Timestepped Stochastic Simulation of 802.11 WLANs

Performance evaluation of computer networks is primarily done using packet-level simulation because analytical methods typically cannot adequately capture the combination of state-dependent control mechanisms (such as TCP congestion control) and stochastic behavior exhibited by networks. However, packet-level simulation becomes prohibitively expensive as link speeds, workloads, and network size increase. Timestepped Stochastic Simulation (TSS) overcomes scalability problems of packet-level simulation by generating a sample path of the system state S(t) at time t=d,2d,... rather than at each packet transmission. In each timestep [t,t+d], the distribution Pr[S(t+d)|S(t)] is obtained analytically, and S(t+d) is sampled from it. This dissertation presents TSS for shared links, specifically, 802.11 WLAN links. Our method computes sample paths of instantaneous goodput N_i(t) for all stations "i" in a WLAN over timesteps of length "d". For accurate modeling of higher layer protocols, "d" should be lesser than their control timescales (e.g., TCP's round-trip time). At typical values of "d" (e.g, 50ms), N_i(t)'s are correlated across timesteps (e.g., a station with high contention window has low goodput for several timesteps) as well as across 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 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

Timestepped Stochastic Simulation of 802.11 WLANs

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

Time Dependent Performance Analysis of Wireless Networks

Many wireless networks are subject to frequent changes in a combination of network topology, traffic demand, and link capacity, such that nonstationary/transient conditions always exist in packet-level network behavior. Although there are extensive studies on the steady-state performance of wireless networks, little work exists on the systematic study of their packet-level time varying behavior. However, it is increasingly noted that wireless networks must not only perform well in steady state, but must also have acceptable performance under nonstationary/transient conditions. Furthermore, numerous applications in today's wireless networks are very critical to the real-time performance of delay, packet delivery ratio, etc, such as safety applications in vehicular networks and military applications in mobile ad hoc networks. Thus, there exists a need for techniques to analyze the time dependent performance of wireless networks. In this dissertation, we develop a performance modeling framework incorporating queuing and stochastic modeling techniques to efficiently evaluate packet-level time dependent performance of vehicular networks (single-hop) and mobile ad hoc networks (multi-hop). For vehicular networks, we consider the dynamic behavior of IEEE 802.11p MAC protocol due to node mobility and model the network hearability as a time varying adjacency matrix. For mobile ad hoc networks, we focus on the dynamic behavior of network layer performance due to rerouting and model the network connectivity as a time varying adjacency matrix. In both types of networks, node queues are modeled by the same fluid flow technique, which follows flow conservation principle to construct differential equations from a pointwise mapping of the steady-state queueing relationships. Numerical results confirm that fluid-flow based performance models are able to respond to the ongoing nonstationary/transient conditions of wireless networks promptly and accurately. Moreover, compared to the computation time of standard discrete event simulator, fluid-flow based model is shown to be a more scalable evaluation tool. In general, our proposed performance model can be used to explore network design alternatives or to get a quick estimate on the performance variation in response to some dynamic changes in network conditions

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 S(t) at time t = δ, 2δ, · · · , rather than at each packet transmission. In each timestep [t, t + δ], the distribution Pr ( S(t + δ) | S(t) ) is obtained analytically, and S(t + δ) is sampled from it. Our method computes sample paths of instantaneous goodput Ni(t) for all stations i in a WLAN over timesteps of length δ. For accurate modeling of higher layer protocols, δ should be lesser than their control timescales (e.g., TCP’s RTT). At typical values of δ (e.g, 50ms), Ni(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 Ni(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 for WLANs is accurate and yields an improvement in simulation runtime of up to two orders of magnitude. 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; and (3) quantification of shortterm goodput unfairness. I