Optimal transmission schedules for lightwave networks embedded with de Bruijn graphs

AbstractWe consider the problem of embedding a virtual de Bruijn topology, both directed and undirected, in a physical optical passive star time and wavelength division multiplexed (TWDM) network and constructing a schedule to transmit packets along all edges of the virtual topology in the shortest possible time. We develop general graph theoretic results and algorithms and using these build optimal embeddings and optimal transmission schedules, assuming certain conditions on the network parameters. We prove our transmission schedules are optimal over all possible embeddings.As a general framework we use a model of the passive star network with fixed tuned receivers and tunable transmitters. Our transmission schedules are optimal regardless of the tuning time. Our results are also applicable to models with one or more fixed tuned transmitters per node. We give results that minimize the number of tunings needed. For the directed de Bruijn topology a single fixed tuning of the transmitter suffices. For the undirected de Bruijn topology two tunings per cycle (or two fixed tuned transmitters per node) suffice and we prove this is the minimum possible

Evaluation of data centre networks and future directions

Traffic forecasts predict a more than threefold increase in the global datacentre workload in coming years, caused by the increasing adoption of cloud and data-intensive applications. Consequently, there has been an unprecedented need for ultra-high throughput and minimal latency. Currently deployed hierarchical architectures using electronic packet switching technologies are costly and energy-inefficient. Very high capacity switches are required to satisfy the enormous bandwidth requirements of cloud datacentres and this limits the overall network scalability. With the maturity of photonic components, turning to optical switching in data centres is a viable option to accommodate greater bandwidth and network flexibility while potentially minimising the latency, cost and power consumption. Various DCN architectures have been proposed to date and this thesis includes a comparative analysis of such electronic and optical topologies to judge their suitability based on network performance parameters and cost/energy effectiveness, while identifying the challenges faced by recent DCN infrastructures. An analytical Layer 2 switching model is introduced that can alleviate the simulation scalability problem and evaluate the performance of the underlying DCN architecture. This model is also used to judge the variation in traffic arrival/offloading at the intermediate queueing stages and the findings are used to derive closed form expressions for traffic arrival rates and delay. The results from the simulated network demonstrate the impact of buffering and versubscription and reveal the potential bottlenecks and network design tradeoffs. TCP traffic forms the bulk of current DCN workload and so the designed network is further modified to include TCP flows generated from a realistic traffic generator for assessing the impact of Layer 4 congestion control on the DCN performance with standard TCP and datacentre specific TCP protocols (DCTCP). Optical DCN architectures mostly concentrate on core-tier switching. However, substantial energy saving is possible by introducing optics in the edge tiers. Hence, a new approach to optical switching is introduced using Optical ToR switches which can offer better delay performance than commodity switches of similiar size, while having far less power dissipation. An all-optical topology has been further outlined for the efficient implementation of the optical switch meeting the future scalability demands

Designs for Wavelength Division Multiplexing Lightwave Networks with Tunable Transceivers

The need of high speed networks, for applications incorporating high performance distributed computing, multimedia communication and real time network services, has provided the impetus for the study of optical networks. Wavelength Division Multiplexing (WDM) has been used widely for studying the throughput performance of optical networks. We studied WDM lightwave networks with tunable transceivers including designs for lightwave networks with limited tuning ranges for transceivers. Transmission schedules and virtual topology embeddings are needed to support high performance distributed computing. How to design the transmission schedule depends on how the virtual topology is embedded in the physical lightwave network. We developed general graph theoretic results and algorithms and using these built optimal embeddings and optimal transmission schedules for de Bruijn graphs and undirected de Bruijn graphs, assuming certain conditions on the network parameters. We proved our transmission schedules are optimal over all possible embeddings. Partitioned Optical Passive Stars(POPS) topology is a physical architecture to scale up local optical passive star networks. POPS data channel can be efficiently utilized for random permutation-based communication patterns. Reliability is important for such a scaled-up network. We analyzed the fault tolerant routing properties of POPs networks. We demonstrated some worst cases due to link errors and the lower bound for connectivity is obtained. Some sufficient approaches were proposed to detect and keep connectivity of the whole system. The current technology only allows the transceivers to be tunable in a small range, a fact ignored in previous studies. We focused on the design of WDM optical passive star networks with tunable transmitters of limited tuning range and fixed wavelength receivers. The limited tuning range has big effects on the maximum delay, the total number of wavelengths which can be used, and the topological embedding. We proposed efficient communication protocols for systems with limited tuning ranges. Different network topologies were analyzed in our study. The relationship between the total number of wavelengths which can be utilized and the embedded topology is established. The optimal embedding algorithms are given for the systems embedded with different virtual topologies