to a space system is very expensive. Instead, software upgrades autonomy and their goals are not necessarily aligned with that and changes of function can be performed through information of the whole system. access to the space system, providing some level of flexibility Four M+ operations are defined in the framework that to address uncertainty [40]. Another approach to increase represent transitions from one stage of modularity to the next space systems’ responsiveness is fractionated satellites, a in terms of required changes in the system architecture and design concept in which modules are placed into separate the increased degree of modularity. In order to identify the fractions that communicate wirelessly to deliver the capability optimal modularity, we have to quantify and compare the of the original monolithic system [29]. value of the system prior to the operation, to the value of Due to the inherent flexibility that comes with distributed the system afterward. Such evaluation requires knowledge of and networked architectures, fractionated spacecraft are con- the system and its environment. The value of the system at sidered a viable solution for accommodating uncertainty in each modularity level can be calculated via any of the standard space systems. This is a departure from large, expensive, system evaluation methods (e.g., scenario analysis, discounted and monolithic satellite systems to a network of small-scale cash flow analysis) and should consider technical, economic and less expensive free-flying satellites that communicate and life cycle parameters. wirelessly. In this architecture, a new fraction can be launched It is worth noting that decisions in the proposed framework to become part of the network of satellites without disruption are based on the aggregate economic value that modular of the rest of the system. This option enables incremental architecture can add to a system by increasing the responsive- development and deployment, and increases system respon- ness to environment uncertainty. Hence, the framework can siveness [41], [38]. be used to evaluate design alternatives that are technically To decide about the level of flexibility of space systems viable, given factors such as physical constraints or perfor- architecture—e.g., through fractionation—one has to consider mance requirements. The proposed model can complement the the level of uncertainty and changes in the environment context dependent deterministic approaches for deciding about together with the cost associated with responding to them. modular architecture. Fractionated architecture—as a flexible architecture—does not come without cost and is not always the best choice for space systems. If applied inappropriately, fractionation may III. CASE STUDY:MONOLITHICANDDISTRIBUTED add no value, increase the cost and complexity, and cause ARCHITECTURES IN SPACE SYSTEMS instability due to multiple paths and feedback loops between Space systems are often required to deal with a large set of fractions. Hence, one has to calculate and compare the system uncertainties throughout their lifecycles, which in turn makes value over its lifetime for different design alternatives and design decisions challenging and, in many cases, intractable, balance it against the potential costs of each alternative, taking i.e., a large number of possible design alternatives should into account the effects of design variables and environment be evaluated against myriad number of uncertainty scenarios. uncertainty parameters, to find the optimal architecture. There are various sources of uncertainty for space systems Several studies have investigated the value proposition of TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 5
"(0(3$5(''(4-+0'$.5(30$69(4' it does not consider the level of modularity (composition) of )31/'5,('/1'8.$3-5:'42(&538/' design alternatives neither in identifying the candidates nor in evaluating them. (3-9('/$5,(/$6&$.' We apply this approach to a case of space systems in which )13/8.$610'1)'53$04-610' 12(3$513'' monolithic satellite systems and fractionated satellites can be, respectively, considered to be at levels of modularity M2 and 3 #(3)13/'451&,$46&' !09-310/(05'80&(35$-05:' M in the architecture spectrum inspired by a general notion 4-/8.$610'' $0''4:45(/'2$3$/(5(34' of modularity. Hence, we can apply the operation M2 → M3 for calculating the value of distributed architecture and graph it against different parameters. To accommodate stakeholders’ 9$.&8.$5(''-453-%8610'1)' 9$.8(''-*(3(0&(' risk tolerance, we use Value at Risk as a measure for the risk of losing the value of distributed architecture. In this case study, we particularly compare monolithic (M2) and fractionated 91/2$3('9$.8(4'1)' $.5(30$69(4' (M3) architecture. However, the proposed framework can also be used to evaluate the transition from fractionated to dynamic- distributed architecture (e.g., Federated satellites [50] and Fig. 2. Steps for generating and evaluating design alternatives Earth observation sensor web [51]) in space systems using the operation M3 → M4. The steps we took in calculating the value of distributed fractionated architecture in space systems [42], [41]. However, architecture are given in Fig. 2. First, we generate design decisions about the level of fractionation are challenging and alternatives based on the proposed modularity spectrum, i.e., depend on a wide range of system components’ characteristics M2 and M3. Next, we derive the mathematical formulation of and the environment uncertainty parameters. On the one hand, the transition operator. In our case we calculate the probability some studies have investigated the systems-level trade-offs in distribution of replacements for subsystems as well as the the transition from monolithic to distributed architecture for associated costs for each design alternative. Next, we run a space systems [8]. These studies have not operationalized the stochastic simulation based on the environment uncertainty systemic trade-offs in quantifying the value that is gained (or and the system parameters to find the probability distribution lost) in the transition from one level of flexibility to another of the value of the transition. Finally, we compare and evaluate at the component-level. On the other hand, a wealth of studies design alternatives based on economic measures such as Value have developed quantitative frameworks to perform tradespace at Risk. exploration that often generate (enumerate) a large number of design alternatives and then evaluate them against a range of scenarios [43], [44], [45], [46], [47]. Without considering IV. COMPUTING VALUE OF DISTRIBUTED ARCHITECTURE the systemic trade-offs (i.e., those of moving from monolithic In this section, we calculate the value of distributed archi- to distributed architecture) in the selection and evaluation tecture and illustrate it for a particular case in satellite systems, of design alternatives, these quantitative frameworks do not based on a simplified variation of fractionated architecture scale well for a large number of possible design alternatives developed as part of System F6 [53], [52]. We assume a and uncertainty scenarios. A unified framework can bridge satellite system that processes the data collected by a sensor two approaches to more effectively select and evaluate design payload and transmits them to earth via a high-speed downlink. alternatives. Moreover, a data connection link from Earth can be estab- In this paper, by developing computational aspects of the lished for maintenance purposes. In a conventional design, modularity and distributed architecture spectrum explained all of the subsystems are integrated and have to be launched in Section II, we combine the systemic intuition (i.e., how together. However, in the fractionated design, subsystems can modularity can improve system responsiveness to uncertainty be separated in flying fractions and launched independently. and what are the associated advantages/disadvantages) in se- The conventional monolithic system is at level M2 and the lecting design alternatives with their quantitative evaluation. fractionated system is at level M3 in the five-stage architecture This approach can enhance decision-making about systems spectrum introduced in Fig. 1. architecture by providing insights about the transition from Subsystems communicate internally through the spacecraft one level of system flexibility to another and aids in selecting bus, which also supplies power to the subsystems. The type and evaluation of different alternatives. The proposed approach (and cost) of a spacecraft bus is determined by the total can complement existing methodologies for assessment of mass of the subsystems it supports. Fractions communicate the value of flexibility in systems architecture design under through an extra Tech Package (F6TP, in the case of System uncertainty (e.g., [26], [48], [49]) by integrating the role of F6) that enables wireless communications among fractions. modularity in improving the system flexibility into the model. The subsystems involved in our analysis are as follows: For example, the method suggested in [48] is based on a (1) Payload: a sensor, (2) Processor: a high performance four-phase procedure (estimating the distribution of future computing unit, (3) Downlink: a high-speed downlink for possibilities, identifying candidate flexibilities, evaluating and transmitting data to earth, (4) Communications module: a choosing flexible designs, and implementing flexibility), yet broadband access to a ground network through Inmarsat I-4 TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 6
F6TP F6TP
PR PL PR DL Bus1 Bus2 PL CM Bus0
F6TP F6TP
DL
CM
Bus3 Bus4
(a) (b)
Fig. 3. (a) Monolithic satellite system (b) Fractionated satellites system, PR: Processor, DL: Downlink, CM: Communications Module, F6: F6TP, PL: Payload [52].
TABLE I COMPONENT COST, MASS, ANDRELIABILITYPARAMETERS. α IS THE can be considered as a lower bound for a given set of system SCALE PARAMETER AND β IS THE SHAPE PARAMETER OF THE WEIBULL parameters. DISTRIBUTIONTHATREPRESENTSSUBSYSTEMSRELIABILITY (MON.: Since we assumed that the system has to function to the MONOLITHIC,FRAC.:FRACTIONATED,PR: PROCESSOR,DL:DOWNLINK, CM: COMMUNICATIONS MODULE, F6: F6TP,PL: PAYLOAD) end of the project lifetime, we can calculate the cost of running a system as the total cost of building and launching Component α β Cost(K$) Mass(kg) its fractions in the beginning of the project and the cost Payload 15 1.7 27,000 50 of replacing them, given uncertainty over the lifetime. We Communications 870 1.7 35,000 70 Downlink 190 1.7 40,000 10 do not consider component costs that are identical for both Processor 90 1.7 30,000 20 architectures, e.g., subsystem design cost. We also assume F6TP 600 1.7 2,000 5 that the cost of building and the mass of a fraction are equal Bus (Mon.) 108 1.7 34,000 260 PL Bus (Frac.) 108 1.7 28,000 180 to the sum of its subsystem costs of building and masses, CM Bus (Frac.) 108 1.7 29,000 200 respectively. Additionally, we assume a linear launch cost, DL Bus (Frac.) 108 1.7 25,000 150 proportional to the total mass of the fraction. PR Bus (Frac.) 108 1.7 26,000 160 It is worth noting that the case study is intended to show how the proposed framework can be applied to a real-world GEO constellation, (5) Bus: spacecraft bus that accommodates system and present the trade-offs of distributed versus mono- subsystems on board, and (6) F6TP: F6 Tech Package that lithic architecture for different possible distributed architec- enables the communications between the fractions while flying ture designs. To this end, we used typical values for space in formation. systems and made few simplistic assumptions. For example, Fig. 3 shows the conceptual arrangement of subsystems for we did not consider the integration cost, however, this can the monolithic system and a possible allocation of subsystems be integrated into the model as an additional cost for each for a fractionated configuration. In Fig. 3a, all of the subsys- subsystem, which results in a shift in the value curve of design tems are integrated and communicate internally through the alternatives. Additionally, we assumed linear launch cost and bus without requiring an F6TP. In Fig. 3b, however, each of did not consider common costs in comparing the value of the four main subsystems is located in a separate fraction, two systems. Although these could substantially change the along with a bus and an F6TP. numerical results of our illustrative case, the model can be easily extended to take more realistic assumptions to study a particular real-world system. A. Value of distributed architecture In the analysis of this case, we compare the value of systems with different architectures, composed of similar main B. Modeling uncertainty subsystems, that fulfill the same overarching goal. Moreover, We take into account technological obsolescence and sub- we assume the systems have to function at an acceptable level system failure as two uncertainties that may affect the system of performance until the end of the project lifetime. Hence, over the lifetime. Other uncertainties can be integrated into one way to quantify the value difference between two systems our model in a similar way. We assume that the uncertainties is to compare the cost of designing, building, launching and have known probability distributions that can be approximated operating them over a fixed project lifetime. Particularly, in from historical data. We classify launch failure and in-orbit our case, we calculate the value of distributed architecture collisions as bus failure so the failure of each subsystem as the difference in cost of running a fractionated system will be only attributed to its own reliability parameters and versus the monolithic system. Note that the value of distributed we assume that subsystem failure times are independent. In architecture could potentially be much higher than what is accordance with [29], we use the Weibull probability distri- obtained through the method presented here, as distributed bution for subsystem failure with probability characteristics architectures also enable scalability and evolvability in the presented in Table I. For technological obsolescence, we usea long run. As a result, this method is a conservative approach, Log-normal distribution and assume subsystem obsolescence especially in the long run and the net value calculated here times are independent. We assume that a subsystem has to TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 7 be replaced when it fails or becomes obsolete in the sense launching subsystems and the probability distributions of their that a new technology is introduced and the subsystem has replacement times. to be upgraded through replacement in order to receive the In a distributed architecture, a fraction has to be deployed benefits of the new technology. We do not consider factors and launched once one of its subsystems requires replacement. such as market competition, demand, and performance level Similarly, for a monolithic architecture, we can consider a in the decision for replacement of obsolete subsystems. system with only one fraction such that the whole system We calculate the probability density function (PDF) of has to be replaced if one of its subsystems becomes obsolete replacement time for subsystems as follows. Suppose obso- or fails. Hence, in order to find the value of a distributed lescence time and failure time of subsystem i are given by architecture, we can compare the cost imposed by each sub- the random variables Oi and Fi, respectively, and the random system replacement in a distributed architecture with that of variable Ti denotes time of replacement. The PDF, gi(t), and an equivalent monolithic architecture over the project lifetime. CDF (cumulative distribution function), Gi(t), of replacement Note that we assume the revenue which is generated by time for subsystem i can be calculated as follows: different distributed and monolithic design alternatives is the same and we only calculate the cost of operating the system. G (t)= p(T ≤ t)=1 − p(T >t) i i i Calculating the revenue generated by each design alternative =1 − p(Oi > t,Fi >t) (1) requires modeling the market uncertainty, the feedback of the =1 − p(Oi >t)p(Fi >t) system to its market, and the system scalability.
=1 − (1 − Φi(t))(1 − Ψi(t)). We formulate the cost of running the system as follows. For each fraction j, suppose a sequence of random variables Differentiating both sides of Eq. 1 yields the following: R1j , R2j ,...,Rnj represents the time between two consecu- − − tive replacements. A new instance of a fraction j has to be gi(t)= ϕi(t)(1 Ψi(t)) + ψi(t)(1 Φi(t)) (2) 1 n deployed at times R0j = 0, i=0 Rij ,..., i=0 Rij for the where Φ and ϕ are the CDF and PDF for obsolescence time, system to function without interruptionP untilP the end of its life- respectively, and Ψ and ψ are the CDF and PDF for failure n time, where n is the largest integer such that i=0 Rij Fig. 4. Total cost of monolithic (M2) vs. fractionated (M3) architecture Fig. 5. Probability distribution for the value obtained through transition from discounted to present time graphed against project lifetime for 10,000 trials. M2 (Integral) to M3 (Fractional) in the modularity and distributed spectrum, The curves represent expected values, and the boxplots depict quartiles of the i.e., project lifetime = 15 years. The vertical line at 0 represents Value at Risk cost. 55% is 0, meaning that area to the left represents 55% of the total area under the curve. The input to the simulation includes subsystem costs, masses, and failure and obsolescence probability distribution param- eters. Table I shows the estimates for costs and masses of discounted to present time. The curves in Fig. 4 represent the the main subsystems (e.g., Payload, Communication module, expected cost of each architecture during the project lifetime. and Downlink), F6 Tech-Package and spacecraft buses that The curves have relatively low slopes in the beginning of the accommodate subsystems on board. The values for spacecraft system lifetime, due to the low probability of obsolescence buses are based on commercially available spacecraft buses, and failure in the early years. The initial cost of running which are chosen according to the subsystems on board and the fractionated system is greater than that of the monolithic their total masses. α and β in Table I respectively represent system due to fractionation cost, i.e., the cost of building the scale parameter and the shape parameter of the Weibull additional subsystems, such as F6TP. However, the expected distribution2 for subsystem failure. We assume a mean value lifetime cost of the monolithic system increases faster over of 1 year3 with a standard deviation of 3 years for the obso- time because the whole system must be deployed and launched lescence probability distribution. We also assume that buses once again when a subsystem fails or becomes obsolete. and F6TP do not become obsolete. Moreover, we consider The boxplots in Fig. 4 depict the probability distribution $30k per kg for launch cost, which is the average cost for of cost for every 3 years. The cost variance at each point commercially available launch vehicles [56]. The discount is the result of two opposing forces. On the one hand, the rate in our simulation is 2%, which is based on a forecast intrinsic property of the underlying stochastic process results of real interest rates from which the inflation premium has in an increase of cost variance by time. On the other hand, been removed and based on the economic assumptions from over the project lifetime, whenever a subsystem is deployed 2014 for 30+ year programs [57]. We run our simulation for and launched due to failure or obsolesce, the time to replace it a project lifetime of up to 30 years, which is well beyond is also reset, which reduces the cost variance. In the monolithic the standard design lifetime of 10 years [29]. All simulation architecture, when a component fails, the time of replacement results are based on 10,000 trials. for the whole system is reset with a high cost. However, in the case of failure of the equivalent component in the fractionated A. Comparing fractionated and monolithic satellite systems architecture, the times to replace the other components do not Fig. 4 illustrates the cost of operating a fractionated satellite change. Instead, a failure results in a lower cost. Fig. 4 shows system, in which each main subsystem is assigned to a that the cost variance for the two systems increases by time. separate fraction, and that of a monolithic system. All costs are However, the monolithic architecture has a higher variance in every time step. This is due to the dominance of the impact 2The PDF and CDF of the Weibull distribution are as follows: of costs associated with each subsystem replacement incident. β β ( x )(β−1)e−(x/α) x ≥ 0 f(x)= α α Fig. 5 depicts the probability distribution of the value of 0 x< 0 a distributed architecture having each main subsystem in a β separate fraction at T =15 years. As a measure of value loss 1 − e−(x/α) x ≥ 0 F (x)= under uncertainty, we use Value at Risk (VaR). As depicted in 0 x< 0 Fig. 5, for p = .55 the net positive gains in transitioning from 3This is based on the assumption that in modular and fractionated satellite systems, computational and sensing subsystems will most likely be silicon- M2 to M3 is positive, meaning that there is a 0.55 probability based whose obsolescence follows Moores law. that the value of distributed architecture falls below zero. TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 9 TABLE II VALUEOF DISTRIBUTED ARCHITECTURE FOR DIFFERENT PAYLOADS (EV: EXPECTED VALUE,VAR: VALUE AT RISK, p = .25) year 5 year 10 year 15 year 20 year 25 year 30 Cost(K$) Weight(Kg) EV VaR EV VaR EV VaR EV VaR EV VaR EV VaR Payload 1 31,652 230 -73 -96 -38 -96 -8 -96 20 -85 45 -66 67 -50 Payload 2 34,132 260 -66 -96 -21 -96 18 -96 54 -64 87 -45 118 -26 Payload 3 40,332 335 -58 -96 4 -96 57 -96 106 -50 150 -17 190 10.13 B. Effects of payloads’ attributes on system value In this section, we run the simulation for different pay- load attributes and calculate the probability distribution of the value that is obtained in transition from monolithic to distributed architecture. Table II shows the effect of payload characteristics (i.e., cost and weight) on the value of distributed architecture. For each payload, Table II shows the expected value (EV) and Value at Risk (VaR, p=0.25) of the value of distributed architecture every five years in the project lifetime. Payload 1, Payload 2, and Payload 3 are progressively heavier and more expensive. The results in Table II show that for a given moment in time during the project lifetime, distributed architecture creates higher value for a system with a more expensive payload and higher mass. It can be observed that a distributed architecture does not add any value to the system with Payload 1 in the first half of the lifetime (e.g., EV=-8 Fig. 6. Effects of F6TPs reliability parameters on value of distributed @year=15). However, it does add value earlier in the lifetime architecture (i.e., project lifetime=15 years). of the system with Payload 2 (e.g., EV=18 @year=15) and Payload 3 (e.g., EV=4 @year=10). Table II shows that, in this case, a distributed architecture is a better choice for more F6TP is short, there will be a huge cost to keep the system expensive payloads with higher masses over a shorter lifetime, functional, due to the large number of replacements of whole all other things being equal. This is because in a monolithic fractions resulting from the F6TP failure and a monolithic system with an expensive payload, a failure in any subsystem architecture is always superior, as expected. Therefore, F6TP’s will result in replacement of the payload, which imposes average lifetime has to be above a certain threshold so that a high cost on the system. However, in the fractionated fractionation is sensible. Moreover, beyond a certain value of system, the payload is only replaced once a component in the F6TP’s average lifetime (e.g., 100 years for β = 1.7), the payload’s fraction—e.g., F6TP, bus or the payload itself— the value of fractionation is not much affected by the F6TP’s fails or becomes obsolete. Hence, when the payload is more reliability parameters because the number of replacements expensive, the cost of fractionation is dominated by the savings of F6TP due to failure is negligible in the given lifetime due to elimination of unnecessary payload replacements in the (i.e., F6TP’s average lifetime is much greater than the project fractionated architecture. lifetime). C. Effects of F6TP’s reliability parameters on system value D. Comparing design alternatives with different distributions Since F6TP is an additional subsystem required for com- of subsystems munications between fractions in a distributed architecture, it Distributed architecture (level M3 in the proposed spectrum) is important to analyze how its parameters affect the value includes a range of architectures with different numbers of of a distributed architecture. Fig. 6 shows the effects of fractions and allocations of subsystems. In this section, we the F6TP reliability parameters on the value of distributed study the effect of subsystem allocation on the value of architecture for the project lifetime of 15 years. In this figure, fractionation. In our case, there are 15 (B4 = 15 [59]) possi- β is the shape parameter of the Weibull distribution that is ble allocations of subsystems into fractions. We demonstrate commonly used in modeling satellite reliability. A Weibull the comparison of design alternatives for four architectures shape parameter greater than one represents an increasing (including the monolithic architecture) with different number failure rate or “wear-out”. β = 1.7 is a typical value in of fractions. However, the same analysis can be applied to modeling reliability of satellites [58]. The value of distributed all possible alternatives with the model being fairly tractable. architecture is highly sensitive to F6TP reliability parameters We compare the fractionation value for the three architectures for its shorter average lifetime. The curves which belong to depicted in Fig. 7 based on the monolithic equivalent archi- higher values of β represent higher increase rate of the value tecture. of distributed architecture against the F6TP’s average lifetime. The architecture in Fig. 7a has two fractions. The Processor For a given shape parameter, when the average lifetime of the and Payload are placed in one, and the Communications mod- TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 10 TABLE III VALUEOF DISTRIBUTED ARCHITECTURE FOR DIFFERENT NUMBEROF FRACTIONS FOR THE CONFIGURATIONS GIVEN IN FIG.7 (EV:EXPECTED VALUE,VAR: VALUE AT RISK, p = .25) year 5 year 10 year 15 year 20 year 25 year 30 EV VaR EV VaR EV VaR EV VaR EV VaR EV VaR Architecture (a) -15 -34 11 -34 34 -50 54 -53 74 -51 92 -46 Architecture (b) -44 -68 -10 -68 18 -68 47 -68 71 -65 94 -50 Architecture (c) -72 -102 -29 -101 11 -102 45 -73 76 -55 106 -35 ule and Downlink are placed in another fraction. Fig. 7b de- picts a system with three fractions. The Payload and Processor %&% %#% ",% %#% ",% %&% ",% !#% ",% $% ",% are in their own fractions, while Communications module and !('*% !('*% !('*% !('*% !('*% Downlink are located together in the same fraction. Finally, Fig. 7c represents a system in which each subsystem is placed $% !#% ",% $% !#% ",% %#% ",% %&% ",% in a separate fraction. !('+% !('+% !('*% !('*% We calculate the probability distribution of the value of transition from monolithic to distributed architecture for each (a) (b) (c) architecture independently and compare the results. The ar- chitectures in Fig. 7 are progressively—from a to c—more Fig. 7. Allocation of subsystems between fractions together with the number of fractions in Table III, (a) two fractions, (b) three fractions, (c) four fractions flexible but more expensive to build. Table III shows the (PR: Processor, DL: Downlink, CM: Communication Module, F6: F6TP, PL: expected value (EV) and Value at Risk (VaR, p=0.25) of the Payload) distributed architecture every five years in the project lifetime for the systems conceptually depicted in Fig. 7. For each fraction in these architectures, we estimated mass and cost loss of an uncertain value, to accommodate the stakeholders’ of the spacecraft bus based on the total mass of subsystems threshold of risk. that are on board and according to commercially available Distributed architectures—and in the case study of this spacecraft buses. paper, fractionated satellites—also increase scalability and Table III shows that systems with a larger number of resilience and foster innovation. For example, to accommodate fractions have a lower value in the earlier years of their uncertainty in the demand, additional modules can be launched lifetime. This is due to the dominance of high fractionation throughout the lifetime of the system and become part of it. cost in the beginning of the lifetime—i.e., the higher cost of Similarly, upon failure of a module the fraction can evolve launching more fractions and the cost of additional subsys- so that the system continues to function. None of these tems. However, later in the system lifetime, the value of a advantages were explicitly considered in assessing the value of distributed architecture in the systems with a larger number of fractionation in our model, which was focused solely on flex- fractions outgrows that of systems with a smaller number of ibility and uncertainty management. Ignoring these additional fractions. This shows that the benefits of responsiveness of the advantages, our proposed approach represents a lower bound system with a larger number of fractions becomes dominant for the value that is obtained in the transition to distributed over a longer lifetime. The results in Table III demonstrate the architecture for the given set of system parameters. We also trade-off between higher flexibility and its associated costs believe that resilience mechanisms can, in theory, be modeled i.e., higher flexibility results in less cost in responding to and integrated into the proposed framework. However, the environment uncertainty, yet making the system more flexible effect of architecture on scalability needs to be modeled by is costly. The results suggest that for projects with longer considering the feedback of the system to its market, some- expected lifetime, it is worth investing on the flexibility of thing that requires an additional layer on top of the proposed the system through higher number of fractions. framework. Quantifying the impact of distributed architecture on creativity mechanisms is even more challenging due to a VI. CONCLUSION need to simultaneously integrate technological, behavioral, and Building on a conceptual systems architecture framework economic factors into the model. Thus, it is often best to keep in this paper, we developed a computational approach for models of these systems features semi-qualitative and separate decisions about the level of modularity of system architecture. from flexibility models, unless the exact context and path of We quantified the value that is gained (or lost) in the transition the system is known. This is rarely the case and often defeats from a monolithic system architecture to a distributed system the original purpose of moving toward distributed architectures architecture. We applied this approach to a simplified case of in the first place. a space system, and compared the value difference between Additionally, in this paper we used a single criteria stochas- the two architectures as a function of uncertainties in various tic decision model under uncertainty to find the architecture system and environment parameters, such as cost, reliability, that optimally respond to the uncertainty in the environ- and technology obsolescence of different subsystems, as well ment. Future research is needed to integrate multiple criteria as the distribution of subsystems among fractions. We used and multiple stakeholders decision models into the proposed Value at Risk, a commonly-used measure for the risk of model. TO APPEAR IN IEEE SYSTEMS JOURNAL, DOI: 10.1109/JSYST.2016.2594290 11 ACKNOWLEDGMENTS [21] C.-C. Huang and A. 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