Zbigniew Lipiński

Maximum Lifetime Problem in Sensor Networks with Limited Channel Capacity

In the paper we analyze the maximum lifetime problem in sensor networks with limited channel capacity for multipoint-to-multipoint and broadcast data transmission services. We show, that in order to achieve an optimal data transmission regarding the maximum lifetime problem we cannot allow for any interference of signals. We propose a new Signal to Interference plus Noise Ratio function and used is to modify the Shannon-Hartley channel capacity formula. For the modified channel capacity formula we solve the maximum lifetime problem in one dimensional regular sensor network

UML-Based Reliability Modeling of Network Services, a UDP Echo Service Case Study

L_N

State Model of Service Reliability

for discussed data transmission services.

Routing Algorithm for Maximizing Lifetime of Wireless Sensor Network for Broadcast Transmission

In the paper, we discuss state space reliability modeling formalism of distributed systems and services compliant with UML metamodel. Behavior of modeled application system we describe in terms of states. Service generation process we represent as a sequence of application system states. State space approach allows us to define dependence between application system components via dependence between components states and states input, output parameters. Reliability of application system component we define for each simply action state. Reliability of a service we express by components reliability in states determined by service generation process. As an example, we analyze reliability of client-server system which components exchange data by means of connectionless protocol. For several deployment configuration of the system, we calculate reliability of UDP Echo service.

Maximum Lifetime of the Wireless Sensor Network and the Gossip Problem

We propose a simple formalism for modelling of a service reliability. A service is defined as an ordered set of states of a modelled application. In the model, a certain reliability is assigned to each application state. Reliability of a service is expressed in terms of above partial reliabilities

Stability Analysis of Routing Strategies for the Maximum Lifetime Problem in One-Dimensional Ad-Hoc Wireless Networks

In the article we discuss solutions of the maximum lifetime broadcasting problem in wireless sensor networks. Due to limited energy resources of the network nodes to find an optimal transmission route of the broadcasted data we minimize the maximum energy consumed by the nodes. We give an analytical solution of the problem in one dimensional regular sensor network for the point-to-point and point-to-multipoint data transmission scheme. We show that in such a network, when the cost of data transmission is a polynomial function of distance between transmitter and receiver, there exist solutions with an equal energy, i.e., all nodes of the network consume the same amount of energy. We assume that in the networks with sensors evenly distributed over some d-dimensional area there always exists an equal energy solution of the problem. To solve the maximum lifetime broadcasting problem in such networks we propose two algorithms. By means of the first algorithm the set of minimum node weight spanning trees in a given network is determined. The second algorithm allows to balance the energy consumption of the sensors for data transmitted along given minimum node weight spanning tree. We show, that the proposed algorithms find an approximate solution of the discussed problem in polynomial time.

Classification of Solutions to the Minimum Energy Problem in One Dimensional Sensor Networks

In the gossip problem each node of the graph G possesses a unique piece of information - the gossip message. A sequence of one-way or two-way communications between pair of nodes is made to spread the messages so that any node of the graph knows all the gossips. The question is, what is the minimum number of calls between pairs of nodes needed to exchange all gossip messages? The solution to the two-way communication gossip problem is that \(2N-4\) calls (\(N\ge 4\)) suffice if and only if the graph contains a four cycle subgraph. For one-way communication problem the classical results states that in a strongly connected graph \(2N-2\) calls (\(N\ge 4\)) suffice. In this paper we consider the gossip problem in the context of saving the energy consumed by the sensor network nodes. In the process of gossiping the network nodes consume their energy resources. The amount of consumed energy depends on the cost of transmission between pairs of nodes, a selected transmission route and the sizes of the gossip messages. For the fixed size of gossip messages and the fixed cost of transmission of one unit of data between pairs of nodes we search for the optimal transmission route of the gossip messages such that the most overloaded node consumes the minimum amount of energy. We define the network lifetime for the gossiping process as the time until the first node of the network runs out of its energy. By minimizing the energy of the most overloaded node we obtain the solution to the network lifetime gossiping problem. In the paper we solve the problem for the one-dimensional regular sensor network. We propose a load balancing algorithm for solving the problem in networks with evenly distributed sensors in a given area such that an equal energy solution of the problem exists. We also propose a data aggregation scheduling algorithm to calculate the minimum number of calls necessary to spread the gossip messages for a given solution of the network lifetime gossiping problem.

Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks

In the paper we discuss solutions of the maximum network lifetime problem in one-dimensional, regular ad-hoc wireless networks. For the problem, nodes of the network generate given amount of data and send it possibly via other nodes to the data collector. To extend the network lifetime the data should be transmitted in such a way, that the energy utilized by the most overloaded node is minimized. We assume, that the nodes use the point-to-point data transmission scheme and the cost of transmission of one unit of data is arbitrary superadditive function of a distance between transmitter and receiver. We show that for the one-dimensional network in which the nodes are evenly distributed on the line and each node generates the same amount of data there exists an equal energy solution of the problem. We treat the amount of data generated by each node and the location of the nodes on the line as the initial parameters of the problem. It is known, that solutions of the problem are very sensitive under change of these parameters. It means, that small change in the value of these parameters can change the optimal transmission graph and the solution. In the paper we analyze stability of obtained equal energy solution under modification of these two sets of parameters.

Maximum lifetime broadcasting problem in sensor networks

We classify of the minimum energy problem in one dimensional wireless sensor networks for the data transmission cost matrix which is a power function of the distance between transmitter and receiver with any real exponent. We show, how these solutions can be utilized to solve the minimum energy problem for the data transmission cost matrix which is a linear combination of two power functions. We define the minimum energy problem in terms of the sensors signal power, transmission time and capacities of transmission channels. We prove, that for the point-to-point data transmission method utilized by the sensors in the physical layer, when the transmitter adjust the power of its radio signal to the distance to the receiver, the optimal transmission is without interference. We also show, that the solutions of the minimum energy problem written in terms of data transmission cost matrix and in terms of the sensor signal power coincide.