An official website of the United States government
The widely-studied radio network model [Chlamtac and Kutten, 1985] is a graph-based description that captures the inherent impact of collisions in wireless communication. In this model, the strong assumption is made that node v receives a message from a neighbor if and only if exactly one of its neighbors broadcasts. We relax this assumption by introducing a new noisy radio network model in which random faults occur at senders or receivers. Specifically, for a constant noise parameter p ∈ [0,1), either every sender has probability p of transmitting noise or every receiver of a single transmission in its neighborhood has probability p of receiving noise. We first study single-message broadcast algorithms in noisy radio networks and show that the Decay algorithm [Bar-Yehuda et al., 1992] remains robust in the noisy model while the diameter-linear algorithm of Gasieniec et al., 2007 does not. We give a modified version of the algorithm of Gasieniec et al., 2007 that is robust to sender and receiver faults, and extend both this modified algorithm and the Decay algorithm to robust multi-message broadcast algorithms, broadcasting Ω(1/log n log log n) and Ω(1/log n) messages per round, respectively. We next investigate the extent to which (network) coding improves throughput in noisy radio networks. In particular, we study the coding cap -- the ratio of the throughput of coding to that of routing -- in noisy radio networks. We address the previously perplexing result of Alon et al. 2014 that worst case coding throughput is no better than worst case routing throughput up to constants: we show that the worst case throughput performance of coding is, in fact, superior to that of routing -- by a Θ(log(n)) gap -- provided receiver faults are introduced. However, we show that sender faults have little effect on throughput. In particular, we show that any coding or routing scheme for the noiseless setting can be transformed to be robust to sender faults with only a constant throughput overhead. These transformations imply that the results of Alon et al., 2014 carry over to noisy radio networks with sender faults as well. As a result, if sender faults are introduced then there exist topologies for which there is a Θ(log log n) gap, but the worst case throughput across all topologies is Θ(1/log n) for both coding and routing.
more »
« less
Improved Throughput for All-or-Nothing Multicommodity Flows with Arbitrary Demands
Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem-the all-or-nothing multicommodity flow (ANF) problem - in arbitrary directed graphs and in the practically relevant but challenging setting where demands can be (much) larger than the edge capacities. Hence, in addition to assigning requests to valid flows for each routed commodity, an admission control mechanism is required which prevents overloading the network when routing commodities.
more »
« less
- Award ID(s):
- 2106917
- PAR ID:
- 10347877
- Publisher / Repository:
- ACM
- Date Published:
- Journal Name:
- ACM SIGMETRICS Performance Evaluation Review
- Volume:
- 49
- Issue:
- 3
- ISSN:
- 0163-5999
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
In a landmark 1981 paper, Valiant and Brebner gave birth to the study of oblivious routing and, simultaneously, introduced its most powerful and ubiquitous method: Valiant load balancing (VLB). By routing messages through a randomly sampled intermediate node, VLB lengthens routing paths by a factor of two but gains the crucial property of obliviousness: it balances load in a completely decentralized manner, with no global knowledge of the communication pattern. Forty years later, with datacenters handling workloads whose communication pattern varies too rapidly to allow centralized coordination, oblivious routing is as relevant as ever, and VLB continues to take center stage as a widely used — and in some settings, provably optimal — way to balance load in the network obliviously to the traffic demands. However, the ability of the network to rapidly reconfigure its interconnection topology gives rise to new possibilities. In this work we revisit the question of whether VLB remains optimal in the novel setting of reconfigurable networks. Prior work showed that VLB achieves the optimal tradeoff between latency and guaranteed throughput. In this work we show that a strictly superior latency-throughput tradeoff is achievable when the throughput bound is relaxed to hold with high probability. The same improved tradeoff is also achievable with guaranteed throughput under time-stationary demands, provided the latency bound is relaxed to hold with high probability and that the network is allowed to be semi-oblivious, using an oblivious (randomized) connection schedule but demand-aware routing. We prove that the latter result is not achievable by any fully-oblivious reconfigurable network design, marking a rare case in which semi-oblivious routing has a provable asymptotic advantage over oblivious routing. Our results are enabled by a novel oblivious routing scheme that improves VLB by stretching routing paths the minimum possible amount — an additive stretch of 1 rather than a multiplicative stretch of 2 — yet still manages to balance load with high probability when either the traffic demand matrix or the network’s interconnection schedule are shuffled by a uniformly random permutation. To analyze our routing scheme we prove an exponential tail bound which may be of independent interest, concerning the distribution of values of a bilinear form on an orbit of a permutation group action.more » « less
-
Oblivious routing has a long history in both the theory and practice of networking. In this work we initiate the formal study of oblivious routing in the context of reconfigurable networks, a new architecture that has recently come to the fore in datacenter networking. These networks allow a rapidly changing bounded-degree pattern of interconnections between nodes, but the network topology and the selection of routing paths must both be oblivious to the traffic demand matrix. Our focus is on the trade-off between maximizing throughput and minimizing latency in these networks. For every constant throughput rate, we characterize (up to a constant factor) the minimum latency achievable by an oblivious reconfigurable network design that satisfies the given throughput guarantee. The trade-off between these two objectives turns out to be surprisingly subtle: the curve depicting it has an unexpected scalloped shape reflecting the fact that load-balancing becomes more difficult when the average length of routing paths is not an integer because equalizing all the path lengths is not possible. The proof of our lower bound uses LP duality to verify that Valiant load balancing is the most efficient oblivious routing scheme when used in combination with an optimally-designed reconfigurable network topology. The proof of our upper bound uses an algebraic construction in which the network nodes are identified with vectors over a finite field, the network topology is described by either the elementary basis or a sequence of Vandermonde matrices, and routing paths are constructed by selecting columns of these matrices to yield the appropriate mixture of path lengths within the shortest possible time interval.more » « less
-
Connected and automated vehicle (CAV) technology is providing urban transportation managers tremendous opportunities for better operation of urban mobility systems. However, there are significant challenges in real-time implementation as the computational time of the corresponding operations optimization model increases exponentially with increasing vehicle numbers. Following the companion paper (Chen et al. 2021), which proposes a novel automated traffic control scheme for isolated intersections, this study proposes a network-level, real-time traffic control framework for CAVs on grid networks. The proposed framework integrates a rhythmic control method with an online routing algorithm to realize collision-free control of all CAVs on a network and achieve superior performance in average vehicle delay, network traffic throughput, and computational scalability. Specifically, we construct a preset network rhythm that all CAVs can follow to move on the network and avoid collisions at all intersections. Based on the network rhythm, we then formulate online routing for the CAVs as a mixed integer linear program, which optimizes the entry times of CAVs at all entrances of the network and their time–space routings in real time. We provide a sufficient condition that the linear programming relaxation of the online routing model yields an optimal integer solution. Extensive numerical tests are conducted to show the performance of the proposed operations management framework under various scenarios. It is illustrated that the framework is capable of achieving negligible delays and increased network throughput. Furthermore, the computational time results are also promising. The CPU time for solving a collision-free control optimization problem with 2,000 vehicles is only 0.3 second on an ordinary personal computer.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1145/3529113.3529121
