We will review some of the major results in random graphs and some of the more challenging open problems. We will cover algorithmic and structural questions. We will touch on newer models, including those related to the WWW.

Random graphs

Today's data centers may contain tens of thousands of computers with significant aggregate bandwidth requirements. The network architecture typically consists of a tree of routing and switching elements with progressively more specialized and expensive equipment moving up the network hierarchy. Unfortunately, even when deploying the highest-end IP switches/routers, resulting topologies may only support 50% of the aggregate bandwidth available at the edge of the network, while still incurring tremendous cost. Non-uniform bandwidth among data center nodes complicates application design and limits overall system performance.In this paper, we show how to leverage largely commodity Ethernet switches to support the full aggregate bandwidth of clusters consisting of tens of thousands of elements. Similar to how clusters of commodity computers have largely replaced more specialized SMPs and MPPs, we argue that appropriately architected and interconnected commodity switches may deliver more performance at less cost than available from today's higher-end solutions. Our approach requires no modifications to the end host network interface, operating system, or applications; critically, it is fully backward compatible with Ethernet, IP, and TCP.

/pdf/a-scalable-commodity-data-center-network-architecture-5evikm9tu4.pdf

A scalable, commodity data center network architecture

It is shown that, particularly for terrestrial cellular telephony, the interference-suppression feature of CDMA (code division multiple access) can result in a many-fold increase in capacity over analog and even over competing digital techniques. A single-cell system, such as a hubbed satellite network, is addressed, and the basic expression for capacity is developed. The corresponding expressions for a multiple-cell system are derived. and the distribution on the number of users supportable per cell is determined. It is concluded that properly augmented and power-controlled multiple-cell CDMA promises a quantum increase in current cellular capacity. >

On the capacity of a cellular CDMA system

https://beloglazov.info/papers/2011-energy-aware-fgcs.pdf

Energy-aware resource allocation heuristics for efficient management of data centers for Cloud computing

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures

/pdf/layering-as-optimization-decomposition-a-mathematical-theory-3t9xhz4cfy.pdf

Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

We discuss the relevance of fairness as a design objective for congestion control mechanisms in the Internet. Specifically, we consider a backbone network shared by a dynamic number of short-lived flows, and study the impact of bandwidth sharing on network performance. In particular, we prove that for a broad class of fair bandwidth allocations, the total number of flows in progress remains finite if the load of every link is less than one. We also show that provided the bandwidth allocation is "sufficiently" fair, performance is optimal in the sense that the throughput of the flows is mainly determined by their access rate. Neither property is guaranteed with unfair bandwidth allocations, when priority is given to one class of flow with respect to another. This suggests current proposals for a differentiated services Internet may lead to suboptimal utilization of network resources.

/pdf/impact-of-fairness-on-internet-performance-4tao337azm.pdf

Impact of fairness on Internet performance

In this paper we study the statistics of the realized throughput of elastic document transfers, accounting for the way network bandwidth is shared dynamically between the randomly varying number of concurrent flows. We first discuss the way TCP realizes statistical bandwidth sharing, illustrating essential properties by means of packet level simulations. Mathematical flow level models based on the theory of stochastic networks are then proposed to explain the observed behavior. A notable result is that first order performance (e.g., mean throughput) is insensitive with respect both to the flow size distribution and the flow arrival process, as long as "sessions" arrive according to a Poisson process. Perceived performance is shown to depend most significantly on whether demand at flow level is less than or greater than available capacity. The models provide a key to understanding the effectiveness of techniques for congestion management and service differentiation.

/pdf/statistical-bandwidth-sharing-a-study-of-congestion-at-flow-385wz3auim.pdf

Statistical bandwidth sharing: a study of congestion at flow level

End-to-end congestion control mechanisms such as those in TCP are not enough to prevent congestion collapse in the Internet, and they must be supplemented by control mechanisms inside the network. The IRTF has singled out random early detection (RED) as one queue management scheme recommended for rapid deployment throughout the Internet. However, RED is not a thoroughly understood scheme-witness for example how the recommended parameter setting, or even the various benefits RED is claimed to provide, have changed over the past few years. In this paper, we describe simple analytic models for RED, and use these models to quantify the benefits (or lack thereof) brought about by RED. In particular, we examine the impact of RED on the loss and delay suffered by bursty and less bursty traffic (such as TCP and UDP traffic, respectively). We find that: (i) RED does eliminate the higher loss bias against bursty traffic observed with tail drop, but not by decreasing the loss rate of bursty traffic, rather by increasing that of non bursty traffic; (ii) the number of consecutive packet drops is higher with RED than tail drop, suggesting RED might not help as anticipated with the global synchronization of TCP flows; (iii) RED can be used to control the average queueing delay in routers and hence the end to end delay, but increases the jitter of non bursty streams. Thus, applications that generate smooth traffic, such as interactive audio applications, will suffer higher loss rates and require large playout buffers, thereby negating at least in part the lower mean delay brought about by RED.

/pdf/analytic-evaluation-of-red-performance-49ga5xh4tz.pdf

Analytic evaluation of RED performance

We consider wireless downlink data channels where the transmission power of each base station is time-shared between a dynamic number of active users as in CDMA/HDR systems. We derive analytical results relating user performance, in terms of blocking probability and data throughput, to cell size and traffic density. These results are used to address a number of practically interesting issues, including the trade-off between cell coverage and cell capacity and the choice of efficient scheduling and admission control schemes.

/pdf/wireless-downlink-data-channels-user-performance-and-cell-2sj6zgt4ed.pdf

Wireless downlink data channels: user performance and cell dimensioning

We compare the performance of three usual allocations, namely max-min fairness, proportional fairness and balanced fairness, in a communication network whose resources are shared by a random number of data flows. The model consists of a network of processor-sharing queues. The vector of service rates, which is constrained by some compact, convex capacity set representing the network resources, is a function of the number of customers in each queue. This function determines the way network resources are allocated. We show that this model is representative of a rich class of wired and wireless networks. We give in this general framework the stability condition of max-min fairness, proportional fairness and balanced fairness and compare their performance on a number of toy networks.

/pdf/a-queueing-analysis-of-max-min-fairness-proportional-2t5926ayiq.pdf

Thomas Bonald

Papers

Impact of fairness on Internet performance

Statistical bandwidth sharing: a study of congestion at flow level

Analytic evaluation of RED performance

Wireless downlink data channels: user performance and cell dimensioning

A queueing analysis of max-min fairness, proportional fairness and balanced fairness