Fabio Cecchi

Throughput of CSMA networks with buffer dynamics

Abstract Random-access algorithms such as the Carrier-Sense Multiple-Access (CSMA) protocol provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years fairly tractable models have been shown to yield remarkably accurate throughput estimates in scenarios with saturated buffers. In contrast, in non-saturated scenarios, where nodes refrain from competition for the medium when their buffers are empty, a complex two-way interaction arises between the activity states and the buffer contents of the various nodes. As a result, the throughput characteristics in such scenarios have largely remained elusive so far. In the present paper we provide a generic structural characterization of the throughput performance and corresponding stability region in terms of the individual saturation throughputs of the various nodes. While the saturation throughputs are difficult to explicitly determine in general, we identify certain cases where these values can be expressed in closed form. In addition, we demonstrate that various lower-dimensional facets of the stability region can be explicitly calculated as well, depending on the neighborhood structure of the interference graph. Illustrative examples and numerical results are presented to illuminate the main analytical findings.

Scheduling of users with markovian time-varying transmission rates

We address the problem of developing a well-performing and implementable scheduler of users with wireless connection to the base station. The main feature of such real-life systems is that the quality conditions of the user channels are time-varying, which turn into the time-varying transmission rate due to different modulation and coding schemes. We assume that this phenomenon follows a Markovian law and most of the discussion is dedicated to the case of three quality conditions of each user, for which we characterize an optimal index policy and show that threshold policies (of giving higher priority to users with higher transmission rate) are not necessarily optimal. For the general case of arbitrary number of quality conditions we design a scheduler and propose its two practical approximations, and illustrate the performance of the proposed index-based schedulers and existing alternatives in a variety of simulation scenarios.

Nearly-optimal scheduling of users with Markovian time-varying transmission rates

We address the problem of developing a well-performing and implementable scheduler of users with wireless connections to the central controller, which arise in areas such as mobile data networks, heterogeneous networks, or vehicular communications systems. The main feature of such systems is that the quality of each users channel is time-varying due to fading. The evolution of the channel over its quality states thus causes a time-varying transmission rate of each user. We consider Markovian channel dynamics, relaxing the common but unrealistic assumption of i.i.d.?channels. We first focus on three-state channels and show that threshold policies (of giving higher priority to users with higher transmission rate) are not necessarily optimal. For the general case we design a scheduler which generalizes the recently proposed Potential Improvement (PI) scheduler, which gives priority to the users who are unlikely to improve their actual transmission rate soon by much. We propose two practical approximations of PI, whose performance is analyzed and compared to existing alternative schedulers in a variety of simulation scenarios. Our computational experiments indicate that the variant of PI, which only relies on the steady-state distribution of the channel, is robust and performs extremely well, and therefore we recommend its use for practical implementation.

Mean-Field Analysis of Ultra-Dense CSMA Networks

Distributed algorithms such as CSMA provide a popular mechanism for sharing the transmission medium among competing users in large-scale wireless networks. Conventional models for CSMA that are amenable for analysis assume that users always have packets to transmit. In contrast, when users do not compete for medium access when their buffers are empty, a complex interaction arises between the activity states and the buffer contents. We develop a meanfield approach to investigate this dynamic interaction for networks with many users. We identify a time-scale separation between the evolution of the activity states and the buffer contents, and obtain a deterministic dynamical system describing the network dynamics on a macroscopic scale. The fixed point of the dynamical system yields highly accurate approximations for the stationary distribution of the buffer contents and packet delay, even when the number of users is relatively moderate.

CSMA networks in a many-sources regime: A mean-field approach

With the rapid advance of the Internet of Everything, both the number of devices and the range of applications that rely on wireless connectivity show huge growth. Driven by these pervasive trends, wireless networks grow in size and complexity, supporting immense numbers of nodes and data volumes, with highly diverse traffic profiles and performance requirements. While well-established methods are available for evaluating the throughput of persistent sessions with saturated buffers, these provide no insight in the delay performance of flows with intermittent packet arrivals. The occurrence of empty buffers in the latter scenario results in a complex interaction between activity states and packet queues, which severely complicates the performance analysis. Motivated by these challenges, we develop a mean-field approach to analyze buffer contents and packet delays in wireless networks in a many-sources regime. The mean-field behavior simplifies the analysis of a large-scale network with packet arrivals and buffer dynamics to a low-dimensional fixed-point calculation for a network with saturated buffers. In particular, the analysis yields explicit expressions for the buffer content and packet delay distribution in terms of the fixed-point solution. Extensive simulation experiments demonstrate that these expressions provide highly accurate approximations, even for a fairly moderate number of sources.

Spatial mean-field limits for ultra-dense random-access networks

Random-access algorithms such as the CSMA protocol provide a popular mechanism for distributed medium access control in wireless networks. In saturated-buffer scenarios the joint activity process in such random-access networks has a product-form stationary distribution which provides useful throughput estimates for persistent traffic flows. However, these results do not capture the relevant performance metrics in unsaturated-buffer scenarios, which in particular arise in an IoT context with highly intermittent traffic sources. Mean-field analysis has emerged as a powerful approach to obtain tractable performance estimates in such situations, and is not only mathematically convenient, but also relevant as wireless networks grow larger and denser with the emergence of IoT applications. A crucial requirement for the classical mean-field framework to apply however is that the node population can be partitioned into a finite number of classes of statistically indistinguishable nodes. The latter condition is a severe restriction since nodes typically have different locations and hence experience different interference constraints. Motivated by the above observations, we develop in the present paper a novel mean-field methodology which does not rely on any exchangeability property. Since the spatiotemporal evolution of the network can no longer be described through a finite-dimensional population process, we adopt a measure-valued state description, and prove that the latter converges to a deterministic limit as the network grows large and dense. The limit process is characterized in terms of a system of partial-differential equations, which exhibit a striking local-global-interaction and time scale separation property. Specifically, the queueing dynamics at any given node are only affected by the global network state through a single parsimonious quantity. The latter quantity corresponds to the fraction of time that no activity occurs within the interference range of that particular node in case of a certain static spatial activation measure. Extensive simulation experiments demonstrate that the solution of the partial-differential equations yields remarkably accurate approximations for the queue length distributions and delay metrics, even when the number of nodes is fairly moderate.

Mean-field analysis of CSMA wireless networks

In recent years both the number and the variety of devices that rely on wireless connectivity have shown huge growth. Consequently, wireless networks are going through a tremendous growth in size and complexity, supporting immense numbers of nodes and data volumes. Well-established methodologies have been developed for evaluating the performance in saturated buffer conditions. However, these provide no insight in the performance of networks with intermittent packet arrivals. The occurrence of empty buffers in the latter scenario results in a complex interaction between activity states and packet queues, which severely complicates the performance analysis. Motivated by these challenges, we develop a mean-field approach to analyze buffer contents and packet delays in a many-sources regime. The mean-field behavior simplifies the analysis of a large-scale network with packet arrivals and buffer dynamics to a low-dimensional fixed-point calculation for a network with saturated buffers. In particular, the analysis yields explicit expressions for the buffer content and packet delay distribution in terms of the fixed-point solution. The method we propose can in fact be extended to more complex scenarios, and generalizations to a queue-based protocol and a multi-hop model are briefly outlined.