Modeling resource management in cellular systems using Petri nets

In cellular communications the transfer of calls, or handoff, between the base stations, and efficient use of resources, or channel allocation schemes are essential features. The capabilities of Petri nets (PN) are used as a novel approach in the analysis of handoff and dynamic channel allocation (DCA) problems. The generalized stochastic Petri net (GSPN) models are obtained and analyzed as continuous time Markov chains derived from the reachability trees. Solution of the Markov chain results in performance indicators which show the impacts of different algorithms on the system behavior.

SURF-2 is a software tool for evaluating system dependability. It is especially designed for an evaluation based system design approach in which multiple design solutions need to be compared from the dependability viewpoint. SURF-2 allows the user to describe the model behavior using generalized stochastic Petri nets (GSPNs) whose reachability graph is then interpreted as a Markov chain, or enter directly a Markov chain. In the case of GSPNs, it enables the models to be verified in terms of their structural properties. The tool supports the evaluation of different measures of dependability, including pointwise measures, asymptotic measures, mean sojourn times and, by superposing a reward structure onto the behavior model, reward measures such as expected performance or cost. These measures are obtained by processing the Markov chain. SURF-2 can be viewed as a toolbox where each tool can operate independently on objects gathered in a database managed by a supervisory task.

The authors describe a method for the performance evaluation of communication networks of distributed systems. This method consists of: logical transition from the network architecture under consideration to an associated Petri net based model and adaptation to a generalized stochastic Petri net (GSPN); automatic generation of the state transition rate diagram of a Markov Chain (MC) from the reachability graph of GSPN due to isomorphism between the stochastic Petri nets and homogeneous MC; computation of the steady state probabilities which are used for the evaluation of system performance indices. The method was implemented in a software package. An application of this method to performance evaluation of a simple three-processor system with distributed common memory is also presented. >

We consider the problem of synthesising parameters affecting transition rates and probabilities in generalised Stochastic Petri Nets (GSPNs). Given a time-bounded property expressed as a probabilisitic temporal logic formula, our method allows computing the parameters values for which the probability of satisfying the property meets a given bound, or is optimised. We develop algorithms based on reducing the parameter synthesis problem for GSPNs to the corresponding problem for continuous-time Markov Chains (CTMCs), for which we can leverage existing synthesis algorithms, while retaining the modelling capabilities and expressive power of GSPNs. We evaluate the usefulness of our approach by synthesising parameters for two case studies.

Generalized Stochastic Petri Nets (GSPNs) are widely used in reliability analysis to model and optimize the dependability of complex systems, enabling assessments of availability, failure probabilities, and repair processes through stochastic timing. This study investigates a repairable redundant retrial system incorporating warm and cold standbys and an unreliable repairer through a Generalized Stochastic Petri Nets. The repairer experiences both active (during repair) and passive (idle) breakdowns. Component and repairer lifetimes are exponentially distributed. A component that fails undergoes immediate repair if the repairer is available; otherwise, it enters a retrial FCFS orbit. A Continuous Time Markov Chain (CTMC) derived from the GSPN model yields steady state probabilities and availability. System reliability and time to first failure are then determined via Laplace transforms. Numerical examples demonstrate the system reliability performance.

In this paper, we extend Petri Nets including Queueing Networks (PNiQs) with several job classes and define Multi Class-PNiQs (MC-PNiQ). A MC-PNiQ is a Generalized Stochastic Petri Net (GSPN) which contains multiclass queueing networks (MC-QNs). This approach allows to combine the advantages of both concepts on the modelling level as well as on the analysis level. The use of MC-QNs permits concise modelling of waiting room, server and queueing and offers many fast analysis algorithms for large multiclass systems. Additionally, GSPN provide the expressiveness and flexibility for modelling of more complicated structures like fork/join, etc. The definition of MC-PNiQs is especially designed to allow a qualitative analysis based on a reduced state space, as well as automated approximate analysis by aggregation of the multi-class queueing nets and replacing them with GSPN elements. The resulting GSPN can then be analyzed with state-of-the-art methods and tools.

In this paper, we use a Generalized Stochastic Petri Net (GSPN) to model multiprocessor parallel processing architectures. It can precisely describe the dynamic operations and states of the system with the reachability graph and the reachability set generated by the GSPN approach. The structural properties and temporal specifications of GSPN are described. Then, the effectiveness of this modeling technique in the case of parallel architecture with common bus structures of shared memory style and with message passing style is investigated in detail.

A common approach for the quantitative analysis of a generalized stochastic Petri net (GSPN) is to generate its entire state space and then solve the corresponding continuous-time Markov chain (CTMC) numerically. This analysis often suffers from two major problems: the state space explosion and the stiffness of the CTMC. In this paper we present parallel algorithms for shared-memory machines that attempt to alleviate both of these difficulties: the large main memory capacity of a multiprocessor can be utilized and long computation times are reduced by efficient parallelization. The algorithms comprise both CTMC construction and numerical steady-state solution. We give experimental results obtained with a Convex SPP1600 shared-memory multiprocessor that show the behavior of the algorithms and the parallel speedups obtained.

Rapid advances of the handheld devices and the emergence of the demanding wireless applications require the cellular networks to support the demanding user needs more effectively. The cellular networks are expected to provide these services under a limited bandwidth. Efficient management of the wireless channels by effective channel allocation algorithms is crucial for the performance of any cellular system. To provide a better channel usage performance, dynamic channel allocation schemes have been proposed. Among these schemes, distributed dynamic channel allocation approaches usually have better performance results. The two important issues that must be carefully addressed in such algorithms are the efficient co-channel interference avoidance and messaging overhead reduction. One of these distributed channel allocation algorithms is the DonorList algorithm, which can effectively manage these two issues. In this paper the channel import efficiency of the DonorList algorithm is evaluated. The performance evaluation results obtained after extensive simulation studies, which were conducted under different traffic load conditions, show that the proposed algorithm provides improvement over the performance of other algorithms recently proposed in the literature.

We discuss the wireless channel allocation problem for data dissemination in mobile computing systems. Methods for accessing data through broadcast and on-demand channels are described. We provide analytical models and cost formulae for the exclusive broadcast channels and the exclusive on-demand channels and propose a dynamic channel allocation algorithm for optimizing system performance. Our performance evaluation shows that dynamic channel allocation significantly improves system performance and the channel allocation algorithm gives us the optimal solution for various system parameter settings.

Automated construction of GSPN models for flexible manufacturing systems

Stochastic Petri nets (SPNs) and generalized stochastic Petri nets (GSPNs) are compared in order to investigate the role of immediate transitions. The comparison is based on the ability of the two formalisms to define models that can be 'scalable' with respect to the initial marking. An intermediate model between (G)SPN structures and (G)SPN systems called 'family' is introduced as a reference for the comparison. It is shown that GSPN families exist that do not have SPN counter- parts. An algorithm is given to reduce GSPN to SPN families in the cases in which this is possible. The application of this structural reduction algorithm allows a more efficient generation of the state space of GSPN systems. >

The stochastic Petri net package (SPNP) is a versatile modeling tool for the solution of generalized stochastic Petri nets (GSPN). The GSPN models are described in the input language for SPNP called C-based SPN language (CSPL). The CSPL is an extension of the C programming language with additional constructs that facilitate easy description of GSPN models. The GSPN models specified to SPNP are actually “GSPN reward models” that are based on the “Markov reward models” paradigm. This provides a powerful modeling environment for dependability analysis, performance analysis, and performability modeling. A number of important Petri net constructs like marking dependency, variable cardinality arc, and enabling functions facilitate the construction of models for complex systems.

International audience

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.