The Bounded Edge Coloring Problem and Offline Crossbar Scheduling

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution value and evaluate the performance of several approximation algorithms, both analytically and experimentally. We show how to approximate an optimal solution with a worst-case performance ratio of $3/2$ and our experimental results demonstrate that the best algorithms produce results that very closely track a lower bound

The Bounded Edge Coloring Problem and Offline Crossbar Scheduling

This paper introduces a variant of the classical edge coloring problem in graphs that can be applied to an offline scheduling problem for crossbar switches. We show that the problem is NP-complete, develop three lower bounds bounds on the optimal solution value and evaluate the performance of several approximation algorithms, both analytically and experimentally. We show how to approximate an optimal solution with a worst-case performance ratio of 3/2 and our experimental results demonstrate that the best algorithms produce results that very closely track a lower bound

Strong Performance Guarantees for Asynchronous Buffered Crossbar Schedulers

Crossbar-based switches are commonly used to implement routers with throughputs up to about 1 Tb/s. The advent of crossbar scheduling algorithms that provide strong performance guarantees now makes it possible to engineer systems that perform well, even under extreme traffic conditions. Until recently, such performance guarantees have only been developed for crossbars that switch cells rather than variable length packets. Cell-based crossbars incur a worst-case bandwidth penalty of up to a factor of two, since they must fragment variable length packets into fixed length cells. In addition, schedulers for cell-based crossbars may fail to deliver the expected performance guarantees when used in routers that forward packets. We show how to obtain performance guarantees for asynchronous crossbars that are directly comparable to those previously developed for synchronous, cell-based crossbars. In particular we define derivatives of the Group by Virtual Output Queue (GVOQ) scheduler of Chuang et al. and the Least Occupied Output First Scheduler of Krishna et al. and show that both can provide strong performance guarantees in systems with speedup 2. Specifically, we show that these schedulers are work-conserving and that they can emulate an output-queued switch using any queueing discipline in the class of restricted Push-In, First-Out queueing disciplines. We also show that there are schedulers for segment-based crossbars, (introduced recently by Katevenis and Passas) that can deliver strong performance guarantees with small buffer requirements and no bandwidth fragmentation

Scheduling in Networks with Limited Buffers

In networks with limited buffer capacity, packet loss can occur at a link even when the average packet arrival rate is low compared to the link's speed. To offer strong loss-rateguarantees, ISPs may need to adopt stringent routing constraints to limit the load at the network links and the routing path length. However, to simultaneously maximize revenue, ISPs should be interested in scheduling algorithms that lead to the least stringent routing constraints. This work attempts to address the ISPs needs as follows. First, by proposing an algorithm that performs well (in terms of routing constraints) on networks of output queued (OQ) routers (that is, ideal routers), and second, by bounding the extra switch fabric speed and buffer capacity required for the emulationof these algorithms in combined input-output queued (CIOQ) routers.The first part of the thesis studies the problem of minimizing the maximum session loss rate in networks of OQ routers. It introduces the Rolling Priority algorithm, a local online scheduling algorithm that offers superior loss guarantees compared to FCFS/Drop Tail and FCFS/Random Drop. Rolling Priority has the following properties: (1) it does not favor any sessions over others at any link, (2) it ensures a proportion of packets from each session are subject to a negligibly small loss probability at every link along the session's path, and (3) maximizes the proportion of packets subject to negligible loss probability. The second part of the thesis studies the emulation of OQ routers using CIOQ. The OQ routers are equipped with a buffer of capacity B packets at every output. For the family of work-conserving scheduling algorithms, we find that whereas every greedy CIOQ policy is valid for the emulation of every OQ algorithm at speedup B, no CIOQ policy is valid at speedup less than the cubic root of B-2 when preemption is allowed. We also find that CCF, a well-studied CIOQ policy, is not valid at any speedup less than B. We then introduce a CIOQ policy CEH, that is valid at speedup greater than the square root of 2(B-1)

Packet-mode emulation of output-queued switches

Most common network protocols (e.g., the Internet Protocol) work with variable size packets, whereas contemporary switches still operate with fixed size cells, which are easier to transmit and buffer. This necessitates packet segmentation and reassembly modules, resulting in significant computation and communication overhead that might be too costly as switches become faster and bigger. It is therefore imperative to investigate an alternative mode of scheduling, in which packets are scheduled contiguously over the switch fabric. This paper studies packet-mode scheduling for the combined input output queued (CIOQ) switch architecture and investigates its cost. We devise frame-based schedulers that allow a packet-mode CIOQ switch with small speedup to mimic an ideal output-queued switch with bounded relative queuing delay. The schedulers are pipelined and are based on matrix decomposition. Our schedulers demonstrate a trade-off between the switch speedup and the relative queuing delay incurred while mimicking an output-queued switch. When the switch is allowed to incur high relative queuing delay, a speedup arbitrarily close to 2 suffices to mimic an ideal output-queued switch. This implies that a packet-mode scheduler does not require a fundamentally higher speedup than a cell-based scheduler. The relative queuing delay can be significantly reduced with just a doubling of the speedup. We further show that it is impossible to achieve zero relative queuing delay (that is, a perfect emulation), regardless of the switch speedup. Finally, we show that a speedup arbitrarily close to 1 suffices to mimic an output-queued switch with a bounded buffer size. Submitted to the regular track

Packet-mode emulation of output-queued switches

Most common network protocols (e.g., the Internet Protocol) work with variable size packets, whereas contemporary switches still operate with fixed size cells, which are easier to transmit and buffer. This necessitates packet segmentation and reassembly modules, resulting in significant computation and communication overhead that might be too costly as switches become faster and bigger. It is therefore imperative to investigate an alternative mode of scheduling, in which packets are scheduled contiguously over the switch fabric. This paper investigates the cost of packet-mode scheduling for the combined input output queued (CIOQ) switch architecture. We devise frame-based schedulers that allow a packetmode CIOQ switch with small speedup to mimic an ideal output-queued switch with bounded relative queuing delay. The schedulers are pipelined and are based on matrix decomposition. Our schedulers demonstrate a trade-off between the switch speedup and the relative queuing delay incurred while mimicking an output-queued switch. When the switch is allowed to incur high relative queuing delay, a speedup arbitrarily close to 2 suffices to mimic an ideal output-queued switch. This implies that packet-mode scheduling does not require higher speedup than a cell-based scheduler. The relative queuing delay can be significantly reduced with just a doubling of the speedup. We further show that it is impossible to achieve zero relative queuing delay (that is, a perfect emulation), regardless of the switch speedup. Finally, we show that a speedup arbitrarily close to 1 suffices to mimic an output-queued switch with a bounded buffer size

Host and Network Optimizations for Performance Enhancement and Energy Efficiency in Data Center Networks

Modern data centers host hundreds of thousands of servers to achieve economies of scale. Such a huge number of servers create challenges for the data center network (DCN) to provide proportionally large bandwidth. In addition, the deployment of virtual machines (VMs) in data centers raises the requirements for efficient resource allocation and find-grained resource sharing. Further, the large number of servers and switches in the data center consume significant amounts of energy. Even though servers become more energy efficient with various energy saving techniques, DCN still accounts for 20% to 50% of the energy consumed by the entire data center. The objective of this dissertation is to enhance DCN performance as well as its energy efficiency by conducting optimizations on both host and network sides. First, as the DCN demands huge bisection bandwidth to interconnect all the servers, we propose a parallel packet switch (PPS) architecture that directly processes variable length packets without segmentation-and-reassembly (SAR). The proposed PPS achieves large bandwidth by combining switching capacities of multiple fabrics, and it further improves the switch throughput by avoiding padding bits in SAR. Second, since certain resource demands of the VM are bursty and demonstrate stochastic nature, to satisfy both deterministic and stochastic demands in VM placement, we propose the Max-Min Multidimensional Stochastic Bin Packing (M3SBP) algorithm. M3SBP calculates an equivalent deterministic value for the stochastic demands, and maximizes the minimum resource utilization ratio of each server. Third, to provide necessary traffic isolation for VMs that share the same physical network adapter, we propose the Flow-level Bandwidth Provisioning (FBP) algorithm. By reducing the flow scheduling problem to multiple stages of packet queuing problems, FBP guarantees the provisioned bandwidth and delay performance for each flow. Finally, while DCNs are typically provisioned with full bisection bandwidth, DCN traffic demonstrates fluctuating patterns, we propose a joint host-network optimization scheme to enhance the energy efficiency of DCNs during off-peak traffic hours. The proposed scheme utilizes a unified representation method that converts the VM placement problem to a routing problem and employs depth-first and best-fit search to find efficient paths for flows