Publisher mobility support in content centric networks
Although the effect of delay on transparency is well appreciated, Publisher mobility support in content centric networks the challenge of maintaining transparency despite the information loss when a simulation is distributed is typically an underestimated one. Publisher mobility support in content centric networks To illustrate this challenge a very simple example is given in this section. Consider a second-order linear autonomous system described second-order numerical integration method that calculates the states at the next time step using the formula where h is the integration step size. Publisher mobility support in content centric networks In words, Heun’s method uses Euler’s method to predict the slope at the next time step and uses the average of the slopes at times t and the trapezoidal rule, to correct the estimate of the state at the next time step. As indicates, this results in a local error that is leading to a global error that is making Heun’s method a second-order method.
The integration of into the first equation of yields the following equation for the estimation of the first state at the next time step This is the equation the solver would use to calculate , if the equations were solved in an integrated way by a single solver. Now, consider a distributed solution of this problem, as illustrated . The two equations are solved by two separate solvers that exchange only the information about the states, which are the variables coupling the two state equations.Assume that the solvers are synchronized and the information exchange is happening without any delay, so that the states are known to both solvers at each time step and there are no sampling and holding effects.
Publisher mobility support in content centric network
Publisher mobility support in content centric networks In this case, becomes an external input for the first solver rather than being a state, and the estimate for the first state at the next time step becomes Notice that the penultimate term in is missing in Also notice that the missing term includes the second state equation of which is not available to the first solver in the distributed setting. This makes the local error instead of because the missing term includes as a multiplier. This increase in error happens despite the fact that a secondorder integrator is being used, and is caused by the distributed architecture. A numerical example can provide further sense of severity of this issue. Consider the system Aone-step numerical integrationwith a step size of gives an error in whereas the error in the distributed solution is, approximately times larger than the nondistributed solution.
Publisher mobility support in content centric networks Furthermore, halving the step size brings the nondistributed solution error down to, one-eighth of the previous error, an improvement that is as theoretically promised by Heun’s method. Publisher mobility support in content centric networks However, the error in the distributed solution reduces only to, only one fourth of the error obtained with , an improvement that is only as predicted by This simple example highlights the fact that distribution in and of itself can be an important source of error. Typically, when systems are distributed, each site in the distributed simulation has access to only the coupling variables and not all the states and state derivates of the other sites, which can reduce the simulation accuracy as illustrated in this example. Thus, distributing the simulation may cause a significant degradation in transparency, and hence receives special attention in this paper. Publisher mobility support in content centric networks