Purpose The purpose of this paper is to model an important aspect of the problem of sensor information integration that arises in wireless communications, where N sensors try to communicate with a receiver using a single un‐shareable radio channel. If several sensors transmit at the same time, their transmissions collide at the receiver resulting in garbled messages and the need for re‐transmission. This is highly undesirable since the sensors are energy‐constrained and the radio interface is known to be the most significant source of energy expenditure. Consequently, it is of paramount importance to design arbitration protocols that are highly efficient in stamping out collisions and that are, at the same time, as lightweight as possible. Design/methodology/approach The receiver advertises a time division multiple access (TDMA) frame consisting of n slots, numbered from 1 to n , where n is an application‐dependent parameter. Each sensor generates uniformly at random, and independently of other sensor, an integer i between 1 and n and transmits in the i ‐th slot of the TDMA frame. If two or more sensors are transmitting in the same slot their messages will be lost to collision. Similarly, slots that carry no transmission are wasted. The authors model the arbitration strategy discussed above as a Bose‐Einstein occupancy problem where N indistinguishable balls are thrown at random into n distinguishable bins and all distinguishable outcomes are considered to be equally likely. Findings In this paper the authors present a distributed probabilistic mechanism that aims to arbitrate between several competing requests by various sensors for the radio channel. The mechanism is simple, energy‐efficient and does not rely on the existence of unique sensor identifiers (IDs). Originality/value The Bose‐Einstein occupancy model presented in this paper will help the receiver to tailor an appropriate number of timeslots in TDMA frame during the integration process, such that collisions are minimized, and hence integration between sensors can be done effectively.
We model an important aspect of the problem of sensor information integration that arises in wireless communications, where N sensors try to communicate with a receiver using a single un-shareable radio channel. If several sensors transmit at the same time their transmissions collide at the receiver resulting in garbled messages and the need for re-transmission. This is highly undesirable since the sensor nodes are energy-constrained and the radio interface is known to be the most significant source of energy expenditure. Consequently, it is of paramount importance to design arbitration protocols that are highly efficient in stamping out collisions and are, at the same time, as lightweight as possible. The main contribution of this paper is to present a distributed probabilistic mechanism that aims to arbitrate between several competing requests by sensor nodes for the radio channel. Our mechanism is simple, energy-efficient and does not rely on the existence of unique sensor identifiers (IDs).
Neighborhood discovery (ND) in a wireless sensor network is a process of identifying the sensors that a given node can communicate directly. In this paper, our main contribution is to model the ND protocol in a wireless sensor network. In ND task, each node is assigned its own N timeslots, with equal slot intervals. In each slot, each node chooses either to transmit or listen, with probabilities p and 1 -- p. Our objectives are to analyze the optimal value of p, and model the formulation of N by mapping the problem into the coupon's collector problem. The simulation results show close match to the theoretical results.
This research is conducted to model flow of traffic on a one lane roadway by partial differential equation (PDE). Then, Finite Difference Method (FDM) is used to solve one-dimensional traffic flow equation. The Finite Difference Method involved is forward difference and central difference. In this problem, the density of cars with fixed ends is considered. The finite difference method (FDM) proceeds by replacing the derivatives in the traffic flow equations by finite difference approximations. This gives a large algebraic system of equations to be solved, which can be solved easily in mathematics software. MATLAB Distributed Computing R2010a software is used to perform the computational experiment while Microsoft Excel is used toillustrated the graphs. In this research, the effect of different step space, h and step time, k are investigated. Besides, comparison between finite difference solutions and analytical solutions will determine the accuracy of finite difference method (FDM).
This paper revisits the comrade matrix approach in finding the greatest common divisor (GCD) of two orthogonal polynomials. The present work investigates on the applications of the QR decomposition with iterative refinement (QRIR) to solve certain systems of linear equations which is generated from the comrade matrix. Besides iterative refinement, an alternative approach of improving the conditioning behavior of the coefficient matrix by normalizing its columns is also considered. As expected the results reveal that QRIR is able to improve the solutions given by QR decomposition while the normalization of the matrix entries do improves the conditioning behavior of the coefficient matrix leading to a good approximate solutions of the GCD.
Purpose The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme. Design/methodology/approach The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities. Findings The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients. Originality/value The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.
Neighborhood discovery (ND) in a wireless sensor network is a process of identifying the sensors that a given node can communicate directly. In ND task, each node is assigned its own N timeslots, with equal slot intervals. In each slot, each node chooses either to transmit or listen, with probabilities p and 1-p respectively. Our objectives are to analyze the optimal value of p, and model the formulation of N by mapping the problem to the occupancy problem, i.e one of the popular problem in probability theory. A number of simulations are performed and the results are compared to the theoretical formulation.
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