Seva Shneer

Enhance & explore: an adaptive algorithm to maximize the utility of wireless networks

The goal of jointly providing efficiency and fairness in wireless networks can be seen as the problem of maximizing a given utility function. In contrast with wired networks, the capacity of wireless networks is typically time-varying and not known explicitly. Hence, as the capacity region is impossible to know or measure exactly, existing scheduling schemes either under-estimate it and are too conservative, or they over-estimate it and suffer from congestion collapse. We propose a new adaptive algorithm, called Enhance & Explore (E&E). It maximizes the utility of the network without requiring any explicit characterization of the capacity region. E&E works above the MAC layer and it does not demand any modification to the existing networking stack. We first evaluate our algorithm theoretically and we prove that it converges to a state of optimal utility. We then evaluate the performance of the algorithm in a WLAN setting, using both simulations and real measurements on a testbed composed of IEEE 802.11 wireless routers. Finally, we investigate a wireless mesh network setting and we find that, when coupled with an efficientmechanismfor congestioncontrol, the E&E algorithm greatly increases the utility achieved by multi-hop networks as well.

Wireless multi-hop networks beyond capacity

Wireless multi-hop local area networks use in general scheduling schemes that assume the network capacity to be known. Indeed in most of the throughput-optimal algorithms the sources are assumed to send at a rate within the capacity region. However, measurements made on real deployments show that the network capacity is usually difficult to characterize and also time-varying. It is therefore important to understand how the network behaves when the sources attempt to transmit at a rate above capacity. Toward this goal, we show 3-phase regime in the effect of the input rate λ on the end-to-end throughput μ of a multi-hop network. First, when λ is smaller than a threshold λ₁, μ is an increasing function of λ. Second, when λ is larger than another threshold λ₂ > λ₁, μ is independent of λ. Third, when λ₁ <; λ <; λ₂, μ decreases with λ. To understand this phenomenon, we capture the relation between the end-to-end throughput and the queue stability with a mathematical model that allows us to explain and derive the exact values of the transition points λi. We then validate experimentally our simulation results with measurements on a testbed composed of five wireless routers.

Stability of a Markov-modulated Markov chain, with application to a wireless network governed by two protocols

We consider a discrete-time Markov chain (Xt,Yt), t = 0, 1, 2,…, where the X-component forms a Markov chain itself. Assume that (Xt) is Harris-ergodic and consider an auxiliary Markov chain {Yt} whose transition probabilities are the averages of transition probabilities of the Y-component of the (X, Y)-chain, where the averaging is weighted by the stationary distribution of the X-component. We first provide natural conditions in terms of test functions ensuring that the Y-chain is positive recurrent and then prove that these conditions are also sufficient for positive recurrence of the original chain (Xt, Yt). The we prove a “multi-dimensional” extension of the result obtained. In the second part of the paper, we apply our results to two versions of a multi-access wireless model governed by two randomised protocols.

Stability and instability of individual nodes in multi-hop wireless CSMA/CA networks

CSMA/CA is a popular random-access algorithm for wireless networks, but its stability properties are poorly understood. We consider a linear multi-hop network of three nodes where the neighbouring nodes interfere with each other and medium access is governed by the CSMA/CA algorithm. We assume that the source node is saturated and packets are forwarded through the network, each node transmitting towards its neighbour on the right. We demonstrate that the queue of the second node is saturated (unstable) and the queue of the third node is stable; this confirms heuristic arguments and simulation results found in the research literature. Providing a rigorous proof for the (in)stability of these nodes is complicated by the fact that neither queue is Markovian when considered in isolation, and the two queues are dependent. We then compute the limiting behavior of node 3, and use this to determine the end-to-end throughput of the network. Finally, we vary the access probabilities of the nodes, and evaluate how this affects the stability and throughput of the system.

Comparing slotted and continuous CSMA: throughputs and fairness

Carrier-Sense Multiple-Access (CSMA) protocols form a popular class of random-access schemes for regulating node activity in wireless networks. We compare the continuous and the time-slotted versions of this protocol in the saturated regime, and show that continuous CSMA has higher aggregate throughput than the slotted protocol, but this comes at the cost of fairness, i.e., the throughput is not evenly distributed across all nodes. We then release the saturation assumption and consider a multi-hop scenario where packets are forwarded through the network and nodes may occasionally empty. We study end-to-end throughput of both continuous and slotted CSMA, and show that slotted CSMA has a higher throughput than the continuous protocol.

A measurement-based algorithm to maximize the utility of wireless networks

The goal of jointly providing fairness and efficiency in wireless networks can be seen as the problem of maximizing a given utility function. The main difficulty when solving this problem is that the capacity region of wireless networks is typically unknown and time-varying, which prevents the usage of traditional optimization tools. As a result, scheduling and congestion control algorithms are either too conservative because they under-estimate the capacity region, or suffer from congestion collapse because they over-estimate it. We propose a new adaptive congestion control algorithm, called Enhance & Explore (E&E). It maximizes the utility of the network without requiring any explicit characterization of the capacity region. E&E works above the MAC layer and is decoupled from the underlying scheduling mechanism. It provably converges to a state of optimal utility. We evaluate the performance of the algorithm in a WLAN setting, using both simulations and measurements on a real testbed composed of IEEE 802.11 wireless routers.

On the Delays in Time-Varying Networks: Does Larger Service-Rate Variance Imply Larger Delays?

In all networks, link or route capacities fluctuate for multiple reasons, e.g., fading and multi-path effects on wireless channels, interference and contending users on a shared medium, varying loads in WAN routers, impedance changes on power-line channels. These fluctuations severely impact packet delays. In this paper, we study delays in time-varying networks. Intuitively, we expect that for a given average service rate, an increased service rate variability yields larger delays. We find that this is not always the case. Using a queuing model that includes time-varying service rates, we show that for certain arrival rates, a queue with larger service rate variance offers smaller average delays than a queue with the same average service rate and lower service rate variance. We also verify these findings on a wireless testbed. We then study the conditions under which using simultaneously two independent paths helps in terms of delays, for example, in hybrid networks where the two paths use different physical layer technologies. We show that using two paths is not always better, in particular for low arrival rates. We also show that the optimal traffic splitting between the two paths depends on the arrival rate.

Gradient bandwidth allocations

We look at bandwidth-sharing networks where bandwidth allocations are not known to maximize a priori any utility function. Instead, we only require the allocation functions to be 0-homogeneous and concave, which are desirable properties in many situations. We show that a certain gradient condition is necessary and sufficient for such allocations to solve an optimization problem leading to important corollaries such as deriving the stability set of these 0-homogeneous concave allocation.