# Timestepped Stochastic Simulation of 802.11 WLANs

##### Abstract

We present Timestepped Stochastic Simulation (TSS) for 802.11 WLANs. TSS
overcomes scalability problems of packet-level simulation by generating a
sample path of the system state $\mathbf{S}(t)$ at time $t = \delta,
2\delta, \cdots$, rather than at each packet transmission.
In each timestep $[t,t+\delta]$, the distribution
$S(t+\delta)|S(t)}$ is obtained analytically
and $S(t+\delta)$ is sampled from it.
Our method computes sample paths of instantaneous goodput $N_i(t)$ for all
stations $i$ in a WLAN over timesteps of length $\delta$. For accurate
modeling of higher layer protocols, $\delta$ should be lesser than their
control timescales (e.g., TCP's RTT).At typical values of $\delta$ (e.g,
$50$ms), $N_i(t)$'s are correlated across both timesteps (e.g., a station with high contention
window has low goodput for several timesteps) and stations (since they
share the same media). To model these correlations, we obtain, jointly
with the $N_i(t)$'s, sample paths of the WLAN's DCF state, which consists
of a contention window and a backoff counter at each station.
Comparisons with packet level simulations show that TSS is accurate and
provides up to two orders of magnitude improvement in simulation runtime.
Our transient analysis of 802.11 complements prior literature
and also yields:
(1) the distribution of the instantaneous aggregate goodput;
(2) the distribution of instantaneous goodput of a tagged station
conditioned on its MAC state;
(3) quantification of short-term goodput unfairness conditioned on the
DCF state;
(4) efficient accurate approximation for the
$n$-fold convolution of the distribution of the total backoff duration
experienced by a tagged packet;
and
(5) a simple closed form expression and its logarithmic approximation
for the collision probability as a function of the number of active
stations.

University of Maryland, College Park, MD 20742-7011 (301)314-1328.

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