Managing deadline miss ratio and sensor data freshness in real-time databases Abstract-The demand for real-time data services is increasing in many applications including e-commerce, agile manufacturing, and telecommunications network management. In these applications, it is desirable to execute transactions within their deadlines, i.e., before the real-world status changes, using fresh (temporally consistent) data. However, meeting these fundamental requirements is challenging due to dynamic workloads and data access patterns in these applications. Further, transaction timeliness and data freshness requirements may conflict. In this paper, we define average/transient deadline miss ratio and new data freshness metrics to let a database administrator specify the desired quality of real-time data services for a specific application. We also present a novel QoS management architecture for real-time databases to support the desired QoS even in the presence of unpredictable workloads and access patterns. To prevent overload and support the desired QoS, the presented architecture applies feedback control, admission control, and flexible freshness management schemes. A simulation study shows that our QoS-aware approach can achieve a near zero miss ratio and perfect freshness, meeting basic requirements for real-time transaction processing. In contrast, baseline approaches fail to support the desired miss ratio and/or freshness in the presence of unpredictable workloads and data access patterns. T HE demand for real-time data services is increasing in many important applications including e-commerce, online stock trading, agile manufacturing, sensor data fusion, traffic control, target tracking, and telecommunications network management. In these applications, transactions should be processed within their deadlines, i.e., before the market, manufacturing, or network status changes, using fresh (temporally consistent) sensor data 1 that reflect the current real-world status. Existing (nonreal-time) databases are poor at supporting timing constraints and temporal consistency of data. Therefore, they do not perform well in these applications.. Real-time databases need to execute transactions within their deadlines using fresh data, but meeting these fundamental requirements is challenging. Generally, transaction execution time and data access pattern are not known a priori, but could vary dynamically. For example, transactions in stock trading may read varying sets of stock prices, and perform different arithmetic/logical operations to maximize the profit considering the current market status. Transactions can be rolled back and restarted due to data/resource conflicts. Further, transaction timeliness and data freshness can often pose conflicting requirements. By preferring user requests to sensor updates, the deadline miss ratio is improved; however, the data freshness might be reduced. Alternatively, the freshness increases if updates receive a higher priority [3] .. To address this problem, we present a novel real-time main memory database architecture called QMF (a QoS management architecture for deadline Miss ratio and data Freshness). QMF provides several QoS parameters to let a database administrator (DBA) specify the desired miss ratio and data freshness for a specific application. QMF applies a feedback-based miss ratio control scheme since feedback control is very effective to support the desired performance when the system model includes uncertainties [13] , [16] , [23] . At each sampling instant, the feedback-based miss ratio controller measures the miss ratio and computes the miss ratio error, i.e., the difference between the desired miss ratio and the measured one. Based on the miss ratio error, the controller computes the control signal, i.e., the required workload adjustment to react to the error. QMF can achieve the desired miss ratio via series of reactions to reduce the error even if an individual reaction is not completely precise. When overloaded, the freshness manager, which manages data freshness in QMF, updates relatively less important sensor data on demand or increase their update periods according to the miss ratio control signal. 2 QMF also applies admission control to incoming transactions under overload conditions. By adapting update workloads before applying admission control, QMF can admit (and process) more transactions.. In our earlier work [8] , we presented an adaptive update policy to balance potentially conflicting miss ratio and freshness requirements. Initially, all data are updated immediately when their new sensor readings arrive. Under overload, some sensor data can be updated on demand to improve the miss ratio as long as the target freshness, perceived by the transactions that commit within their 1 . In this paper, we do not restrict the notion of sensor data to the data provided by physical sensors. Instead, we consider a broad meaning of sensor data. Any data item, whose value reflects the time-varying realworld status, is considered a sensor data item.. 2. The freshness manager is an actuator from the control theory perspective. We do not consider a separate controller for freshness management, since miss ratio and data freshness requirements can conflict leading to an unstable feedback control system that may oscillate between many deadline misses and freshness violations.. deadlines, is supported. The adaptive update policy can effectively balance miss ratio and data freshness requirements [8] . It contrasts to the existing database update policy commonly accepted in the real-time database research such as [3] , [9] , [17] , which is fixed and not adaptable regardless of the current system status. However, the adaptive update policy has a potential disadvantage. Consider a case in which real-time transactions with tight deadlines need to access a sensor data object that is updated on demand. The transactions may have to miss their deadlines waiting for the on-demand update. Or, to meet their deadlines, they may have to use a stale version of the data, outdated since the last on-demand update, even though the chances are small. 3 Neither is desirable. To prevent potential deadline misses or stale data accesses due to the delay for on-demand updates, we present an alternative approach in which all data are updated immediately. In this approach, we present novel notions of QoD (Quality of Data) and flexible validity intervals to manage the freshness. 4 When overloaded, update periods of some sensor data can be relaxed within the specified range of QoD to reduce the update workload, if necessary. However, sensor data are always maintained fresh in terms of flexible validity intervals. Therefore, the age of sensor data is always bounded. (A detailed discussion is given in Section 4.). Real-time databases should determine the frequency of sensor data updates considering the rate at which the realworld status changes (or may change) [17] . For this reason, we measured the average intertrade time of popular stock items using the real-time NYSE trade information, which is streamed into an online trading laboratory at the University of Virginia. From these studies, we derived a range of sensor update periods used for our simulation study (discussed in detail in Section 6). Unlike our work presented in this paper, existing real-time database work such as [1] , [3] , [9] do not consider actual data freshness semantics, mainly determined by the update frequency, for performance evaluation.. Based on performance evaluation results, we show that QMF can support stringent QoS requirements for a large range of workloads and access patterns. QMF achieves a near zero miss ratio and perfect freshness even given dynamic workloads and data access patterns. 5 In contrast, several baseline approaches, including best existing algorithms for timeliness and freshness trade-off in real-time databases [3] , fail to support the specified miss ratio and/or data freshness. Further, our approach achieves a higher throughput than the baselines. This is because QMF can avoid overload conditions, which can cause many deadline misses, by carefully adapting the system behavior in the feedback loop as discussed before.. The rest of the paper is organized as follows: Section 2 describes our real-time database model. Flexible sensor update schemes are presented in Sections 3 and 4. In Section 5, our QoS management architecture including the feedback control scheme is described. The performance evaluation results are presented in Section 6. Related work is discussed in Section 7. Finally, Section 8 concludes the paper and discusses future work. Processing real-time transactions within their deadlines using fresh data is essential but challenging. To address the problem, we have 1. defined QoS metrics in terms of miss ratio and novel data freshness metrics to let a DBA specify the desired QoS, 2. introduced flexible QoD management schemes, 3. presented a new QoS management architecture that can support the desired QoS even given dynamic workloads and access patterns, and 4. designed real-time database workloads considering the real-time data semantics observed in NYSE trade traces and transaction execution times modeling high performance main memory databases. In an extensive simulation study, QMF achieved a significant performance improvement compared to several baselines including best existing algorithms for miss ratio and freshness trade-off in real-time databases, while supporting the target miss ratio and freshness (except for bursty workloads). As one of the first work on QoS management in real-time databases, the significance of our work will increase as the demand for (and importance of) real-time data services increases. In the future, we will further investigate the timeliness and freshness issues in both centralized and distributed real-time databases. . For more information on this or any computing topic, please visit our Digital Library at www.computer.org/publications/dlib. Considering the abundance of QoS and database research work separately, relatively less work has been done on realtime database QoS management [3] , [20] . This can be a serious problem; it has been reported that approximately $420 million revenue loss resulted due to late, i.e., nonrealtime, e-commerce transaction processing in 1999 [2] .. Adelberg et al. have found that timeliness and freshness requirements may conflict in real-time databases [3] . To balance the conflicting requirements, they presented several algorithms for scheduling sensor data updates and user transactions. Our flexible freshness management schemes extend their work by dynamically adapting the update policy or periods, if necessary, to manage overloads. Consequently, QMF achieves a better performance as discussed before.. Other aspects of the real-time database performance can be traded off to improve the miss ratio. In [15] and [20] , the correctness of answers to queries can be traded off to enhance timeliness by using the database sampling and milestone approach [12] , respectively. In these approaches, the accuracy of the result can be improved as the sampling or computation progresses, while returning approximate answers to the queries, if necessary, to meet their deadlines. An adaptable security manager is proposed in [18] , in which the database security level can be temporarily degraded to enhance timeliness. These approaches carefully trade off conflicting performance metrics, and thereby significantly improve the miss ratio. Conceptually, our flexible freshness management scheme is analogous to these approaches in terms of performance trade-off. However, it is hard to directly compare our freshness metrics to their performance metrics, i.e., accuracy of query results and data security. Also, a naive combination of our scheme with theirs may cause unexpected side effects incurring intolerable inaccuracy of query results or security risks, which are beyond the scope of this paper.. Feedback control has been applied to QoS management and real-time scheduling [11] , [13] , [23] due to its robustness against unpredictable operating environments [16] . However, these work do not consider real-time transaction processing and freshness management issues; therefore, they are not directly comparable to our work. Feedback control has also been recognized as a viable approach to manage the (non-real-time) database performance [21] , [22] . They substantially improved the database throughput/ response time by applying high level notions of feedback control, i.e., performance observation and dynamic adaptation of the system behavior in a conceptual feedback loop. However, they intend to manage the database throughput, which is known to be very different from managing the miss ratio of real-time transactions [9] , [17] . Generally, a lot of work remains to be done to manage the database QoS, since the related research is still in its infancy.

O B I I O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Social media institutionalization in the U.S. federal government a b s t r a c tNew technology adoption Institutionalization Social media U.S. federal government Social media adoption changes the existing organizational technology paradigm of public sector organizations. This paper explains the internal decisions that are necessary before new technologies can be used to support the strategic mission of a government organization and which behavioral and technological changes are integrat ed into the organization's standard operating procedures. This is an important theoretical contribution, because social media technologies are developed and hosted by third parties outside of government, with government's role limited to reactively evaluating their internal needs, strategic alignment, and existing routines. Evidence from qualitative interviews with social media directors in the U.S. federal government and a digital ethnography of their online practices expand the existing theory of social media adoption by adding two distinct activities: strategic alignment and routinization which lead to the institutionalization of new technologies. Social media use among the federal agencies in the U.S. executive and legislative branches has become an accepted technology use to interact with the public in general, with other government agencies, and also to collaborate internally. The adoption of social technologies that are owned by third parties oftentimes constitutes a challenge for public man agers. They have to rely on external technology platforms designed and hosted outside of government, which involves uncertainty of changes in the platforms, and uncontrollable cybersecurity risks that have to be mitigated by the platform providers. Agencies cannot opt out of revisions of the technology. They cannot hire contractors to outsource changes or request customization services to platforms to accommodate govern ment needs. Public managers in charge of social media accounts are therefore exposed to constant changes of the platforms and at the same time have to deal with emergent citizen and employee behavior that challenge government's one directional communication paradigm. The social behavior and culture evolving around social media technologies puts agencies in a reactive mode and formal mechanisms, such as social media policies and organizational structures subsequently have to be adapted as a result of the observed user behavior and technological changes (Mergel and Bretschneider 2013) .. Most of the experience using social media was derived from President Obama's first presidential campaign in 2008 and replicated in his second run for office in 2012 (see for example : Shirky, 2011; Smith, 2009) . Social media was heavily used by campaign staff to increase citizen participation and helped to influence online users of so cial media sites to change their behavior: people were moved from online interactions with the candidate to offline actions such as register ing to vote and then showing up at the voting booths on Election Day. Social media played a crucial role in targeting citizens who have already registered, but were unsure who to vote for and also to use those with a clear choice to convince their friends in their online networks to vote for the candidates (Hong and Nadler 2012) . Even though a political cam paign has some parallels to the goals of a communication strategy in the public sector, the most common mission relevant communication focuses on educating and informing the public. The goal is usually to passively inform the public, potentially improve transparency of opera tions, and if possible improve buy in for government actions. Calls for action, such as specific behavioral changes are left to certain agencies in volved in emergency situations, such as food or drug recalls or disaster preparedness and response.. Government agencies evaluate how social media can support their mission beyond the formal informing and educating goals and potential innovative practices that social media tools allow them to implement. These strategic decisions are highly context specific. Organizations like NASA that is fan based have very different organizational missions than regulatory agencies with an enforcement mandate. The decisions on how to institutionalize social media and integrate new routines in the existing communication strategy are therefore highly individual to each government organization and evolve over time as Mergel and Bretschneider (2013) in their phased model of social media implemen tation showed.. The research questions addressed in this article are: how do government agencies in the U.S. federal government agencies of the executive branch approach the formalization and institutional ization of social media by adapting their internal organizational and institutional norms and regulations and standard operating procedures? Social media innovations are occurring inside and outside of govern ment. Technology companies are changing the technology itself and cit izens are changing their behavior. Government agencies are therefore experiencing a need for constant realignment. Otherwise the routinized use might lead to what Rogers calls misalignment and the organizatons might abandon or reduce to minimally invasive practices, such as return to old routines of only publishing after action reports and press releases.. In conclusion, social media adoption is impacted by institutional and organizational mechanisms that direct the degree and extent of adop tion. The institutional mechanisms are oftentimes out of the control of the public managers interviewed for this study. Overarching institution al norms and regulations evolve as social media practices emerge and administrative needs evolve that result in formalization of behavior. Organizational governance mechanisms as a result then include chang es in management practices, such as the establishment of roles and re sponsibilities, or retroactive budget allocations for capacity building. Both, institutional and organizational governance mechanisms, influ ence the interactivity of online tactics.. Similar to previous waves of e government and ICT adoption, social media adoption follows a diffusion curve (Rogers, 1976 (Rogers, , 1995 (Rogers, , 2005 . In early stages of the adoption of a new technology, there seems to be enough bureaucratic discretion to experiment with a variety of social media tools and modes of online interactions, however as organizations are making positive and negative experiences with social media, more and more institutional and organizational governance processes and procedures are designed to be in alignment with the hierarchical norms and standard operating procedures of the accepted technology standards.. This study also shows that while many institutional and organi zational routines and norms are persistent across waves of technol ogy innovations, external triggers create motivation to adapt new technologies. Even if there might be a phase of innovative behavior that is pushing the boundaries of the acceptable use of technology, the responses of the bureaucracy itself result in new routines and adaption of the standard operating procedures (Simon, 1976) . As the organization adapts the existing standard operating proce dures, increasingly existing norms are adjusted to the novel context, providing context for the use and autonomy for organizational embeddedness.. User acceptance both inside government and outside of govern ment by citizens is clearly high, what this study shows is that technol ogy acceptance has to be aligned with the organizational mission, fit into the existing organizational needs, standard operating procedures and acceptable IT standards that are currently in place or replace procedures that have become obsolete (Davis, 1989; Venkatesh & Davis, 2000) .

B I B O O B I I O O O O O O O O O O B B I B I I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O B I I O O O O O O O O O O O O O B I O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O B I O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Trust management in vehicular ad hoc network: a systematic review The basis of vehicular ad hoc networks (VANETs) is the exchange of data between entities, and making a decision on received data/event is usually based on information provided by other entities. Many researchers utilize the concept of trust to assess the trustworthiness of the received data. Nevertheless, the lack of a review to sum up the best available research on specific questions on trust management in vehicular ad hoc networks is sensible. This paper presents a systematic literature review to provide comprehensive and unbiased information about various current trust conceptions, proposals, problems, and solutions in VANETs to increase quality of data in transportation. For the purpose of the writing of this paper, a total of 111 articles related to the trust model in VANETs published between 2005 and 2014 were extracted from the most relevant scientific sources (IEEE Computer Society, ACM Digital Library, Springer Link, Science Direct, and Wiley Online Library). Finally, ten articles were eventually analyzed due to several reasons such as relevancy and comprehensiveness of discussion presented in the articles. Using the systematic method of review, this paper succeeds to reveal the main challenges and requirements for trust in VANETs and future research within this scope.Keywords: Systematic literature review; Trust management; VANET; Trust metric 1 ReviewVehicular ad hoc networks (VANETs) are a class of ad hoc networks that consist of vehicles and roadside units (RSUs). VANETs were originally created to enhance safety on the road using cooperative collision warning via vehicle-to-vehicle (V2V) and vehicle-to-infrastructure (V2I) communication. In V2V communication, vehicles send and receive messages to and from one another. These messages can alert signals about road congestion, accidents ahead, or information about traffic on a given route. V2I communication takes place between nodes and roadside infrastructure and involves finding the nearest cheapest gas station, internet services, online toll payment, etc.According to [1] , the applications in VANETs are categorized into safety and non-safety applications. The basis In order to overcome these threats and increase security, several concepts have been proposed by researchers. Wei and Chen [3] stated that authentication is one method for ensuring the integrity of transmitted messages. In [4] , the reputation of a vehicle is introduced to evaluate the reliability of received data. Dotzer et al. also stated that a common method to deal with the safety threats in VANETs is to establish trust relationships and detect selfish and malicious entities [5] .Security is one of the main issues in VANETs, and trust is a key element of security [6] . Hence, since VANETs are based upon data exchange among vehicles, trustworthiness of data is of great importance. In addition, data communication between trusted vehicles directly affects The trust model enables vehicles to distinguish trustworthy vehicles or messages from untrustworthy ones. It leads to reducing the risk of vehicles being misguided by other malicious vehicles. Due to the importance of data and its quality in VANETs as well as the impact of trustworthiness on the quality of applications, this study has conducted a systematic review of current research that aim at managing trust in vehicular ad hoc networks.. In this review, we have analyzed various studies focusing on trust models. Based on this analyze, we have extracted the methods and metrics that are required for designing and managing a trust model. We have concluded that none of the proposed trust models have achieved all the desired properties. Therefore, we developed a framework including probability module, plausibility module, trust measurement module, and decision making module. These modules are based on fuzzy logic. In terms of contributions to the theory, this paper gathers published works on trust models and allows researchers to find possible avenues for future studies in this area.. Looking into the future, development of a lightweight intelligence trust model for VANETs that satisfies all the desired properties of a trust model is sensible.

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I B I B B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Application of structural topology optimisation to perforated steel beams This paper focuses on the application of structural topology optimisation technique to design steel perforated I-sections as a first attempt to replace the traditional cellular beams and better understand the mechanisms involved when subjected to bending and shear actions. An optimum web opening configuration is suggested based on the results of parametric studies. A FE analysis is further employed to determine the performance of the optimised beam in comparison to the conventional widely used cellular type beam. It is found that the optimised beam overperforms in terms of load carrying capacities, deformations, and stress intensities. Barriers to the implementation of the topology optimisation technique to the routine design of beam web are highlighted. The judicious placement of holes in the webs of steel beams has been employed to design lighter and stiffer beams for over 100 years. The research focuses on steel I-section beams with perforations in the web which are variously known as; castellated beams (with hexagonal openings) and cellular beams (with circular openings) under the ''umbrella'' of perforated beams. The most important benefits when using such sections are the improved weight-to-stiffness ratio, the ability to integrate building services into the structural depth and the perceived aesthetic appeal of the beam [1] . The literature on the structural behaviour of steel I-section beams with standard circular, rectangular, and hexagonal web opening configurations is extensive [2] [3] [4] [5] [6] . The constant desire for improvement and mature level of understanding of the structural action of perforated steel sections has recently led to novel opening shapes being investigated [7] [8] [9] . The novel opening shapes are claimed to have beneficial fabrication, structural performance, usage in terms of service investigation and aesthetic qualities when compared to standard opening types.. The aesthetics of cellular beams have long been a crucial design consideration. The switch from castellated style beams to cellular beams in the early 1990s has been attributed to the perceived aesthetic appeal of the circular opening [1, 5] . More recently the ''Angelina'' style beam was first suggested by Claude Vasconi, an architect, with the consideration of aesthetic appeal at the fore [10, 11] .. The progression of the design of beams with web openings, from the original castellated design to the currently used cellular design and the newly developed sinusoidal design clearly shows that ultimate mechanical performance of the section is not always the aim of development. Aesthetic appeal may justify the development of a new section in the absence of any mechanical performance gains.. All of the opening shapes and configurations previously considered in the literature are constrained by the requirement that they can be manufactured by the profile cutting procedure. The profile cutting procedure, also known as castellation, is a method of manufacturing beams with web openings whereby a ''parent'' steel I-section is selected and a zig-zag pattern is (oxy or plasma) cut along the web of the section. The sections are then expanded and welded along the teeth of the zig-zag to form a deeper section with web openings (Fig. 1a) . It is obvious that if a beam is to be formed using this process the possible geometry of the web openings is constrained. The profile cutting procedure is currently regarded as the most economical and standardised method of fabricating beams with web openings. The only exception being when wide elongated web openings are considered.. More recently an alternative fabrication technique, plate assembly (Fig. 1b) , has been adopted by several leading fabricators of cellular beams. The plate assembly technique offers significantly increased design freedom in terms of the shape and layout of web hence elongated web openings can be accommodated as well as non-periodically spaced web openings of various sizes and shapes. It is, however, considered an expensive solution due the long welding line along the plates (web and flanges) and the demanding requirements for accuracy when the perforations are engraved.. Nowadays the latter fabrication method is considered as more advantageous and adaptive to the needs of the architect and design engineer, hence it becomes more and more prevalent and efficient for steel construction.. To this point, no research found in the literature presenting any formal structural optimisation studies that have been performed with the aim of improving the design of steel I-section beam web opening shapes used in civil engineering and particularly building applications. Previous advancements in web opening configurations have rather relied upon engineering intuition and experience. Structural topology optimisation is a design tool which can be used to determine information on the optimum number, shape and size of openings within a user defined structural domain. The web design of an I-section steel beam is developed using topology optimisation. When compared to a conventional cellular beam, it was found that the topology optimised beam has advantageous structural behaviour in terms of the initial stiffness, the yield load, and the stress profile. The investigation was therefore considered to be an effective proof of concept demonstrating that there are more effective ways of distributing the material within the beam web depth in order to enhance the structural performance of a lightweight perforated section.. It is worth mentioning that the effort required to develop the topology optimised beam web design was not trivial. It would be necessary to perform such lengthy topology optimisation, geometry extraction and load verification procedure for every new section, span or load combination considered. Moreover, the load Rigid Elements Fig. 10 . FE model and loading approach taken in parametric study. capacity of the optimised beam web cannot be verified using standardised design equations due to the complexity of the new geometry.. It should be noted that when interpreting the results of the topology optimisation studies, only the opening pattern emerging in the centre of the beam (Fig. 11) is of interest in terms of developing a web opening type that could be periodically applied along the length of the beam.. It was found that the ratio of the flange thickness to the web thickness did not alter the resulting optimal topology, but the actual shape of the suggested web opening was altered (Fig. 12) . The depth of the section did have an impact on the optimal topology (Fig. 13) . In the depth range between 270 mm and approximately 750 mm, it was found that the optimal opening topology was consistent. For shallower beams, it was found that an elongated cross shape was the most efficient design. In the case of beams deeper than 750 mm, extra openings were recommended by the topology optimisation results to keep a balance between stiffness and weight.. The consistency of the results in the depth range between 270 mm and 750 mm indicate that the same topology is optimal for most of beam sections that may be found in practice.. It was found that as the depth, a, of the large central opening is increased the buckling load capacity of the beam web reduces. It was also found that as the width, c, is increased, the buckling load of the beam web is also reduced. These relationships are intuitively correct. The relationship between the depth, b, of the cross-over and the buckling load is more complex. It was concluded that the relationship between the cross-over depth and the buckling load is approximately linear until a limiting value is reached, at which point the buckling load tends to an approximately constant value. For the web configurations investigated, it was estimated that the cross-over depth at which the buckling load tends to a constant value was between 0.5 and 0.6 times the beam depth.. The limiting shear buckling capacity was reached when the web buckled along the edge of the central web opening (Fig. 20a) rather than the edge of the perimeter opening (Fig. 20b) . It can be concluded from this that if the edge length of the perimeter opening is maintained below the edge length of the central opening the shear buckling capacity of the web will not be altered.. Significant yielding and distortion of the web in the cross-over area zone (Fig. 21 ) was observed in tests 1-32 from Table 4 , where the value c was defined as 1.00, prior to the buckling load being reached. This would indicate that the critical failure mode in these instances is not the web buckling, but a Vierendeel type failure which cannot be accurately modelled using the local study approach [45] .. In the course of the parametric study a major limitation of this topology optimised beam web architecture, as currently described, was identified. It became apparent that the method of defining the geometry of the topology optimised beam web leads to misalignment of the web struts across the cross-over point (Fig. 22) . This misalignment of the web struts generates an uneven stress distribution across the breadth of the strut. The resulting increased stress towards the edge of the opening, promotes a premature buckling along the web opening.. Consequently, it is recommended that a future study is conducted to investigate the impact of aligning the web struts. It is anticipated that alignments of the web struts will enhance the buckling characteristics of the beam web. The results of the topology optimisation studies are presented in the form of element density plots in Fig. 3 . Note that the element density plots represent the optimal material distribution upon convergence of the optimisation. The red 1 (light colour) zones represent the solid material, whilst the blue (dark colour) zones represent the suggested locations for openings. The transitional zones represent material of an intermediate density.. It is observed that a complex and irregular truss-like design was formed. It is also noted that more material appeared to be distributed to areas of high shear, towards the supports. Where bending forces are predominant in the flanges, towards the mid-span, the topology optimisation suggested the placement of no web material. It is also appeared that the beam web elements, as suggested by the topology optimisation, follow lines of the principle stresses in the beam web. 1 For interpretation of colour in Fig. 3, 4, 5, 11, 12, and 13 , the reader is referred to the web version of this article.. It is generally the case that structures designed using topology optimisation will have a more complex geometry than those developed from engineering intuition. This can limit the applicability of topology optimisation derived designs in practice as it may not be possible to manufacture them.. The issue of manufacturability has been addressed through the inclusion of manufacturing constraints in the topology optimisation problem. Suggested manufacturing constraints include: symmetry, casting constraints [32] , extrusion constraints [40] , and pattern graduation [41] . More recently a novel approach has been suggested for enforcing vertical beam like elements only in topology optimisation results [42] .. Following, a symmetry constrained topology optimisation was performed. Lines of symmetry about the centreline and longitudinal axis of the beam were specified in both vertical and horizontal planes and a topology optimisation was performed using a volume fraction constraint of 0.4. The results of the symmetry constrained topology optimisation study (Fig. 4) showed a more rational truss-like design with rhomboidal web openings which periodically change along the length of the beam. Similarly, a large opening was suggested at the mid-span of the beam. It became visible that the material is distributed within the beam web according to the ratio of shear and bending moment acting on the section.. It is evident that none of the designs suggested in the topology optimisation study could be manufacturable using the profile cutting procedure. The plate assembly technique, therefore, need to be implemented to realise the designs.. The yield load of the cellular beam is found to be 188.15 kN with a corresponding deflection of 23.58 mm. The yield load of the optimised beam is found to be 207.96 kN with a corresponding deflection of 19.21 mm. The expected ultimate load of the optimised beam is also going to be higher than the cellular beam. Load against mid-span deflection plots for the analyses (Fig. 7) show that the optimised beam is stiffer than the cellular beam in the linear region. It is worth to note that the analyses with the optimised models stopped suddenly due to high stress concentrations at the mid-span of the beam sections. Healing the non-convergence issue at this stage in order to capture the post-elastic behaviour of the beams is beyond the scope of this study, as the stiffness and yielding loads are essentially compared. In addition, such a weak design at the mid-span of the optimised beam is not anticipated to be used in practice.. Von Mises stress plots (Figs. 8 and 9) for both examined beams at the yield load level, show that despite some high localised stress concentrations in the optimised beam due to corners resulted from the openings' shape, the stress distribution is generally more uniform. In contrast stresses in the cellular beam tend to increase significantly towards the supports, and therefore the connections.. It is further observed that the cellular beam suffered a localised buckling failure in the web-posts towards the support. On the other hand, the primary failure mode of the optimised beam is difficult to be concluded from this preliminary investigation. Localised buckling within the web depth is observed at failure. Also, high stress concentrations in the vicinity of the large central web opening are found, whilst both of these features are observed to occur concurrently.. Each of the web configurations described was analysed using the Radioss FEM. The buckling load was defined as the point at Table 5 Constraints applied to local model for topology optimised web buckling study.

O O B I I O O O O O O O O O O O B I I O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Optimal key systems A key system is represented by an ordered rooted tree. We construct trees minimizing relevant cost functions. Our application concerns interactive voice response (IVR), or automated telephone operators, for navigation purposes. We determine the optimal design of key systems where alternatives are ordered. Such a system can be represented by an ordered rooted tree

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Selecting representative benchmark inputs for exploring microprocessor design spaces The design process of a microprocessor requires representative workloads to steer the search process toward an optimum design point for the target application domain. However, considering a broad set of workloads to cover the large space of potential workloads is infeasible given how time-consuming design space exploration typically is. Hence, it is crucial to select a small yet representative set of workloads, which leads to a shorter design cycle while yielding a (near) optimal design.Prior work has mostly looked into selecting representative benchmarks; however, limited attention was given to the selection of benchmark inputs and how this affects workload representativeness during design space exploration. Using a set of 1,000 inputs for a number of embedded benchmarks and a design space with around 1,700 design points, we find that selecting a single or three random input(s) per benchmark potentially (in a worst-case scenario) leads to a suboptimal design that is 56% and 33% off, on average, relative to the optimal design in our design space in terms of Energy-Delay Product (EDP). We then propose and evaluate a number of methods for selecting representative inputs and show that we can find the optimum design point with as few as three inputs. Designing a microprocessor core involves making a large number of tradeoffs. Computer architects need to decide on a large number of design choices such as core type (out of order versus in order), pipeline depth and width, clock frequency, cache size and organization, branch predictor type and configuration, various buffer sizes, and so forth. Making these design choices not only involves considering performance but also requires taking into account other criteria or constraints such as energy and power consumption, temperature, chip area, cost, reliability, and so forth. In fact, for many of today's systems, these constraints are at least as equally important as performance, if not first-order design targets. The huge design space along with the complex, multiobjective optimization criteria makes design space exploration a challenging problem.. To make things even worse, architects and designers typically rely on detailed cycleaccurate simulation during the exploration. In other words, the evaluation of each possible design point under consideration involves time-consuming detailed simulation, which makes the whole design process extremely challenging, especially given the short time to market.. Exploring the design space reliably requires representative workloads. Workloads that are nonrepresentative for the envisioned target workloads may lead to suboptimal designs, for example, designs with poor performance and/or excess power consumption. In other words, the final design hinges on the workloads used during the exploration and design cycle. The importance of having representative workloads is well known, and several prior works have proposed methods to evaluate benchmark representativeness; see, for example, Eeckhout et al. [2002] and Yi et al. [2003] . Next to being representative, a benchmark suite should also be relatively small: Simulating a very broad set of benchmarks is not only time-consuming but also requires a lot of simulation resources, which can be costly. Hence, the key challenge when composing a benchmark suite is that it should be relatively small while being representative.. Most of the prior work on the topic of workload selection has focused on selecting representative benchmarks, and limited effort has been geared toward exploring the impact of the benchmark inputs. While runtime behavior may be relatively insensitive to the inputs for some applications, other applications may be very sensitive. For example, a streaming application, such as a filter operation, may be largely input insensitive as the application executes the same code and accesses memory in a highly predictable way no matter what input it is given. On the other hand, a video application that decodes an action movie with lots of complex scenery versus a recording of a news reader with little variation across subsequent frames is likely to lead to different code regions being executed, as well as different memory access patterns being observed, which in turn leads to different runtime behavior.. In this article, we quantify how sensitive design space exploration is to benchmark inputs, and we subsequently present methods for identifying representative inputs for reliable design space exploration. Using 1,000 inputs for a set of 20 embedded benchmarks while considering a core microarchitecture design space with approximately 1,700 design points, we find that selecting a single randomly chosen input per benchmark may (in a worst-case scenario) lead to a design point with an Energy-Delay Product (EDP) that is 56% worse, on average, compared to the optimum design point (the design point with the minimum EDP in our design space for the benchmarks and inputs considered in this study); three randomly chosen inputs may still lead to a design point that is 33% worse. We then present three methods for selecting representative benchmark inputs, with each method representing a different tradeoff in time complexity versus accuracy. The most accurate method identifies three representative inputs that lead to the optimum design point during design space exploration. The fastest method, which requires a single, relatively fast profiling run for each potential input to identify two representative inputs, yields a design point that is within 3.7% on average compared to the optimum design point.. Overall, we make the following contributions in this article:. -We study how sensitive microarchitecture design space exploration is with respect to benchmark inputs. Whereas prior work focused on selecting representative benchmarks, this article is the first to comprehensively explore the impact of benchmark inputs during design space exploration. We find benchmark inputs to have a significant impact on the final design point. -We quantify that the common practice of randomly selecting a single (or few) benchmark input(s) may lead to suboptimal designs with significant deficiencies compared to the optimal design point. -We present and evaluate several methods for selecting representative inputs, making the design space exploration more reliable and leading to better performing design points. These methods vary in the way they characterize inputs, leading to varying degrees of time complexity, as well as representativeness of the selected inputs.. We believe this work is both important and timely. Given the end of Dennard scaling [Dennard et al. 1974] in the presence of continued transistor integration via Moore's Law, there is a trend toward specialization in order to keep improving performance and energy efficiency [Esmaeilzadeh et al. 2011; Hameed et al. 2010; Venkatesh et al. 2010] . Designing application-specific processors and/or accelerators is a promising and fruitful avenue in this direction. This work quantifies the importance of representative benchmark inputs to the quality of the final design point and provides a method for identifying representative inputs when specializing a processor design for a particular application. We hope this work will help researchers and developers design high-performance yet energy-efficient processors across a broad range of workloads by paying attention to having representative benchmark inputs. In this article, we provide a comprehensive study to emphasize the sensitivity of design space exploration to benchmark inputs. Because using a large number of inputs to drive design space exploration is infeasible, we propose a number of methods to find a reduced set of inputs. The representativeness of the set of inputs produced by these methods is evaluated in the article.. Our setup to study input sensitivity for design space exploration involves 1,000 inputs for 20 embedded benchmarks and a design space consisting of around 1,700 design points. We use EDP as our optimization criterion, and we focus on the average EDP deficiency across all inputs, when the worst possible input(s) are used during design space exploration. This is a case that should be avoided at all cost because it is unknown a priori whether the selected inputs are representative or not. Using a single randomly selected input, the design space exploration could lead to an average worst-case EDP deficiency of 56% compared to the design point with minimum EDP. When using three randomly selected inputs, the worst-case EDP deficiency can be reduced to 33%. However, these high-deficiency numbers can be greatly reduced by the three methods proposed in this article: filtered input selection, input selection through microarchitectural-independent characterization (BBV selection), and minmedian-max selection. If we apply two levels of filtering before randomly selecting three inputs, we reduce the worst-case EDP deficiency to 6.7% on average. BBV selection achieves an EDP deficiency of 3.7% with two inputs selected; min-median-max selection finds the design point with minimum EDP (i.e., 0% deficiency) by using no more thanr three inputs. BBV selection and min-median-max selection are more effective than filtered selection while incurring a lower overall cost.. Overall, we hope this article increases awareness to benchmark inputs and its importance to design space exploration. As nowadays architecture research and development is increasingly data driven, it requires researchers and designers to pay close attention to selecting representative benchmark inputs. We believe this is going to be even more necessary as we resort to application-specific and domain-specific specialization of processor hardware to sustain the performance and energy-efficiency growth curve in the absence of Dennard scaling. We first set up a limited experiment to further motivate the problem and gain some initial insight before diving into a systematic evaluation of the importance of benchmark inputs during design space exploration. We consider one benchmark from the MiBench benchmark suite [Guthaus et al. 2001] , namely, sha, a secure hash algorithm, with five inputs and five processor configurations. The five inputs were randomly selected from the 1,000 input sets provided through KDataSets [Chen et al. 2010] , and the five processor configurations are shown in Table I ; we consider superscalar in-order processors and vary issue width, data and instruction cache size, branch predictor configuration, and pipeline depth. We simulate these processor configurations using the gem5 simulator [Binkert et al. 2011] . Figure 1 reports normalized EDP for each of the five inputs across these five processor configurations, along with the average EDP across all inputs. The EDP values are normalized against the processor that is optimal for the given input. Hence, an EDP value of 1 denotes the optimal processor configuration for a given input (e.g., configuration 0 for input C), and the closer the normalized EDP values are to 1, the better. It is immediately clear from the results shown in Figure 1 that configuration 0 is the most optimal processor configuration (i.e., the one with the lowest EDP) across all five inputs: For most inputs, its EDP is close to 1 and it has the lowest EDP on average (see the "average" bars in the graph). The same result would be obtained in case inputs A, B, or C would have been chosen to guide the design space exploration. However, using inputs D or E during design space exploration would have led us to believe that configuration 4 is most optimal. The risk now is that if configuration 4 were to be deployed in the field, an end-user using another input, for example, input C, would experience a 73% worse EDP compared to configuration 0. The pitfall here is that it is unclear at design time whether we are in the case of inputs D or E or one of the other inputs. In other words, using a nonrepresentative input to drive the design space exploration may lead to a design point with poor performance for other inputs, and this is hard to know a priori (if at all possible) without doing a full exploration. This case study motivates the need for a methodology for identifying representative inputs for design space exploration. The remainder of the article will further investigate and quantify the pitfall of nonrepresentative inputs in a systematic way and will present methods for identifying representative inputs so as to minimize the chance of ending up with a design point during design space exploration that could lead to suboptimal and even poor performance for unseen inputs when deployed in the field. It is well known that having representative benchmarks is key to design space explorations, as using nonrepresentative benchmarks may lead, or is likely to lead, to suboptimal design points. As a result, substantial prior work has been done toward identifying representative benchmarks; however, to the best of our knowledge, no comprehensive study was previously published regarding the impact of benchmark inputs on design space exploration.. We now discuss some of the prior work in benchmark selection, followed by a description of prior work in generating and evaluating benchmark inputs and design space exploration methods. We now give a detailed overview of the design space and the workloads considered in this article. We also describe our modeling infrastructure to efficiently explore the huge design space, as well as the optimization criterion we are targeting.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Resource-Aware Distributed Scheduling Strategies for Large-Scale Computational Cluster/Grid Systems Abstract-In this paper, we propose distributed algorithms referred to as Resource-Aware Dynamic Incremental Scheduling (RADIS) strategies. Our strategies are specifically designed to handle large volumes of computationally intensive arbitrarily divisible loads submitted for processing at cluster/grid systems involving multiple sources and sinks (processing nodes). We consider a real-life scenario, wherein the buffer space (memory) available at the sinks (required for holding and processing the loads) varies over time, and the loads have deadlines and propose efficient "pull-based" scheduling strategies with an admission control policy that ensures that the admitted loads are processed, satisfying their deadline requirements. The design of our proposed strategies adopts the divisible load paradigm, referred to as the divisible load theory (DLT), which is shown to be efficient in handling large volume loads. We demonstrate detailed workings of the proposed algorithms via a simulation study by using real-life parameters obtained from a major physics experiment. S CHEDULING in grid systems is a challenging task, as it involves coordinating multiple computational sites for resource sharing and scheduling in an efficient manner. These systems are exclusively meant for handling large volumes of computational loads such as data generated in the high-energy nuclear physics experiments [10] , bioinformatics [11] , astronomical computations, etc. These applications demand new strategies for collecting, sharing, transferring, and analyzing the data. This relatively new era of computing, referred to as grid computing [19] , expands collaborations and intense data analysis, coupled with increasing computational and networking capabilities.. In general, a grid computing environment is comprised of large groups of diverse geographically distributed resources (clusters) that are collected into a virtual computer for high-performance computation. Grid computing creates middleware and standards to function between these computers and networks. It allows full resource sharing among individuals, research institutes, and corporate organizations. It dynamically allocates the idle computing capability to the needed users at remote sites. The large number and diverse nature of these computing resources and their users pose a significant challenge to efficiently schedule the loads and utilize the resources. The motivation for our work stems from the challenges in managing and utilizing computing resources in grids as efficiently as possible. To date, there has been little or no work on resource-aware distributed dynamic scheduling of largevolume divisible loads with deadline requirements on a cluster node in a grid environment.. In this work, we propose Resource-Aware Dynamic Incremental Scheduling (RADIS) strategies for situations wherein processing for several divisible (partitionable) loads need to be completed within their respective deadline requirements, while the processing nodes have finite capacity constraints. Divisible loads are a class of loads that require homogeneous processing and can be partitioned into arbitrary smaller fractions [12] . These load portions, which bear no dependence relationships among themselves, can then be assigned to individual nodes for processing. We provide a detailed analysis of our algorithms and demonstrate their performance by using a simulation study, with real-life parameters derived from high-energy nuclear physics experiments discussed in [10] . The analytical flexibility offered by the divisible load theory (DLT) is thoroughly exploited to design resource-conscious algorithms that make the best use of the available resources in a cluster. We employ both interleaving and noninterleaving techniques to process tasks (jobs) that are admitted into the system and discuss their usefulness. Our systematic design clearly elicits the advantages offered by our strategies. The paper is organized as follows: In Section 2, we provide the research background and related work for grid and cluster scheduling and DLT. In Section 3, we formalize the multisource and multisink problem at a cluster node in a grid system. In Section 4, we discuss our scheduling strategies. In Section 5, we discuss the performance of our algorithms and their workings and highlight their advantages with a simulation study. In Section 6, we provide the conclusions. In this paper, we have proposed distributed scheduling strategies for processing multiple divisible loads on grid systems. As in real-life situations, we have considered the dynamic arrival of loads, the buffer capacity constraints at the sink nodes, and the deadline requirement of the loads to be processed. We have proposed three schemes of RADIS and have rigorously analyzed and evaluated their performance. In our simulations, for all the schemes, the number of sinks that participate in the processing in an iteration are allowed to vary, which is reflective of real-life situations. The impact of load sizes, load deadlines, and buffer size variations are also captured in our simulation study.. In the schemes proposed in this paper, the CN performs the admissibility test, determines the loads to be processed and the sinks that participate in an iteration, computes the scheduling parameters required for the sink nodes for determining the schedule, and communicates them to the sink nodes. The sink nodes perform the buffer estimation, estimate the amount of load fractions to be processed based on the scheduling parameters received from the CN, determine the amount of load fractions to be requested from the source nodes based on the actual buffer availability at the start of an iteration, and communicate the difference between the estimated and the actual amounts of load processed in an iteration to the CN. The sink nodes also request and process the amount of load fractions thus determined. In our schemes, the scheduling is done in a distributed manner (the load fractions are computed at the sink nodes), and only ð4 þ rÞ variables (where r is the number of sources that are scheduled in an iteration) are communicated from the CN to the sink nodes. Hence, the effectiveness of our schemes is more pronounced in larger systems.. The strategies shown here are explicitly designed for a group of computing nodes within a cluster node, which is part of a grid infrastructure. The proposed strategies can be tuned to work across several cluster nodes by considering communication delays. One of the ways on how the strategies could be tuned follows the work presented in [6] for Ethernet networks. Another limitation in our schemes is the single-point admissibility testing performed by the CN. However, one could implement a distributed approach by using leader-election-like algorithms [20] to make it more fault tolerant.. We infer and observe the following based on our work presented in this paper:. . The DLT paradigm has been proven to be a valid tool for handling large-scale computational loads on cluster/grid systems. . Though our algorithm is shown to provide the best effort schedules, the underestimation of buffer availability enables our scheme not to miss the deadlines for the accepted loads. . All the proposed scheduling strategies are scalable, are relevant in real-life situations, and are shown to be useful under different scenarios. . In grid systems, with high-speed links, concurrent communication in different links is certainly a viable model for handling large-scale computational loads such as the one addressed in this paper. However, when the underlying grid system has slower links, for handling multiple loads, alternative models with nonzero communication delays, which are proposed using the DLT paradigm [1] , should be considered. . Although we have proposed a scheme for buffer estimation at sink nodes, it may be noted that the design of the buffer estimation strategy is a topic in itself, and other strategies such as the use of a fading memory could be "plugged into" the RADIS strategies. In supervising a very active research area, he has published extensively in the areas of parallel processor and grid scheduling, ad hoc radio networks, telecommunications network planning, asynchronous transfer mode (ATM) switching, queuing, and Petri networks. He has authored, coauthored, or edited four books in the areas of performance evaluation, scheduling, and network planning. He is a fellow of the IEEE.. . For more information on this or any other computing topic, please visit our Digital Library at www.computer.org/publications/dlib. In this section, we present some of the works that are relevant to the problem addressed in this paper. For divisible loads, research since 1988 has established that optimal allocation/scheduling of a divisible load to processors and links can be solved through the use of a very tractable linear model formulation, referred to as DLT. The contributions in [23] , [24] looked at the problem of seeking optimal solutions for scheduling "large-grained" computations on loosely coupled processor systems. The study by Agrawal and Jagadish [23] focused on single-level tree architecture, whereas the one by Cheng and Robertazzi [24] considered daisy-chained systems. DLT is rich in such features as easy computation, a schematic language, equivalent network element modeling, results for infinitesized networks, and numerous applications. This linear theory formulation opens up attractive modeling possibilities for systems incorporating communication and computation issues, as in parallel, distributed, and grid computing. Here, the optimality, involving solution time and speedup, is defined in the context of a specific scheduling policy and interconnection topology. The linear model formulation usually produces optimal solutions through linear equation solutions. In simpler models, recursive algebra also produces optimal solutions. The model can take into account heterogeneous processor and link speeds, as well as relative computation and communication intensity.. DLT can model a wide variety of approaches with respect to load distribution (sequential or concurrent), communications (store and forward and virtual cut-through switching), and hardware availability (the presence or absence of front-end processors). Front-end processors allow a processor to both communicate and compute simultaneously by assuming communication duties. In addition to the monograph [22] , a survey on the results until 2003 has been published in [12] . DLT has been proven to be remarkably flexible. The DLT model allows analytical tractability to derive a rich set of results regarding several important properties of the proposed strategies and to analyze their performance. DLT also offers an exciting opportunity to optimally schedule multiple divisible loads in grid computing. The usefulness of DLT in terms of its applicability is demonstrated in several real-life applications, for example, parallel video encoding [3] , image processing [14] , large matrix computations [15] , and database applications [17] , [18] .. Moges et al. [7] studied divisible load scheduling strategy, with communication delays and two source nodes. Kim [13] has proposed a mathematical model in which simultaneous communication to several nodes is carried out. This model suits a cluster node in our grid system infrastructure. A very directly relevant material to the problem addressed in our paper is in [10] , where Wong et al. use an incremental recursive strategy (modified incremental balancing strategy (IBS) algorithm) for offline scheduling of multiple loads in a grid environment. Recently, memory-constrained problem formulations for grid systems are also considered. Wu and Sun [8] studied memory-conscious task scheduling for grid systems. Kim and Weissman [9] presented a genetic algorithm approach for decomposable data processing on largescale data grids. Marchal et al. [4] considered scheduling divisible loads for generic large-scale platforms. Another study that may be useful in the cluster systems context is of Ghose et al. [2] , wherein time varying speeds of links and processors in the network are considered in the modeling to evolve an adaptive load distribution strategy. Beaumont et al. [5] discussed some open-ended problems and issues pertaining to divisible load scheduling. We refer astute readers to the papers mentioned above for an up-to-date look at the literature related to the problem addressed in this paper.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


The traffic phases of road networks We study the relation between the average traffic flow and the vehicle density on road networks that we call 2D-traffic fundamental diagram. We show that this diagram presents mainly four phases. We analyze different cases. First, the case of a junction managed with a priority rule is presented, four traffic phases are identified and described, and a good analytic approximation of the fundamental diagram is obtained by computing a generalized eigenvalue of the dynamics of the system. Then, the model is extended to the case of two junctions, and finally to a regular city. The system still presents mainly four phases. The role of a critical circuit of non-priority roads appears clearly in the two junctions case. In Section 4, we use traffic light controls to improve the traffic diagram. We present the improvements obtained by open-loop, local feedback, and global feedback strategies. A comparison based on the response times to reach the stationary regime is also given. Finally, we show the importance of the design of the junction. It appears that if the junction is enough large, the traffic is almost not slowed down by the junction. The purpose of this paper is the discussion of the traffic phases appearing in road networks. These phases appear clearly on what we call the 2D traffic fundamental diagram. This diagram gives the relation between the average flow and the car density in the network. The 2D traffic fundamental diagram is an extension to road networks of the well-known fundamental diagram studied mainly for a unique road in traffic literature such as in (Derrida and Evans, 1994; Fukui and Ishibashi, 1996; Nagel and Schreckenberg, 1992; Blank, 2000; Wang et al., 2000; Chowdhury et al., 2000; Helbing, 2001; Lotito et al., 2005) . This relation between the car density and the car flow has been observed on a highway since 1935 by Greenshields (1935) .. Microscopic traffic on a road network has been studied in statistical physics with a cellular automata point of view in (Chowdhury et al., 2000; Biham et al., 1992; Molera et al., 1995b; Cuesta et al., 1993; Molera et al., 1995a) similar to the modeling done here. These works are mainly about numerical simulations showing a threshold density where blocking appears for somewhat different modeling, often stochastic. The case of two roads with one junction without turning possibilities with a stochastic modeling has been studied in detail in Ishibashi, 1996, 2001a,b) . In (Brockfeld et al., 2001) , the traffic light optimization of a city is done with an automatic control point of view.. Recently, other attempts to extend this fundamental diagram to the 2D cases have been done in (Geroliminis and Daganzo, 2007; Daganzo and Geroliminis, 2008; Geroliminis and Daganzo, 2008; Buisson and Ladier, 2009; Helbing, 2009) in traffic literature. Daganzo and Geroliminis (2008) , using a variational traffic theory (Daganzo, 2005; Daganzo, 2007, 2008) , have shown the existence of a concave macroscopic fundamental diagram first on a ring, then on a network using an aggregation method. Experimental studies (e.g. Buisson and Ladier, 2009 ) have shown that heterogeneity in traffic measurements may have a strong impact on the shape of the fundamental diagram built using the aggregation approach of Daganzo and Geroliminis (2008) .. More recently, Helbing (2009) , using queuing theory, has derived fundamental diagrams for a traffic model with junctions in the saturated and unsaturated cases.. Here we propose a new 2D traffic model obtained from Petri net modeling and maxplus algebra. This paper belongs to a sequence of works presented in conferences (Farhi et al., 2005 (Farhi et al., , 2007 , available online (Farhi, 2009a,b) , a thesis (Farhi, 2008) , and a companion paper (Farhi et al., 2009) . We give the first full synthesis of what we have understood on the traffic phases. In (Farhi et al., 2005 (Farhi et al., , 2007 Farhi, 2009b Farhi, , 2008 Farhi et al., 2009 ) the models are presented using Petri nets and maxplus algebra formalisms. Here we avoid these formalisms and use only dynamical systems in the standard algebra framework. Our point of view is close to the cellular automata one where interactions of a large number of simplified vehicles are studied in asymptotic regimes. Our point of view is different from the two approaches (DaganzoGeroliminis and Helbing) discussed previously. Our models are simpler but the systems can be analyzed more deeply. In particular the fundamental diagram is obtained (numerically or analytically) for the complete set of possible densities. The different traffic phases can be deduced from the obtained diagram instead of making a specific analysis for each traffic situation (under or over saturated traffic), as for example, in (Helbing, 2009) .. We consider various closed regular road networks cut in cells which can contain at most one car. At a junction, a car leaving can turn. To enter the junction, we consider the priority to the right policy (a vehicle gives way to vehicles approaching from the right at intersections) or the use of traffic lights with various strategies. The roads are one-way streets without possibility of overtaking. A car in a cell enters the next cell as soon as it is freed. We observe through simulation or by mathematical analysis (in the simplest case) four phases :. • Free phase: This phase corresponds to low densities. After a finite transitional time, the vehicles separate enough to be able to move freely. The average flow is equal to the density.. • Saturation phase: This phase corresponds to average densities. The junctions serve with their maximal flow. There is no jam downstream of the junctions. The average flow is constant (independent of the density).. • Recession phase: This phase corresponds to densities large enough to jam places downstream of the junctions. The average flow decreases with the density.. • Freeze phase: This phase corresponds to high densities, where the number of vehicles is large enough to fill a circuit of roads. Once such a full circuit is constituted, the traffic is frozen and the average flow vanishes.. The simplest case studied is a system of two circular roads with only one junction managed with the priority to the right rule. In this case, the dynamics is given. It is additively homogeneous of degree one. We can prove the existence of an average flow which is close to a generalized eigenvalue obtained analytically. We are particularly interested in the dependence of these quantities with respect to the density, but the ratio (r) between the number of cells of the non-priority road and the number of cells of the priority road also plays an important role in the determination of the four phases.. Then, we study the case of four roads with two junctions. We show numerically that the fundamental diagram has the same shape as in the previous case, but now r has to be interpreted as the ratio between the length of a non-priority road circuit and the length of a priority road circuit. When we extend the analysis to a larger network, the same kind of results persists.. The four phases exist in the presence of traffic light control, but the length of the saturation phase can be enlarged and the freeze phase reduced, almost without any impact on the free phase. Moreover, we show that the number of cells of the junction plays an important role. In our simple model, if we consider a junction of two cells, instead of one cell, we suppress the saturation phase and multiply by two the maximal flow.. Throughout this paper, we consider closed networks with a fixed number of vehicles and wait until a stationary or periodic regime is established 1 to compute the average flow as a function of a given density. Nevertheless, the fundamental diagrams have a sense for open systems when the density evolves slowly with respect to the car speed. The diagram can be useful to describe the behavior of zones of real towns with homogeneous structure of roads and junctions.. Numerical simulations are done with the Scicoslab software. They use the maxplus arithmetic of this software very useful to describe large dynamical systems in a matrix may. These simulations have played an important role to understand the different phases of the system before being able to derive them sometimes analytically. The main contribution of this paper is the discussion of the phases that can appear in the traffic on a road network. We discuss in detail the four traffic phases (free, saturation, recession and freeze phases) first on elementary systems and then on larger road systems. We identify a key parameter that is a ratio between the sum of the sizes of the non-priority roads and the sum of the sizes of the priority roads. We discuss how the freeze phase appears when a circuit of non-priority road jam is created. On the fundamental diagram, we study the improvement obtained thanks to open loop, local and global feedback traffic light policies. The importance of the junction capacity optimization is revealed clearly by this diagram.. The analytic results are obtained only in the case of two roads with one junction. It would be interesting to analyze the simplest case of two circuits of non-priority roads of different sizes in greater detail to find out if there exists a new phenomenon.. More realistic models should confirm the very natural qualitative results obtained here, but it would be worthwhile to see them on a large set of more sophisticated simulations.. The fundamental diagram should have sense also in the case of open networks for zones of a system where the car density stay almost fixed. The fundamental diagram must be considered, for traffic, as the analogue of the ideal gas law. It should be useful to build 2D fluid macroscopic traffic models based on this law but this possibility has not been explored for the moment.

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