Queuing networks with finite capacity are widely discussed in performance analysis literature. One approach to address the finite capacity of stations involves the implementation of a skip-over policy. Under this policy, when a customer arrives at a saturated station, service at that station is skipped, and the customer is rerouted based on the predefined network routing protocol. Skip-over networks have been extensively investigated, and they exhibit a product-form stationary distribution under the exponential assumptions of Jackson networks. However, a comprehensive understanding of the celebrated Arrival Theorem for this class of product-form models is still lacking and relies on certain conjectures. This paper makes three contributions: (i) it provides an in-depth comprehension of the Arrival Theorem for skip-over networks by offering a proof for the conjectures outlined in existing literature, (ii) it introduces a Mean Value Analysis (MVA) algorithm tailored for this type of queuing networks, and (iii) it explores the implications of these findings on the class of product-form queuing networks with fetching and repetitive service discipline.

In this paper, we present the first remote timing attack based on formal stochastic models. Our attack uses queuing models from the field of performance evaluation to estimate the service times of different classes of network requests. By using Bayesian statistics, we then identify opportunities for remote timing attacks by answering the following inverse question: what is the probability that a given network request belongs to a target class, given an estimate of its service time? Our experimental evaluation on popular web applications and websites shows that our investigation is not just a theoretical exercise, because our attack outperforms existing empirical approaches in terms of standard performance figures. We believe that the formal foundations put forward in this paper can be successfully applied to the creation of principled remote timing attacks which are more effective, because better equipped to deal with the complexity of the problem they are trying to solve.

BACKGROUND: Emerging and re-emerging infectious diseases such as Zika, SARS, ncovid19 and Pertussis, pose a compelling challenge for epidemiologists due to their significant impact on global public health. In this context, computational models and computer simulations are one of the available research tools that epidemiologists can exploit to better understand the spreading characteristics of these diseases and to decide on vaccination policies, human interaction controls, and other social measures to counter, mitigate or simply delay the spread of the infectious diseases. Nevertheless, the construction of mathematical models for these diseases and their solutions remain a challenging tasks due to the fact that little effort has been devoted to the definition of a general framework easily accessible even by researchers without advanced modelling and mathematical skills. RESULTS: In this paper we describe a new general modeling framework to study epidemiological systems, whose novelties and strengths are: (1) the use of a graphical formalism to simplify the model creation phase; (2) the implementation of an R package providing a friendly interface to access the analysis techniques implemented in the framework; (3) a high level of portability and reproducibility granted by the containerization of all analysis techniques implemented in the framework; (4) a well-defined schema and related infrastructure to allow users to easily integrate their own analysis workflow in the framework. Then, the effectiveness of this framework is showed through a case of study in which we investigate the pertussis epidemiology in Italy. CONCLUSIONS: We propose a new general modeling framework for the analysis of epidemiological systems, which exploits Petri Net graphical formalism, R environment, and Docker containerization to derive a tool easily accessible by any researcher even without advanced mathematical and computational skills. Moreover, the framework was implemented following the guidelines defined by Reproducible Bioinformatics Project so it guarantees reproducible analysis and makes simple the developed of new user-defined workflows.

Computational Biology is a fast-growing field that is enriched by different data-driven methodological approaches and by findings and applications in a broad range of biological areas. Fundamental to these approaches are the mathematical and computational models used to describe the different state s at microscopic (for example a biochemical reaction), mesoscopic (the signalling effects at tissue level), and macroscopic levels (physiological and pathological effects) of biological processes. In this paper we address the problem of combining two powerful classes of methodologies: Flux Balance Analysis (FBA) methods which are now producing a revolution in biotechnology and medicine, and Petri Nets (PNs) which allow system generalisation and are central to various mathematical treatments, for example Ordinary Differential Equation (ODE) specification of the biosystem under study. While the former is limited to modelling metabolic networks, i.e. does not account for intermittent dynamical signalling events, the latter is hampered by the need for a large amount of metabolic data. A first result presented in this paper is the identification of three types of cross-talks between PNs and FBA methods and their dependencies on available data. We exemplify our insights with the analysis of a pancreatic cancer model. We discuss how our reasoning framework provides a biologically and mathematically grounded decision making setting for the integration of regulatory, signalling, and metabolic networks and greatly increases model interpretability and reusability. We discuss how the parameters of PN and FBA models can be tuned and combined together so to highlight the computational effort needed to perform this task. We conclude with speculations and suggestions on this new promising research direction.

BACKGROUND: Multiple Sclerosis (MS) is an immune-mediated inflammatory disease of the Central Nervous System (CNS) which damages the myelin sheath enveloping nerve cells thus causing severe physical disability in patients. Relapsing Remitting Multiple Sclerosis (RRMS) is one of the most common form of MS in adults and is characterized by a series of neurologic symptoms, followed by periods of remission. Recently, many treatments were proposed and studied to contrast the RRMS progression. Among these drugs, daclizumab (commercial name Zinbryta), an antibody tailored against the Interleukin-2 receptor of T cells, exhibited promising results, but its efficacy was accompanied by an increased frequency of serious adverse events. Manifested side effects consisted of infections, encephalitis, and liver damages. Therefore daclizumab has been withdrawn from the market worldwide. Another interesting case of RRMS regards its progression in pregnant women where a smaller incidence of relapses until the delivery has been observed. RESULTS: In this paper we propose a new methodology for studying RRMS, which we implemented in GreatSPN, a state-of-the-art open-source suite for modelling and analyzing complex systems through the Petri Net (PN) formalism. This methodology exploits: (a) an extended Colored PN formalism to provide a compact graphical description of the system and to automatically derive a set of ODEs encoding the system dynamics and (b) the Latin Hypercube Sampling with PRCC index to calibrate ODE parameters for reproducing the real behaviours in healthy and MS subjects.To show the effectiveness of such methodology a model of RRMS has been constructed and studied. Two different scenarios of RRMS were thus considered. In the former scenario the effect of the daclizumab administration is investigated, while in the latter one RRMS was studied in pregnant women. CONCLUSIONS: We propose a new computational methodology to study RRMS disease. Moreover, we show that model generated and calibrated according to this methodology is able to reproduce the expected behaviours.

The analysis of a queue that serves batches of customers with a novel service policy is presented in this paper, showing that a closed steady-state distribution of the number of customers in the queue can be derived for a very general setting of its parameters. Two output processes are flowing out of this queue depending on the fact that single customers are removed from the queue upon completion of a service, or bulks of customers of a fixed size are departing from the queue at the completion of the service's. Based on the expression of the steady-state distribution which assumes a Poisson arrival process, specific parameter configurations are identified that make the queue quasi-reversible, depending on the output process of interest. Since quasi-reversible queues are very important in the context of product form queueing networks, these results have relevant impacts on their own as well as when considered as the basis for possible computationally efficient approximations. Comparisons among the results obtained for different parameter settings are provided using both stochastic order arguments and numerical experiments. Future research directions are proposed considering also the many practical applications of this model ranging from flexible manufacturing, to logistics, to transportation systems.

Stochastic Symmetric Nets (SSNs) are a High-Level Stochastic Petri Net formalism which provides a parametric system description and an efficient analysis technique that exploit system symmetries to automatically aggregate its states. Even if significant reductions can be achieved in highly symmetric models, the reduced state space can still be too large to derive and/or solve the underlying stochastic process, so that Monte Carlo simulation and fluid approximation remain the only viable ways that need to be explored. In this paper, we contribute to this line of research by proposing a new approach based on fluid approximation to automatically derive from an SSN model a set of ordinary differential equations (ODEs) which mimic the system behavior, and by showing how the SSN formalism allows us to define an efficient translation method which reduces the size of the corresponding ODE system with an automatic exploitation of system symmetries. Additionally, some case studies are presented to show the effectiveness of the method and the relevance of its application in practical cases.

BACKGROUND: Cancer stem cell theory suggests that cancers are derived by a population of cells named Cancer Stem Cells (CSCs) that are involved in the growth and in the progression of tumors, and lead to a hierarchical structure characterized by differentiated cell population. This cell heterogeneity affects the choice of cancer therapies, since many current cancer treatments have limited or no impact at all on CSC population, while they reveal a positive effect on the differentiated cell populations. RESULTS: In this paper we investigated the effect of vaccination on a cancer hierarchical structure through a multi-level model representing both population and molecular aspects. The population level is modeled by a system of Ordinary Differential Equations (ODEs) describing the cancer population's dynamics. The molecular level is modeled using the Petri Net (PN) formalism to detail part of the proliferation pathway. Moreover, we propose a new methodology which exploits the temporal behavior derived from the molecular level to parameterize the ODE system modeling populations. Using this multi-level model we studied the ErbB2-driven vaccination effect in breast cancer. CONCLUSIONS: We propose a multi-level model that describes the inter-dependencies between population and genetic levels, and that can be efficiently used to estimate the efficacy of drug and vaccine therapies in cancer models, given the availability of molecular data on the cancer driving force.

The increasing demand for customer centric evaluation of systems, mostly related with the assessment of the quality of service that they can deliver, requires the development of techniques properly designed to model and to study the movement of specific entities generically referred to as "customers". Stochastic Well-Formed Net(SWN) are naturally suited for the representation of systems in which "customers" of different categories compete for the use of common resources. Color classes of SWN are easily associated with these different categories, leaving to the peculiar features of the formalism the possibility of exploiting all the symmetries existing into the representation for the efficient and effective computation of the measures of interest. Within this application context, the computation of first passage time distribution measures in Stochastic Well-Formed Net (SWN) is becoming of primary interest. Customers however are not primitive entities in the formalism and an approach similar to that previously developed for Generalized Stochastic Petri Nets (GSPN) is suggested to overcome this problem in which P-semiflows are used to identify the circulating "customers". In this paper we propose an original algorithm for computing some P-semiflows of colored PNs (in particular of SWNs) in parametric form by exploiting the peculiarities of the objective of this investigation, and extend the customer centric first passage time computation approach previously developed for GSPNs, to make it suitable for SWN models. Moreover, the paper proposes an enhancement of the SWN notation in order to provide a way to ease the modeler in the specification of customer scheduling policies that may affect the computation of first passage time distributions. This extension, inspired by Queueing Petri Nets, adds to SWN some "syntactic sugar" that allows to include in the model queueing places which are automatically replaced by appropriate submodels, before solving the model.

This paper presents an extension of the generalized stochastic Petri net (GSPN) formalism that enables the computation of first passage time distributions. The tagged customer technique typical of queuing networks is adapted to the GSPN context by providing a formal definition and an automatic computation of the groups of tokens that can be identified as customers, i.e. classes of homogeneous entities behaving in a similar manner. Passage times are identified through the concept of events that correspond to the firing of transitions placed at the boundaries of a subnet. The extended model obtained with this specifications is translated into an ordinary GSPN by isolating a customer from the group and highlighting its path through the net thus obtaining a representation suited for the passage time analysis. Proofs are provided to show the equivalence between these models with respect to their steady-state distributions. An important and original aspect treated in this paper is the possibility of specifying several scheduling policies of tokens at places, an information not present in ordinary GSPN models, but that is vital for the precise computation of first passage time distributions as shown by a few results computed for a simple Flexible Manufacturing application.

In this paper, we show the structural characteristics that a particular class of generalized stochastic Petri nets must exhibit in order for their stationary probabilities to have a product-form. Sufficient conditions for identifying such a class are derived and proven with the development of a series of transformations that can also be used to construct, for any GSPN of the class, an equivalent SPN. These resulting SPNs represent the structures that can be analyzed with standard methods for product-form SPNs to establish whether the original GSPNs have product-form solutions and to compute their performance indices with effective approaches based on computationally efficient algorithms that avoid the generation of their underlying state spaces.

We consider a particular class of Stochastic Petri Nets whose stationary probabilities at arbitrary instants exhibit a product form. We study these nets at specific instants in the steady state that occur directly after the firing of a transition. We focus our attention on the instant after tokens are removed from the places specified by a transition's input bag and just before tokens are entered into the places specified by the same transition's output bag. We show that the stationary probabilities at “arrival instants” are related to corresponding stationary probabilities at arbitrary instants in net(s) with lower load. We then show how one of the “arrival” theorems can be applied to the derivation of a formula for the mean sojourn time of a token in a place at steady state. This is the basis for the development of a Mean Value Analysis algorithm for the computation of performance indices for Product-Form Stochastic Petri Nets.

The class of Petri nets obtained by eliminating timing from generalized stochastic Petri net (GSPN) models while preserving the qualitative behavior is identified. Structural results for those nets are derived, obtaining the first structural analysis of Petri nets with priority and inhibitor arcs. A revision of the GSPN definition based on the structural properties of the models is presented. It is shown that for a (wide) class of nets, the definition of firing probabilities of conflicting immediate transitions does not require the information on reachable markings. Identification of the class of models for which the net-level specification is possible is also based on the structural analysis results. The procedure for the model specification is illustrated by means of an example. It is also shown that a net-level specification of the model associated with efficient structural analysis techniques can have a substantial impact on model analysis.>

A colored generalized stochastic Petri net (CGSPN) model was used to study the correctness and performance of the Lamport concurrent algorithm to solve the mutual exclusion problem on machines lacking an atomic test and set instruction. In particular, a parametric formal proof of liveness is developed based on the structure and initial state of the model. The performance evaluation is based on a Markovian analysis that exploits the symmetries of the model to reduce the cost of the numerical solution. Both kinds of analysis are supported by efficient algorithms. The potential of the GSPN modeling technique is illustrated on an academic but nontrivial example of an application from distributed systems.>

TOPNET is a software package for the simulation of communication networks that is being developed with the aim of exploiting as much as possible the visual aspects of a simulation experiment. The communication network topology and architecture are described by drawings, the system dynamics are represented with a class of timed Petri nets, the simulation experiment is controlled through menus and buttons activated with a mouse, and results are graphically displayed on the screen. With the help of an example, the main characteristics of the user interface and the internal architecture of TOPNET are described.>

Petri nets in which random delays are associated with atomic transitions are defined in a comprehensive framework that contains most of the models already proposed in the literature. To include generally distributed firing times into the model one must specify the way in which the next transition to fire is chosen, and how the model keeps track of its past history; this set of specifications is called an execution policy. A discussion is presented of the impact that different execution policies have on semantics of the mode, as well as the characteristics of the stochastic process associated with each of these policies. When the execution policy is completely specified by the transition with the minimum delay (race policy) and the firing distributions are of the phase type, an algorithm is provided that automatically converts the stochastic process into a continuous time homogeneous Markov chain. An execution policy based on the choice of the next transition to fire independently of the associated delay (preselection policy) is introduced, and its semantics is discussed together with possible implementation strategies.>

A technique is presented whereby queueing network models and generalized stochastic Petri nets are combined in such a way as to exploit the best features of both modeling techniques. The resulting hierarchical modeling approach is useful in the solution of complex models of system behavior. The authors have chosen two examples from the recent literature to illustrate the power and scope of this technique. They also demonstrate how folding of the generalized stochastic Petri net models for these two examples is useful in obtaining efficiently solvable, approximate models (bounding models).>

Recursive relations are derived for the exact computation of the steady-state probability distribution of some queuing models with passive resources that can be used to analyze the performance of multiple-bus multiprocessor system architectures. The most general case that can be shown to admit a product-form solution is described, and a recursive solution is obtained taking into account, considering different processor access rates, different memory selection probabilities, and a first-come-first-served bus scheduling policy. Several simpler cases allowing easier model solutions are also considered. Numerical evaluations for large computing systems with nonuniform memory references show the usefulness of the results.>

A class of Petri nets in which transitions can fire either immediately or after an exponentially distributed random time since their enabling (GSPN), is used to define performance models for Flexible Manufacturing Systems. An example is discussed in which the analysis of the GSPN model yields results that are more reliable than those obtained with a currently used method based on queueing networks. Detailed GSPN models are shown that allow accurate analyses of the effects that different scheduling policies and pallet mixes have on system performance.

A high-level Petri net model of the software architecture of an experimental MIMD multiprocessor system for Artificial Intelligence applications is derived by direct translation of the code corresponding to the assumed workload. Hardware architectural constraints are then easily added, and formal reduction rules are used to simplify the model, which is then further approximated to obtain a performance model of the system based on generalized stochastic Petri nets. From the latter model it is possible to estimate the optimal multiprogramming level of each processor so as to achieve the maximum performance in terms of overall throughput (number of tasks completed per unit time).

Much work has been done on the modeling of hardware resources; far fewer studies have been conducted on the impact of software systems on the underlying hardware. The authors address one such case in which blocking is present because of critical sections of code; this cannot be treated within the framework of product-form queuing network models. They show how a combination of generalized stochastic petri nets and queuing networks can easily model the situation under consideration. In addition, they show how a simple extension of this model can be applied to studying realistic systems with several domains.

We develop Generalized Stochastic Petri Net models for several priority queueing disciplines. The building blocks of these models are explained and many variants are easily derivable from them. We then combine these building blocks with product-form queueing network models. Numerical results are provided that illustrate the effectiveness of the method.

A consistent specification of quantitative processing characteristics is of crucial importance in order to obtain an efficient logical and physical database design. In this paper we propose a flow analysis of a Petri net representation of the interaction among operations within an organization function. The result of this analysis is the automa tic derivation of the operation activation frequencies. The project environment to which this analysis is relevant is also described.

Generalized Stochastic Petri Nets (GSPNs) are presented and are applied to the performance evaluation of multiprocessor systems. GSPNs are derived from standard Petri nets by partitioning the set of transitions into two subsets comprising timed and immediate transitions. An exponentially distributed random firing time is associated with each timed transition, whereas immediate transitions fire in zero time. It is shown that GSPNs are equivalent to continuous-time stochastic processes, and solution methods for the derivation of the steady state probability distribution are presented. Examples of application of GSPN models to the performance evaluation of multiprocessor systems show the usefulness and the effectiveness of this modeling tool. 1.

Graph models have been proposed by many authors as a useful tool for the analysis of peculiar features of computer systems such as concurrency, synchronization, communication, and cooperation among subsystems. Much of the work in this field is related to the original ideas developed by C. A. Petri. These graph models are today generally known as Petri Nets (PNs).

Stochastic models of contention for shared resources in an experimental multiprocessor prototype are presented and are validated with simulation and measurement results. Three modeling techniques are used (stochastic Petri nets, Markov chains, and queueing networks) that represent the system operations as Markovian stochastic processes. Each technique is best suited to a specific stage of the analysis. An integrated use of these techniques represents a very powerful tool for the performance analysis of multiprocessor systems and provides ways of investigating several extensions of the prototype architecture. Simulation results and measurements performed on the hardware prototype validate the analysis and show that the accuracy of the analytical results is excellent.

Markovian models are developed for the performance analysis and comparison of several single bus multiprocessor architectures. Processors are assumed to cooperate in a message passing fashion, and messages are exchanged through common memory areas. Four architectures are considered in this paper which differ in the location of the common memory modules. Contention for shared resources is modeled and the corresponding efficiency loss is studied. Numerical results are obtained for the processing power of each architecture, introducing simplifying assumptions that allow a compact Markovian system description.