Bad Markings Research Articles

On an iterative deadlock prevention approach for automated manufacturing systems

In Hu (Transactions of the Institute of Measurement and Control 33:59–76, 2011), Petri nets are utilized to describe, analyse and control automated manufacturing systems (AMS). In order to suppress deadlock occurrences in AMS, a method to derive the bad markings iteratively using a mixed integer programming-based algorithm is proposed. To validate the effectiveness and efficiency of the proposed approach, two examples were demonstrated in Hu (Transactions of the Institute of Measurement and Control 33:59–76, 2011). This paper shows that the uncontrolled Petri net model in one of the examples is incorrect. It is also shown that the structural complexity of the computed monitors for both examples can be reduced with the same or more permissive system behaviours.

Optimal Supervisory Control of Flexible Manufacturing Systems by Petri Nets: A Set Classification Approach

Supervisory control is usually considered as an external control mechanism to a system by controlling the occurrences of its controllable events. There exist Petri net models whose legal reachability spaces are nonconvex. In this case, they cannot be optimally controlled by the conjunctions of linear constraints. For Petri net models of flexible manufacturing systems, this work proposes a method to classify the legal markings into several subsets. Each subset is associated with a linear constraint that can forbid all first-met bad markings. Then, the disjunctions of the obtained constraints can make all legal markings reachable and forbid all first-met bad markings, i.e., the controlled net is live and maximally permissive. An integer linear programming model is formulated to minimize the number of the constraints. A supervisory structure is also proposed to implement the disjunctions of the constraints. Finally, examples are provided to illustrate the proposed method.

Challenges to Food Security in India

Food security is access to enough food by all people at all time for an active and healthy life. India is truly developing now and its income, infrastructure, per capita income has also developed .But the major problem faced by India is “the problem food management and it’s distribution”. Agriculture is very important to India, employing 55% of its population and providing 16.5% of its annual GDP. Today, India ranks second worldwide in farm output..India is the largest producer in the world of milk, cashew nuts, coconuts, tea, ginger, turmeric and black pepper. It also has the world’s largest cattle population (281 million). It is the second largest producer of wheat, rice, sugar, groundnut and inland fish. It is the third largest producer of tobacco. India accounts for 10% of the world fruit production with first rank in the production of banana. Despite ensuring ample availability of food, existence of food insecurity at the micro-level in the country has remained a formidable challenge for India. In the recently released Global Hunger Index of 2013, India ranked 63rd out of 120 countries and this report is quite disturbing because India is one of the largest producers of food in the world. Still India is not in the condition to meet the basic food requirements of people. There are many people in India who strive hard even for the square meals. I don’t say that people in village areas are facing this problem, but also people in major cities face the same problems!!Lack of food supply and the nutritional deficiency causes not only a bad mark for the country’s image in the international level, but also causes adverse effect on country’s developing economic policies and it’s structure. Mismanagement of food products and it’s supply also puts country under many dreadful diseases too! This paper is focused on the several foods security issues prevalent in the Indian scenario. Data are taken from relevant sources to analysis the gravity of the food security issues in India. It also covered the several development programmes taken up by the Indian government to counter various food security issues including several schemes and yojanas. India’s biggest challenge still remains ensuring food and nutritional security to its masses.

Maximally permissive liveness-enforcing supervisor with lowest implementation cost for flexible manufacturing systems

This paper develops a place invariant based deadlock prevention method to obtain a maximally permissive Petri net supervisor with the lowest implementation cost. A supervisor consists of a set of control places and the arcs connecting control places to transitions. We assign an implementation cost for each control place and control and observation costs for each transition. Based on reachability graph analysis, maximal permissiveness can be achieved by designing place invariants that prohibit all first-met bad markings but no legal markings. By solving an integer linear programming problem (ILPP), a set of optimal control places are obtained and the objective function is used to minimize the implementation cost of the final supervisor. A vector covering approach is used to reduce the number of considered markings, aiming to reduce the computational overhead of the proposed method. Finally, a number of examples are proposed to illustrate the proposed approach.

Reaching most states via refining controller regions for supervisors of two well-known S3PRs

Deadlock control of flexible manufacturing systems (FMS) using Petri nets has been a very active research topic for the past two decades. Siphon-based deadlock control of FMS suffers from reaching fewer states than those of optimal control. This paper proposes three sets of siphon-based liveness-enforcing supervisors (LES) for a well-known FMS to obtain near optimal solutions. The first set includes 11 control places (monitors) providing 21,363 good states. The second set consists of 14 monitors providing 21,562 good states, the same as that using the method of the first-met bad marking (FBM) (based on an iterative method using reachability graph analysis) but with fewer monitors and control arcs. This result is achieved by refining some monitors into several monitors with smaller controller regions, causing fewer disturbances to the original uncontrolled model. The third set contains 15 monitors providing 21,573 good states – the best suboptimal solution so far in the literature. This result is obtained by further shrinking the controller region of the second set. Formal proof of the correctness is provided. Although reaching eight states fewer than that by the set-covering approach, it does not employ weighted control arcs and runs more efficiently. It also computes all lost states based on invariant without reachability analysis. Application to another well-known example is also illustrated.

Most permissive liveness-enforcing Petri net supervisors for flexible manufacturing systems

This paper presents a deadlock prevention approach to find a maximally permissive liveness-enforcing pure Petri net supervisor, expressed by a set of monitors, for a flexible manufacturing system (FMS), if such a supervisor exists. Otherwise, it derives the most permissive one in the sense that there are no other Petri net supervisors that are more permissive than it. The proposed approach computes the reachability graph of a plant model only once. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBMs) are reduced to two smaller ones, namely the minimal covering set of legal markings and the minimal covered set of FBMs. At each iteration, an FBM is selected. By solving an integer linear programming problem (ILPP), a place invariant (PI) is designed to prevent the FBM from being reached while no marking in the minimal covering set of legal markings is forbidden. If the ILPP has no solution, implying that there is no maximally permissive Petri net supervisor for the plant net model, another ILPP is designed to remove the least number of legal markings whose reachability conditions contradict others. Then, a PI is redesigned to ensure that the remaining legal markings are reachable. This process is carried out until no FBM can be reached. Finally, a most permissive liveness-enforcing supervisor is obtained. FMS examples are presented to illustrate the proposed approaches.

On structural minimality of optimal supervisors for flexible manufacturing systems

This paper develops a place invariant based deadlock prevention method to obtain an optimal, i.e., maximally permissive, liveness-enforcing Petri net supervisor with a minimal supervisory structure that means the minimal number of control places. Maximal permissiveness can be achieved by designing place invariants that make all legal markings reachable while all first-met bad markings unreachable. An integer linear programming problem is formulated to compute all place invariants and its objective function minimizes the number of place invariants, aiming to yield a minimal supervisory structure. Importantly, we develop a technique to greatly improve the efficiency of the proposed method by reducing the number of constraints and variables in the integer linear programming problem under consideration. A number of examples from the literature are used to illustrate the proposed approaches.

Behaviorally Optimal and Structurally Simple Liveness-Enforcing Supervisors of Flexible Manufacturing Systems

This paper presents two iterative deadlock prevention policies for flexible manufacturing systems (FMSs). Both can find a maximally permissive liveness-enforcing supervisor with a small number of control places. A vector covering approach is used to obtain a minimal covering set of legal markings and a minimal covered set of first-met bad markings (FBMs), which are much smaller than the sets of legal markings and FBMs, respectively. At each iteration, by solving an integer linear programming problem (ILPP), a place invariant (PI) associated with a control place is designed to forbid as many FBMs as possible, and no markings in the minimal covering set of legal markings are forbidden. The objective function of the ILPP maximizes the number of FBMs that are forbidden by the PI. Then, the forbidden FBMs by the PI are removed from the minimal covered set of FBMs. This process is carried out until all FBMs are forbidden. Two ILPP design techniques are developed for the control policies. Though the proposed methods cannot in general guarantee the minimality of the supervisory structure, they reduce the overall computational time greatly, which is shown by numerical studies. Finally, a number of FMS examples from the literature are presented to illustrate the proposed methods.

“A Morning Since Eight of Just Pure Grill”: A Multischool Qualitative Study of Student Abuse

Previous medical student abuse research employed quantitative surveys that failed to explore factors thought to contribute to abuse and students' actions in the face of abuse. This study examined medical student abuse narratives to identify types of perceived abuse, factors cited by students as contributing to abuse, and students' actions at the time of abuse. A qualitative design was adopted employing 22 individual and 32 group interviews to elicit narratives of professionalism dilemmas from 200 medical students at two 5-year undergraduate programs and one 4-year graduate entry program (England, Wales, and Australia) between 2007 and 2009. Thematic analysis of abuse narratives was conducted. Of 833 professionalism dilemma narratives, 86 (10%) involved perceived medical student abuse. Within these narratives, students reported mostly covert, status-related abuse, direct verbal abuse, and sexual harassment and discrimination. Some narrators described multiple factors contributing to abuse (individual, work, and/or organization); most cited factors focusing on individuals. Despite the abuse typically recounted with negative emotion, few participants reported resisting at the time of abuse by challenging or reporting the perpetrator. Participants gave a variety of reasons for this inaction (e.g., anxiety about receiving bad marks from the perpetrator) and for resisting (e.g., the abuse was affecting their education negatively). Although narratives focused predominantly on individual factors contributing to abuse and responses to abuse, educators should focus on the dynamic interplay between individual and organizational factors to combat abuse. Several opportunities to mitigate this continuing blight on the conscience of the profession are described.

Enumeration of lost states of a suboptimal control model of a well-known S 3 PR

Deadlocks halt a system completely causing a significant financial loss to a company. To resolve this problem, deadlock prevention (by adding monitors to problematic siphons) has been quite a popular research. Uzam and Zhou applied region analysis to a well-known S3PR to achieve a near-maximum permissive control policy. However, they do not list the lost states, which is essential to improve the control model. The lost states can be obtained by reachability analysis, which is a rather tedious process. Without theory, one could waste much time failing to reach more states and there is no effective solution so far in the literature. Thus, it is important to find out the condition where more states can be reached. If no more states can be reached, one should simply stop and remain satisfied with the suboptimal model obtained or employ weighted control arcs to reach more states. It is desirable to compute the gain of states without the costly reachability analysis when an alternative control policy is employed. It is interesting to explore which live states are lost in the first-met bad marking (FBM) method, which has not yet been available in the literature. This study presents the very first method to compute all lost states based on invariant without reachability analysis.

Defending Face: Elementary Structures, University Students, and Bad Mark Narratives

Defending Face: Elementary Structures, University Students, and Bad Mark Narratives

Formal theory of state loss of Siphon-based deadlock prevention

Deadlocks stop a system completely, leading to significant financial loss to a company. Uzam and Zhou propose selecting first-met bad marking (FBM) from the reachability graph of a given Petri net model. A monitor (hence a P-invariant) is added and marked with the number of tokens less than the sum of tokens in all marked operation places. This causes some live states to no longer be reachable. Piroddi et al. further increase it to maximally permissive states using the set-covering approach. However, there are weighted control (WC) arcs, which are more difficult to analyse than the ordinary control net by Uzam and Zhou. Huang et al. also employ WC near the end of the mixed integer programming (MIP) iteration steps and avoid reachability analysis (unlike the above two approaches). Experimentally, it runs faster than the above two approaches. However, all WC places are redundant. To avoid WC while not losing live states, the authors need to understand why state loss occurs. This study proposes developing a formal theory for state loss.

Improvement of Suboptimal Siphon- and FBM-Based Control Model of a Well-Known ${\rm S}^{3}{\rm PR}$

Siphon-based deadlock control of Flexible Manufacturing System (FMS) runs faster by avoiding reachability analysis, but reaches fewer states than an optimal. First-met bad marking (FBM) method requires more monitors, but reaches more states by refining some monitors with smaller (hence less disturbed) controller regions. However, the same refinement leads to more monitors for other siphons, which can be combined without losing states. This paper develops the formal theory to uncover the secret behind the above discrepancy. It improves the siphon-based approach to reach more states while using fewer monitors.

Design of a Maximally Permissive Liveness- Enforcing Petri Net Supervisor for Flexible Manufacturing Systems

Deadlock prevention plays an important role in the modeling and control of flexible manufacturing systems (FMS). This paper presents a novel and computationally efficient method to design optimal control places, and an iteration approach that only computes the reachability graph of a plant Petri net model once in order to obtain a maximally permissive liveness-enforcing supervisor for an FMS. By using a vector covering approach, a minimal covering set of legal markings and a minimal covered set of first-met bad markings (FBM) are computed. At each iteration, an FBM from the minimal covered set is selected. By solving an integer linear programming problem, a place invariant is designed to prevent the FBM from being reached and no marking in the minimal covering set of legal markings is forbidden. This process is carried out until no FBM can be reached. In order to make the considered problem computationally tractable, binary decision diagrams (BDD) are used to compute the sets of legal markings and FBM, and solve the vector covering problem to get a minimal covering set of legal markings and a minimal covered set of FBM. Finally, a number of FMS examples are presented to illustrate the proposed approaches.

Design of a maximally permissive liveness-enforcing supervisor with a compressed supervisory structure for flexible manufacturing systems

In this paper, a deadlock prevention policy for flexible manufacturing systems (FMS) is proposed, which can obtain a maximally permissive liveness-enforcing Petri net supervisor while the number of control places is compressed. By using a vector covering approach, the sets of legal markings and first-met bad markings (FBM) are reduced to two small ones, i.e., the minimal covering set of legal markings and the minimal covered set of FBM. A maximally permissive control purpose can be achieved by designing control places such that all markings in the minimal covered set of FBM are forbidden and no marking in the minimal covering set of legal markings is forbidden. An integer linear programming problem is designed to minimize the number of control places under an assumption that a control place is associated with a P-semiflow. The resulting net has the minimal number of control places on the premise that the assumption holds, and possesses all permissive states of a plant. The only problem of the proposed method is its computational complexity that makes it inapplicable to large-scale Petri net models. An FMS example from the literature is presented to illustrate the proposed method.

Local and global deadlock prevention policies for resource allocation systems using partially generated reachability graphs

This paper considers the deadlock prevention problem for a class of conjunctive/disjunctive resource allocation systems (C/D-RAS) which cover relatively general cases in which the multiple resource acquisitions and flexible routings are allowed. First, an improved siphon-based liveness characterization for the Petri nets modeling C/D-RAS is proposed. Subsequently, this characterization facilitates the utilization of a mixed integer programming (MIP) based deadlock prevention policy that can well avoid the explicit enumeration of both siphons and the reachable states. The resulting policy is implemented by an iterative algorithm each step of which is characterized as an MIP formulation in conjunction with both a bad marking detection and a feedback control operation. Finally, the deadlock prevention policy developed in this paper is, respectively, characterized by the local and global ones so as to realize a trade-off between the behavior permissiveness and the structural simplicity of the supervisor. Both the theoretical and experimental results validate the effectiveness and efficiency of such an approach.

Comments on "An iterative synthesis approach to petri net based deadlock prevention policy for flexible manufacturing systems"

In the above paper, it proposes a deadlock prevention policy for a flexible manufacturing system (FMS), which needs the complete state enumeration of the FMS that is modeled with Petri nets. The reachability graph of a Petri-net model is divided into two parts: the live zone (LZ) and the deadlock zone (DZ). The states in the LZ of the reachability graph of a Petri net constitute the legal behavior of the net from the viewpoint of deadlock prevention. The concept of first-met bad markings is proposed. A first-met bad marking is a node in DZ, whose father nodes are in LZ. The deadlock prevention policy is used in an iterative way. At each iteration, a first-met bad marking is identified from the reachability graph of a Petri net to be controlled. The reachability of a first-met bad marking is prohibited by adding a monitor, establishing a marking invariance relationship between the additional monitor and the activity places that are marked under the first-met bad marking. To achieve this, without a formal proof, [Lemma 1] is developed as shown in this article.

An Iterative Synthesis Approach to Petri Net-Based Deadlock Prevention Policy for Flexible Manufacturing Systems

This paper proposes an iterative synthesis approach to Petri net (PN)-based deadlock prevention policy for flexible manufacturing systems (FMS). Given the PN model (PNM) of an FMS prone to deadlock, the goal is to synthesize a live controlled PNM. Its use for FMS control guarantees its deadlock-free operation and high performance in terms of resource utilization and system throughput. The proposed method is an iterative approach. At each iteration, a first-met bad marking is singled out from the reachability graph of a given PNM. The objective is to prevent this marking from being reached via a place invariant of the PN. A well-established invariant-based control method is used to derive a control place. This process is carried out until the net model becomes live. The proposed method is generally applicable, easy to use, effective, and straightforward although its off-line computation is of exponential complexity. Two FMS are used to show its effectiveness and applicability

An improved iterative synthesis method for liveness enforcing supervisors of flexible manufacturing systems

Our previous work presented a Petri net-based iterative synthesis policy for deadlock prevention in flexible manufacturing systems (FMS). Given the Petri net model of an FMS prone to deadlock, it aims to synthesize a live controlled Petri net. Its use for FMS control guarantees its deadlock-free operation and high performance in terms of resource utilization and system throughput. At each iteration, a first-met bad marking is singled out from the reachability graph of the Petri net. A well-established invariant-based control method is used to prevent it from being reached. This process is carried out until the net model becomes live. The method proposed is generally applicable, easy to use, effective, and straightforward, although its off-line computation is of exponential complexity. This paper presents two improvements: (a) using the Petri net reduction approach to simplify very large Petri net models so as to alleviate computation effort; and (2) simplifying the invariant-based control method. A number of FMS deadlock problems from the literature are used to illustrate them.

Brief remarks on the unilateral use of force

There can be no doubt that the NATO action in Kosovo can (and must) be seen as legitimate, while, on the other hand, the jamming of the Security Council by China and Russia cannot. The actual lawfulness of the initiative, however, is more debatable, even though arguments based both on the UN Charter and on the law of state responsibility can be made in its favour and indeed become persuasive when seen together with, and in light of, Resolution 1244 (1999) of the Security Council. Nevertheless, it is essential that new 'community' mechanisms be found in the future in order to avoid being restricted to a choice between the 'Zorro' principle (as applied in Kosovo) and the Munich policy. A revival of Resolution 'Dean Acheson' (1950) and a deepening of the notion of 'state crime' and its consequences provide, among others, possibilities for limiting the need for legitimate but legally dubious unilateral uses of force. The task of a commentator may be both easy and difficult: easy since one may simply hand out good and bad marks and have the final word on the subject; difficult since, if the main authors have examined the issues thoroughly and intelligently, there may remain little to be said. It is definitely a case of the latter in taking up the task of commenting upon the articles by Ruth Wedgwood and Vera Gowlland-Debbas. Both authors have covered the issues in great depth and, what is more, I find myself largely in agreement with them. These authors have focused on a single debate seen at different angles — a debate that can be summarized in two short questions: — when is unilateral action lawful? and — when such an action is unlawful, can it be legitimate?