Timestepped Stochastic Simulation of 802.11 WLANs

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## 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.