Abridged Petri Nets

A new graphical framework, Abridged Petri Nets (APNs) is introduced for bottom-up modeling of complex stochastic systems. APNs are similar to Stochastic Petri Nets (SPNs) in as much as they both rely on component-based representation of system state space, in contrast to Markov chains that explicitly model the states of an entire system. In both frameworks, so-called tokens (denoted as small circles) represent individual entities comprising the system; however, SPN graphs contain two distinct types of nodes (called places and transitions) with transitions serving the purpose of routing tokens among places. As a result, a pair of place nodes in SPNs can be linked to each other only via a transient stop, a transition node. In contrast, APN graphs link place nodes directly by arcs (transitions), similar to state space diagrams for Markov chains, and separate transition nodes are not needed. Tokens in APN are distinct and have labels that can assume both discrete values ("colors") and continuous values ("ages"), both of which can change during simulation. Component interactions are modeled in APNs using triggers, which are either inhibitors or enablers (the inhibitors' opposites). Hierarchical construction of APNs rely on using stacks (layers) of submodels with automatically matching color policies. As a result, APNs provide at least the same modeling power as SPNs, but, as demonstrated by means of several examples, the resulting models are often more compact and transparent, therefore facilitating more efficient performance evaluation of complex systems.Comment: 17 figure

Towards resilient supply chain networks

In the past decade, events like 9/11 terror attacks, the recent financial crisis and other major crisis has proved that there is strong interaction and interdependency of a supply chain network with its external environments in various channels and thus a need to focus on building resiliency (in short, the ability of the system to recover from damage or disruption) of the entire network system. Although literature has discussed some way of improving resiliency of an individual firm which is a member of the network system, it lacked to capture a holistic view of the supply chain network. Pertaining to this observation, this work proposes to improve resiliency of a supply chain network from a system’s perspective rather concentrate on an individual firm. For this purpose, this thesis proposes a conceptual framework to promote early identification and timely information of the disruptions arising in a supply chain network and timely sharing of this information among all the members of the network. The key principle emphasized in this thesis is that recovery from an inevitable disruption has a better possibility if a member of the supply chain network has an early indication or knowledge of the upcoming disruption. A discrete event dynamic system simulation tool called Petri nets is utilized to realize the proposed conceptual framework. Furthermore, the practical benefits and implications of the proposed model and tool are demonstrated with help of two case studies. This thesis has several contributions to the field of operation management and supply chain. First, a new paradigm for supply chain management to avoid large scale failures such as financial crisis is available to the field, which may be applied by governments or regulatory bodies. Second, a new framework which allows for a quantitative analysis of failures of an entire supply chain network is available to the field, which is easy to be used. Third, a novel application of Petri nets to this new problem in supply chain management is available

Erlang analysis of cellular networks using stochastic Petri nets and user-in-the-loop extension for demand control

Abstract—Cellular networks face severe challenges due to the expected growth of application data rate demand with an increase rate of 100 % per year. Over-provisioning capacity has been the standard approach to reduce the risk of overload situations. Traditionally in telephony networks, call blocking and overload probability have been analyzed using the Erlang-B and Erlang-C formulas, which model limited capacity communication systems without or with session request buffers, respectively. While a closed-form expression exists for the blocking probability for constant load and service, a steady-state Markov chain (MC) analysis can always provide more detailed data, as long as the Markov property of the arrival and service processes hold. However, there is a significant modeling advantage by using the stochastic Petri net (SPN) paradigm to model the details of such a system. In addition, software tool support allows getting numeric analysis results quickly by solving the state probabilities in the background and without the need to run any simulation. Because of this efficiency, the equivalent SPN model of the Engset, Erlang-B and Erlang-C situation is introduced as novelty in this paper. Going beyond the original Erlang scenario, the user-in-the-loop (UIL) approach of demand shaping by closed-loop control is studied as an extension. In UIL, demand control is implemented by a dynamic usage-based tariff which motivates users to reduce or postpone the use of applications on their smart phone in times of light to severe congestion. In this paper, the effect of load on the price and demand reduction is modeled with an SPN based on the classical Erlang Markov chain structure. Numeric results are easily obtained and presented in this paper, including probability density functions (PDF) of the load situation, and a parameter analysis showing the effectiveness of UIL to reduce the overload probability. Keywords—User-in-the-loop (UIL); demand shaping; demand control; congestion; Erlang; stochastic Petri-net (SPN). I

Survivability modeling for cyber-physical systems subject to data corruption

Cyber-physical critical infrastructures are created when traditional physical infrastructure is supplemented with advanced monitoring, control, computing, and communication capability. More intelligent decision support and improved efficacy, dependability, and security are expected. Quantitative models and evaluation methods are required for determining the extent to which a cyber-physical infrastructure improves on its physical predecessors. It is essential that these models reflect both cyber and physical aspects of operation and failure. In this dissertation, we propose quantitative models for dependability attributes, in particular, survivability, of cyber-physical systems. Any malfunction or security breach, whether cyber or physical, that causes the system operation to depart from specifications will affect these dependability attributes. Our focus is on data corruption, which compromises decision support -- the fundamental role played by cyber infrastructure. The first research contribution of this work is a Petri net model for information exchange in cyber-physical systems, which facilitates i) evaluation of the extent of data corruption at a given time, and ii) illuminates the service degradation caused by propagation of corrupt data through the cyber infrastructure. In the second research contribution, we propose metrics and an evaluation method for survivability, which captures the extent of functionality retained by a system after a disruptive event. We illustrate the application of our methods through case studies on smart grids, intelligent water distribution networks, and intelligent transportation systems. Data, cyber infrastructure, and intelligent control are part and parcel of nearly every critical infrastructure that underpins daily life in developed countries. Our work provides means for quantifying and predicting the service degradation caused when cyber infrastructure fails to serve its intended purpose. It can also serve as the foundation for efforts to fortify critical systems and mitigate inevitable failures --Abstract, page iii

Towards Simple Models for Energy-Performance Trade-Offs in Data Centers

In this paper we advocate the use of simple stochastic models to analyse the energy-performance trade-off in data centres. Recently such trade-offs have received increased attention, however, the tools used to make such trade-offs are largely based on simulation and real-life experiments. Although simulations studies are very helpful, we think that simple analytical models, or models based on stochastic Petri nets (or similar description techniques) can be very fruitful in guiding design processes in the early phases.\ud Similarly, we do think that experimental work is very important, however, its results come "after the fact" in the sense that the system has been built already once the experiments are being performed. Our claim is that the\ud use of simple models early in the design phase provides a very good return on investment. This short paper presents some preliminary models that can be used for early-in-design trade-off analyses

Toward a Resilient Holistic Supply Chain Network System: Concept, Review and Future Direction

The recent financial crisis and other major crises have suggested that there are some strong interactions and interdependence between several supply chains and their external environments in various ways. A set of supply chains that are interdependent is called a holistic supply chain network (H-SCN) in this paper. There is a need to focus on building the resilience (in short, the ability of a system to recover from damage or disruption) of an entire H-SCN as it is believed that such a network system is strongly relevant to the recent economic recession that is triggered by financial crises. The objectives of this paper are to provide a classification of different SCNs in literature, leading to the identification of a new type of SCN system, i.e., an H-SCN, and to discuss the state of knowledge on the resilience of SCNs, particularly of an H-SCN. A systematic review approach is applied in this paper. Another contribution of this paper is the provision of a more comprehensive definition and description of resilient systems, including SCN systems. A final contribution of this paper is the proposal of the future directions of research on resilient SCN systems, particularly resilient H-SCN systems.postprin

Quantitative and Qualitative Models for Managing Risk Interdependencies in Supply Chain

The interdependent nature of supply chain elements and events requires risk systems must be assessed as an interrelated framework to optimize their management and integrate effectively with other decision-making tools in uncertain environments. This research shows a synthesis and analysis of the main qualitative/quantitative methods that have been used in the literature considering the treatment of event dependencies in supply chain risk management in the period 2003– 2018. The results revealed that the integration with disruption analysis tools and artificial intelligence methods are the most common types adopted, with increasing trend and effectiveness of Bayesian and fuzzy theory approache