Real and complex analysis, 3rd ed.
Real and complex analysis, 3rd ed.
Exact sampling with coupled Markov chains and applications to statistical mechanics
Proceedings of the seventh international conference on Random structures and algorithms
Proceedings of the 9th annual international conference on Mobile computing and networking
On the Stationary Distribution of Speed and Location of Random Waypoint
IEEE Transactions on Mobile Computing
Delay and resource analysis in MANETs in presence of throwboxes
Performance Evaluation
Distribution of path durations in mobile ad hoc networks and path selection
IEEE/ACM Transactions on Networking (TON)
On clustering phenomenon in mobile partitioned networks
Proceedings of the 1st ACM SIGMOBILE workshop on Mobility models
Compound TCP with Random Losses
NETWORKING '09 Proceedings of the 8th International IFIP-TC 6 Networking Conference
A prsimonious model of mobile partitioned networks with clustering
COMSNETS'09 Proceedings of the First international conference on COMmunication Systems And NETworks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Modelling mobility: a discrete revolution
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Modelling mobility: A discrete revolution
Ad Hoc Networks
Spatial node distribution of manhattan path based random waypoint mobility models with applications
SIROCCO'09 Proceedings of the 16th international conference on Structural Information and Communication Complexity
Information spreading in dynamic graphs
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
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The simulation of mobility models such as the random waypoint often cause subtle problems, for example the decay of average speed as the simulation progresses, a difference between the long term distribution of nodes and the initial one, and sometimes the instability of the model. All of this has to do with time averages versus event averages. This is a well understood, but little known topic, called Palm calculus. In this paper we first give a very short primer on Palm calculus. Then we apply it to the random waypoint model and variants (with pause time, random walk). We show how to simply obtain the stationary distribution of nodes and speeds, on a connected (possibly non-convex) area. We derive a closed form for the density of node location on a square or a disk. We also show how to perform a perfect (i.e. transient free) simulation without computing complicated integrals. Last, we analyze decay and explain it as either convergence to steady state or lack of convergence.