Alexander Kostin

Reachability analysis in T-invariant-less Petri nets

An algorithm for reachability analysis in place/transition Petri nets having no transition invariants (T-invariants) is proposed. Given a Petri net with initial and target markings, a so-called complemented Petri net is created first that consists of the given Petri net and an additional complementary transition. Thereby, the reachability task is reduced to computation and investigation of those minimal-support and linearly combined T-invariants of the complemented Petri net, in which the complementary transition fires only once. Then, for each T-invariant with a single firing of the complementary transition, the algorithm will try to create a reachability path from the given initial marking to the target marking.

A simple and fast multi-class piecewise linear pattern classifier

A simple and fast multi-class piecewise linear classifier is proposed and implemented. For a pair of classes, the piecewise linear boundary is a collection of segments of hyperplanes created as perpendicular bisectors of line segments linking centroids of the classes or parts of classes. For a multi-class problem, a binary partition tree is initially created which represents a hierarchical division of given pattern classes into groups, with each non-leaf node corresponding to some group. After that, a piecewise linear boundary is constructed for each non-leaf node of the partition tree as for a two-class problem. The resulting piecewise linear boundary is a set of boundaries corresponding to all non-leaf nodes of the tree. The basic data structures of algorithms of synthesis of a piecewise linear classifier and classification of unknown patterns are described. The proposed classifier is compared with a number of known pattern classifiers by benchmarking with the use of real-world data sets.

Performance study of a wireless mobile ad hoc network with orientation-dependent internode communication scheme

A Petri-net-based simulation model of a wireless mobile ad hoc network is developed and studied. The model covers all the fundamental aspects of behaviour of such a network and uses a novel scheme of orientation-dependent or sector-dependent internode communication, with random states of links. The proposed scheme enables representation of reliability aspects of wireless communication, such as fading effects, interferences, presence of obstacles and weather conditions in a general and rather easy way. The simulation model was implemented in terms of a class of extended Petri nets to explicitly represent parallelism of events and processes in the WLAN as a distributed system. In the simulation, the behaviour of four fundamental performance metrics - packet delivery ratio, average number of hops, relative network traffic and end-to-end delay - were investigated with varying distance of transmission and different combinations of model parameters. Copyright

A randomized contention-based load-balancing protocol for a distributed multiserver queuing system

A novel protocol for load balancing in distributed multiserver queuing systems is proposed. The protocol is based on an anonymous multicast communication in a network of servers or workers. A formal description of the protocol in terms of a state diagram is given. The complexity issues of the protocol are considered. The protocol was investigated by the use of a simulation model in terms of a class of the extended Petri nets and implemented as a prototype system on a group of computers in a LAN of Ethernet type. The results of simulation and prototype-system studies of a distributed queuing system with the proposed protocol are compared to the behavior of an ideal, centralized queuing system. Limitations and possible extensions to the protocol are outlined.

Winsim: a tool for performance evaluation of parallel and distributed systems

A simulation system Winsim for modeling of parallel and distributed systems is presented. Winsim is based on a class of extended Petri nets, has a simple graphical user interface, high level programming language possibilities for complex data processing, enables simulation of systems consisting of a large number of processes, and provides fast simulation. The paper considers the basic features of the system, outlines its architecture, and gives an example of a simulation model of a distributed mutual exclusion algorithm developed and implemented in Winsim.

Anycast tree-based routing in mobile wireless sensor networks with multiple sinks

A routing scheme for wireless sensor networks with mobile sensors and mobile multiple sinks is proposed and studied. The scheme is based on expanding ring search, anycast messaging and reactive mode with maintaining route state information in sensors. As a result of a successful routing request issued by the sensor, it becomes a member of a routing tree with some sink as a root. Anycast messaging is used only at the stage of establishing a path from a sensor to a sink. Replies from sinks are always forwarded in unicast mode. This considerably reduces network traffic and, as a result, energy consumption by sensors. To take into account routing conditions for network nodes in receiving messages from different directions, the receiving area of each node is assumed to consist of a number of sectors, considered as independent links with random change of link states in time. The proposed routing scheme was investigated with the use of a detailed simulation model, implemented in terms of a class of extended Petri nets. In simulation the following performance metrics were investigated versus time-to-live value: response ratio, relative network traffic and relative energy consumption. These metrics were considered for a number of combinations of parameters, such as the number of sinks, sensor availability and link availability. The results of simulation were compared with published characteristics of a similar model, in which sensors do not maintain any routing state information, and is proved to outperform it.

Yet another reachability algorithm for Petri nets

A new algorithm for the determination of reachability of a marking in generalized Petri nets is proposed. The algorithm is based on the matrix-equation approach. Given a Petri net, a so called complemented Petri net is created that consists of the given Petri net and a complementary transition with input and output places depending on the initial and target markings. Then the reachability task is reduced to the investigation of T-invariants of the complemented Petri net. Using a technique of search for T-invariants, the algorithm determines minimal-support T-invariants, that include the complementary transition, and then calculates the finite set of their linear combinations. For each T-invariant, the algorithm tries to create sequentially all reachability paths from the given initial marking to the target marking or determines that there are no such paths at all. During creation of the reachability paths, the algorithm needs memory only for storing the reachability path being created. If it is sufficient to determine only one firing sequence that transforms the initial marking into the target one, then the algorithm may be terminated after successful creation of the first reachability path.

The novel algorithm for determining the reachability in acyclic Petri nets

A novel algorithm for determining the reachability of a marking in acyclic Petri nets is proposed. For this algorithm, a Petri net is represented in the matrix form, with a given pair of initial and target markings. The algorithm is based on the creation of a temporal ordering relation for transition firings and on using this relation for determining the shortest sequence of transition firings transforming the initial marking into the target one. By solving the fundamental equation of the Petri net, the algorithm determines initially whether the target marking is reachable from the given initial marking, and, in case it is, produces the shortest sequence of transition firings which transforms the initial marking into the target one.

Performance study of a wireless mobile ad hoc network with orientation-dependent inter-node communication links

A Petri-net-based simulation model of a wireless mobile ad hoc network is studied. The model includes a parameterized mobility model and a novel scheme of orientation-dependent inter-node communication links with random states. In simulation, three fundamental performance metrics — packet delivery rate, average number of hops and relative network traffic — are investigated under different combinations of model parameters.

Simulation of a novel leader election protocol with the use of Petri nets

A novel leader election protocol for a distributed system is presented. The proposed scheme is based on reliable multicast. The use of multicast considerably simplifies the protocol since the group members do not need to know each others addresses to communicate. Another advantage of using multicast is that members do not have to make any reconfiguration if some members crash, join or leave the group. The paper describes the proposed protocol and discusses the results of the detailed simulation in terms of extended Petri nets.