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Publication# Perfect Simulations for Random Trip Mobility Models

Abstract

The random trip model was recently proposed as a generic mobility model that contains many particular mo-bility models, including the widely-known random waypoint and random walks, and accommodates more realistic sce-narios. The probability distribution of the movement of a mobile in all these models typically varies with time and converges to a steady state" distribution (viz. station-ary distribution), whenever the last exists. Protocol per-formance during this transient phase and in steady-state may differ significantly. This justifies the interest in per-fect sampling of the initial node mobility state, so that the simulation of the node mobility is perfect, i.e. it is in steady state throughout a simulation. In this work, we describe im-plementation of the perfect sampling for some random trip models. Our tool produces a perfect sample of the node mobility state, which is then used as input to the widely-used ns-2 network simulator. We further show some simu-lation results for a particular random trip mobility model, based on a real-world road map. The performance met-rics that we consider include various node communication properties and their evolution with time. The results demon-strate difference between transient and steady-state phases and that the transient phase can be long lasting (in the or-der of a typical simulation duration), if the initial state is drawn from a non steady-state distribution. The results give strong arguments in favor to running perfect simula-tions. Our perfect sampling tool is available to public at: http://www.cs.rice.edu/santa/research/mobility.

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Random walk

In mathematics, a random walk is a random process that describes a path that consists of a succession of random steps on some mathematical space. An elementary example of a random walk is the random walk on the integer number line which starts at 0, and at each step moves +1 or −1 with equal probability. Other examples include the path traced by a molecule as it travels in a liquid or a gas (see Brownian motion), the search path of a foraging animal, or the price of a fluctuating stock and the financial status of a gambler.

Simulation

A simulation is the imitation of the operation of a real-world process or system over time. Simulations require the use of models; the model represents the key characteristics or behaviors of the selected system or process, whereas the simulation represents the evolution of the model over time. Often, computers are used to execute the simulation. Simulation is used in many contexts, such as simulation of technology for performance tuning or optimizing, safety engineering, testing, training, education, and video games.

Steady state

In systems theory, a system or a process is in a steady state if the variables (called state variables) which define the behavior of the system or the process are unchanging in time. In continuous time, this means that for those properties p of the system, the partial derivative with respect to time is zero and remains so: In discrete time, it means that the first difference of each property is zero and remains so: The concept of a steady state has relevance in many fields, in particular thermodynamics, economics, and engineering.

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