A very fast scheduling system is proposed and experimentally investigated. The system consists of a job shop manager and dynamic models of machines. A schedule is created in the course of a close cooperation with models of the machines that generate driving events for the scheduler. The system is implemented with a new class of extended Petri nets and runs in the environment of the Petri-net tool WINSIM. The scheduler creates a schedule sequentially, without any form of enumerative search. To investigate the scheduler performance, a large number of experiments were conducted with the use of few strategies. Due to a unique mechanism of monitoring of triggering events in the Petri net, the developed scheduler runs at least hundreds of times faster than any known single-processor job shop scheduler.

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.

In wireless networks, reducing the number of redundant packets is one of the important mechanisms to minimize the required network bandwidth and the power consumed by network nodes. In this paper, an efficient and stateless flooding mechanism for anycast routing in wireless mobile ad hoc networks is proposed. The mechanism uses the technique of expanding ring search to decrease the related message traffic. A model of this mechanism is described. Based on this model, an extensive simulation study, together with real field experiments, has been conducted to investigate the performance of the proposed mechanism for anycast server localization. The simulation model has been developed in terms of a class of extended Petri nets that provide the possibility to conveniently represent parallelism of events and processes in the network. In simulation and real work experiments, fundamental performance metrics—response ratio, relative traffic and average response time—were investigated with varying distance of transmission and different combinations of model parameters. The obtained results show that the proposed approach to server localization in mobile ad hoc networks has good characteristics. As was demonstrated with a prototype system, the proposed routing method can be easily implemented at the application layer, without any changes at lower layers of the network protocol stack.

An improved method of dynamic route establishment between sensors and sinks is proposed for wireless sensor networks. The method is based on the use of an anycast-based restricted flooding technique and does not require the accumulation and maintenance of state information in network nodes. The proposed scheme is implemented as a simulation model in terms of extended Petri nets. The developed model was investigated in extensive simulation experiments. The behaviour of the model was evaluated with the use of a few practically important performance metrics. Keywords-component; Anycast routing, Modeling, Petri nets, Simulation, Wireless sensor networks

For a square area of an arbitrary size, populated by a given number of WLAN stations, uniformly distributed in the area, the exact probability distribution of distance between pairs of the nearest stations is derived. The derived probability distribution is compared with the Rayleigh probability law that describes the distance between points in an infinite Poisson point field.

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 internode 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.

Summary The paper illustrates the improvements in logging while drilling (LWD) images and subsequent formation evaluation by using a new methodology for depth and survey measurements corrections. LWD depth measurements are often considered inaccurate and, therefore, not as reliable for well-to-well correlations, correlations with data acquired with wireline measurements and formation layer thickness determinations. The reasons for these inaccuracies generally originate from the traditional practice that LWD depth is purposely made equal to the driller's depth, which is a static pipe length measurement made by tape at the surface. There is almost always a difference between the actual measured depth (MD) of the LWD sensor downhole and this static pipe measurement, because downhole the drillpipe is subject to an environment that is not representative of the derrick (e.g., varying drilling mechanical conditions and temperature changes). Here, we demonstrate the applications of the method, which allows dynamic driller's depth correction for the effects of drillstring weight, downhole friction, weight on bit, thermal expansion, residual rig heave, and tide. Another significant inaccuracy source is a standard practice of calculating borehole position from stationary survey points typically taken every 90 feet (ft) using the minimum curvature method. Neglecting the complex borehole shape between survey stations can lead to a systematic error in determining the borehole position. We consider using continuous inclination and azimuth measurements along with stationary surveys to correct these errors. We provide comparisons of LWD images before and after the depth and survey corrections to illustrate how the measurement errors affect formation dips interpreted from the images. We demonstrate how improved accuracy allows filtering out the artifacts and provides more decisive and accurate identification of geologic features. We show how using the corrected 3D position improves accuracy of the formation thicknesses calculations and therefore improves the reservoir summation results. As a result, we propose a borehole 3D position measurement that is accurate, consistent between wells (regardless of rig type or bottomhole assembly [BHA] configuration), and independent of the drilling mode. Using this new measurement significantly improves the quality of the formation evaluation.

D048 A New Methodology for Effectively Correcting LWD Depth Measurements G.A. Bordakov* (Schlumberger) A.V. Kostin (Schlumberger) J. Rasmus (Schlumberger) & H. Laastad (Statoil) SUMMARY LWD or drilling derived logging depths can be inaccurate and therefore unreliable for well-to-well correlations correlations to offset well data and formation thickness determinations. These inaccuracies generally originate from the fact that the LWD depth measurement is purposely made to equal the driller’s depth. The actual depth of the measurements downhole is rarely equal to this static pipe measurement for the primary reason that while drilling the drillpipe is subject to an environment that is not

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.

This paper will describe a new method for improving Logging While Drilling (LWD) depth accuracy. Case studies that describe this technique will also be presented. It is generally accepted that using the Drillers depth measurement for LWD applications has been the most practical solution to a complex depth problem. The various sources of depth errors have also been described and quantified in the industry. Two of the main contributors to drillpipe based depth error are mechanical stretch and thermal expansion. Of these, the mechanical stretch is governed largely by the well profile, linear weight of the pipe, and the frictional forces that can be calculated using industry standard torque and drag calculations. The coefficient of linear thermal expansion of the drillstring components and the distributed temperature of the drillstring assembly at the time of measurement govern the change in length due to temperature. To compensate for these effects requires a series of algorithms that identify the mechanical condition of the drillstring at the time of measurement based on the operational drilling mode. Then, a standard torque and drag model is used to calculate the mechanical stretch, and a thermal expansion algorithm subsequently applies the temperature component of the depth correction. The results of these computations are a corrected logging depth, and an improved time to depth conversion file that can be used to recalculate the logging data. The results from case study data strongly support that; uncorrected standard LWD depth accuracy today is often at least as good as that provided by comparable wireline logs; and that LWD depth can be significantly improved using this technique. This new method for improving logging depth will lead to enhanced single well evaluation and the improved well-to-well correlation of reservoir features, and hence the value of the reservoir model.

A novel anycasting protocol for timed asynchronous distributed multiserver systems is proposed. It is based on an anonymous multicast communication in a network of servers. In contrast with known approaches, the task of selection of a server in the given group is shifted from clients and the network to the servers that make a selection decision themselves as a result of a negotiation. The protocol was investigated with the use of a detailed simulation model using a class of the extended Petri nets. The results of simulation study of the proposed protocol are compared to the behavior of an ideal, centralized multiserver queuing system.

A leader election protocol for timed asynchronous distributed systems is presented. The proposed scheme is based on reliable multicast where all participating processes of the group will receive protocol messages. In this protocol, the group members do not need to know each other's addresses to communicate. Also, they do not have to make any reconfiguration if some members crash, join or leave the group. The paper describes the proposed protocol, estimates its performance in simulation and compares this simulation with an analytical model. It is found that the communication complexity of the protocol is of O(N). As simulation formalism, a class of extended Petri nets was used.

A new reachability algorithm for general Petri nets is proposed. Given a Petri net with an initial and a 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 calculation and investigation of transition invariants (T-invariants) of the complemented Petri net. The algorithm finds all minimal-support T-invariants of the complemented Petri net and then calculates a finite set of linear combinations of minimal-support T-invariants, in which the complementary transition fires only once. Finally, for each T-invariant with a single firing of the complementary transition, the algorithm tries to create a reachability path from initial to target marking or determines that there is no such path.