Blocking behaviors of crosstalk-free optical Banyan networks on vertical stacking

Banyan networks are attractive for constructing directional coupler (DC)-based optical switching networks for their small depth and self-routing capability. Crosstalk between optical signals passing through the same DC is an intrinsic drawback in DC-based optical networks. Vertical stacking of multiple copies of an optical banyan network is a novel scheme for building nonblocking (crosstalk-free) optical switching networks. The resulting network, namely vertically stacked optical banyan (VSOB) network, preserves all the properties of the banyan network, but increases the hardware cost significantly. Though much work has been done for determining the minimum number of stacked copies (planes) required for a nonblocking VSOB network, little is known on analyzing the blocking probabilities of VSOB networks that do not meet the nonblocking condition (i.e., with fewer stacked copies than required by the nonblocking condition). In this paper, we analyze the blocking probabilities of VSOB networks and develop their upper and lower bounds with respect to the number of planes in the networks. These bounds depict accurately the overall blocking behaviors of VSOB networks and agree with the conditions of strictly nonblocking and rearrangeably nonblocking VSOB networks respectively. Extensive simulation on a network simulator with both random routing and packing strategy has shown that the blocking probabilities of both strategies fall nicely within our bounds, and the blocking probability of packing strategy actually matches the lower bound. The proposed bounds are significant because they reveal the inherent relationships between blocking probability and network hardware cost in terms of the number of planes, and provide network developers a quantitative guidance to trade blocking probability for hardware cost. In particular, our bounds provide network designers an effective tool to estimate the minimum and maximum blocking probabilities of VSOB networks in which different routing strategies may be applied. An interesting conclusion drawn from our work that has practical applications is that the hardware cost of a VSOB network can be reduced dramatically if a predictable and almost negligible nonzero blocking probability is allowed.Xiaohong Jiang; Hong Shen; Khandker, Md.M.-ur-R.; Horiguchi, S

Crosstalk-free Conjugate Networks for Optical Multicast Switching

High-speed photonic switching networks can switch optical signals at the rate of several terabits per second. However, they suffer from an intrinsic crosstalk problem when two optical signals cross at the same switch element. To avoid crosstalk, active connections must be node-disjoint in the switching network. In this paper, we propose a sequence of decomposition and merge operations, called conjugate transformation, performed on each switch element to tackle this problem. The network resulting from this transformation is called conjugate network. By using the numbering-schemes of networks, we prove that if the route assignments in the original network are link-disjoint, their corresponding ones in the conjugate network would be node-disjoint. Thus, traditional nonblocking switching networks can be transformed into crosstalk-free optical switches in a routine manner. Furthermore, we show that crosstalk-free multicast switches can also be obtained from existing nonblocking multicast switches via the same conjugate transformation.Comment: 10 page

Stencils and problem partitionings: Their influence on the performance of multiple processor systems

Given a discretization stencil, partitioning the problem domain is an important first step for the efficient solution of partial differential equations on multiple processor systems. Partitions are derived that minimize interprocessor communication when the number of processors is known a priori and each domain partition is assigned to a different processor. This partitioning technique uses the stencil structure to select appropriate partition shapes. For square problem domains, it is shown that non-standard partitions (e.g., hexagons) are frequently preferable to the standard square partitions for a variety of commonly used stencils. This investigation is concluded with a formalization of the relationship between partition shape, stencil structure, and architecture, allowing selection of optimal partitions for a variety of parallel systems

Upper Bound Analysis and Routing in Optical Benes Networks

Multistage Interconnection Networks (MIN) are popular in switching and communication applications. It has been used in telecommunication and parallel computing systems for many years. The new challenge facing optical MIN is crosstalk, which is caused by coupling two signals within a switching element. Crosstalk is not too big an issue in the Electrical Domain, but due to the stringent Bit Error Rate (BER) constraint, it is a big major concern in the Optical Domain. In this research dissertation, we will study the blocking probability in the optical network and we will study the deterministic conditions for strictly non-blocking Vertical Stacked Optical Benes Networks (VSOBN) with and without worst-case scenarios. We will establish the upper bound on blocking probability of Vertical Stacked Optical Benes Networks with respect to the number of planes used when the non-blocking requirement is not met. We will then study routing in WDM Benes networks and propose a new routing algorithm so that the number of wavelengths can be reduced. Since routing in WDM optical network is an NP-hard problem, many heuristic algorithms are designed by many researchers to perform this routing. We will also develop a genetic algorithm, simulated annealing algorithm and ant colony technique and apply these AI algorithms to route the connections in WDM Benes network

Work-Conserving Distributed Schedulers

Buffered multistage interconnection networks offer one of the most scalable and cost-effective approaches to building high capacity routers and switches. Unfortunately, the performance of such systems has been difficult to predict in the presence of the extreme traffic conditions that can arise in Internet routers. Recent work introduced the idea of distributed scheduling, to regulate the flow of traffic in such systems. This work demonstrated (using simulation and experimental measurements) that distributed scheduling can en-able robust performance, even in the presence of adversarial traffic patterns. In this paper, we show that appropriately designed distributed scheduling algorithms are provably work-conserving for speedups of 2 or more. Two of the three algorithms presented were inspired by algorithms previously developed for crossbar scheduling. The third has no direct counterpart in the crossbar scheduling context. In our analysis, we show that distributed schedulers based on blocking flows in small-depth acyclic flow graphs can be work-conserving, just as certain crossbar schedulers based on maximal bipartite matchings have been shown to be work-conserving. We also study the performance of practical variants of the work-conserving algorithms with speedups less than 2, using simulation. These studies demonstrate that distributed scheduling ensures excellent performance under extreme traffic conditions for speedups of less than 1.5

An Aggregate Scalable Scheme for Expanding the Crossbar Switch Network; Design and Performance Analysis

New computer network topology, called Penta-S, is simulated. This network is built of cross bar switch modules. Each module connects 32 computer nodes. Each node has two ports, one connects the node to the crossbar switch module and the other connects the node to a correspondent client node in another module through a shuffle link. The performance of this network is simulated under various network sizes, packet lengths and loads. The results are compared with those obtained from Macramé project for Clos multistage interconnection network and 2D-Grid network. The throughput of Penta-S falls between the throughput of Clos and the throughput of 2D-Grid networks. The maximum throughput of Penta-S was obtained at packet length of 128 bytes. Also the throughput grows linearly with the network size. On the opposite of Clos and 2D-Grid networks, the per-node throughput of Penta-S improves as the network size grows. The per-packet latency proved to be better than that of Clos network for large packet lengths and high loads. Also the packet latency proved to be nearly constant against various loads. The cost-efficiency of Penta-S proved to be better than those of 2D-Grid and Clos networks for large number of nodes (>200 nodes in the case of 2D-Grid and >350 nodes in the case of Clos).On the opposite of other networks, the cost-efficiency of Penta-S grows as its size grows. So this topology suits large networks and high traffic loads

Probabilistic structural mechanics research for parallel processing computers

Aerospace structures and spacecraft are a complex assemblage of structural components that are subjected to a variety of complex, cyclic, and transient loading conditions. Significant modeling uncertainties are present in these structures, in addition to the inherent randomness of material properties and loads. To properly account for these uncertainties in evaluating and assessing the reliability of these components and structures, probabilistic structural mechanics (PSM) procedures must be used. Much research has focused on basic theory development and the development of approximate analytic solution methods in random vibrations and structural reliability. Practical application of PSM methods was hampered by their computationally intense nature. Solution of PSM problems requires repeated analyses of structures that are often large, and exhibit nonlinear and/or dynamic response behavior. These methods are all inherently parallel and ideally suited to implementation on parallel processing computers. New hardware architectures and innovative control software and solution methodologies are needed to make solution of large scale PSM problems practical

On the impact of communication complexity in the design of parallel numerical algorithms

This paper describes two models of the cost of data movement in parallel numerical algorithms. One model is a generalization of an approach due to Hockney, and is suitable for shared memory multiprocessors where each processor has vector capabilities. The other model is applicable to highly parallel nonshared memory MIMD systems. In the second model, algorithm performance is characterized in terms of the communication network design. Techniques used in VLSI complexity theory are also brought in, and algorithm independent upper bounds on system performance are derived for several problems that are important to scientific computation