A Deadlock – Free Routing Algorithm for Torus Network

TORUS is a n-dimensional network topology. Each dimension will have k nodes.  A routing algorithm determines the sequence of channels for a packet to traverse from the source to destination. A new router design that significantly reduces the main drawback of worm hole switching – latency, is presented in this paper. Worm-hole switching is combined with virtual channel to provide better performance. Packet deadlock is avoided by verifying the freeness of the nodes before sending the packets to that node. The traditional ‘wormhole switching’ mechanism for routing in the torus network has the disadvantages such as link contention, message latency, need for large buffer size and finally a massive deadlock may appear. The recently proposed ‘clue’ algorithm, has the disadvantages such as difficulty in cut through the link by the packets, says nothing about loss of packets between a hop and storage overhead and complexity in dividing the virtual channels. We proposed an ‘Advanced Clue’ algorithm by combining the concepts of clue and flow controlled clue and also overcome the disadvantages of clue. We use two virtual channels and a buffer which gives a combination of clue and flow controlled clue. We also propose conditions that satisfy the reliability of the packet delivery between hops. The packet will be sent to the next hop and buffered in the current hop. The sending hop will set a timer and wait for the acknowledgement. If the acknowledgement is not arrived till the timer expired then, the packet will be resend, and otherwise the packet will be removed from the buffer. Keywords: Torus, Virtual channels, Cut – through Switching, Wormhole switching

Performance evaluation of network-on-chip interconnect architectures

With a communication design style, Network-on-Chips (NoCs) have been proposed as a new Multi-Processor System-on-Chip paradigm. Simulation and functional validation are essential to assess the correctness and performance of the NoC design. In this thesis, a cycle-accurate NoC simulation system in Verilog HDL is developed to evaluate the performance of various NoC architectures. First, a library of NoC components is developed based on an existing design. Each NoC architecture to be evaluated is constructed from the library according to the topology description which specifies the network topology, network size, and routing algorithm. The network performance of four NoC architectures under uniform and three non-uniform traffic patterns is tested on ModelSim 6.4. The developed NoC simulation system provides useful resources for the future development of the FPGA-based NoC emulation system

Resource placement, data rearrangement, and Hamiltonian cycles in torus networks

Many parallel machines, both commercial and experimental, have been/are being designed with toroidal interconnection networks. For a given number of nodes, the torus has a relatively larger diameter, but better cost/performance tradeoffs, such as higher channel bandwidth, and lower node degree, when compared to the hypercube. Thus, the torus is becoming a popular topology for the interconnection network of a high performance parallel computers. In a multicomputer, the resources, such as I/O devices or software packages, are distributed over the networks. The first part of the thesis investigates efficient methods of distributing resources in a torus network. Three classes of placement methods are studied. They are (1) distant-t placement problem: in this case, any non-resource node is at a distance of at most t from some resource nodes, (2) j-adjacency problem: here, a non-resource node is adjacent to at least j resource nodes, and (3) generalized placement problem: a non-resource node must be a distance of at most t from at least j resource nodes. This resource placement technique can be applied to allocating spare processors to provide fault-tolerance in the case of the processor failures. Some efficient spare processor placement methods and reconfiguration schemes in the case of processor failures are also described. In a torus based parallel system, some algorithms give best performance if the data are distributed to processors numbered in Cartesian order; in some other cases, it is better to distribute the data to processors numbered in Gray code order. Since the placement patterns may be changed dynamically, it is essential to find efficient methods of rearranging the data from Gray code order to Cartesian order and vice versa. In the second part of the thesis, some efficient methods for data transfer from Cartesian order to radix order and vice versa are developed. The last part of the thesis gives results on generating edge disjoint Hamiltonian cycles in k-ary n-cubes, hypercubes, and 2D tori. These edge disjoint cycles are quite useful for many communication algorithms

Adaptive deadlock- and livelock-free routing with all minimal paths in Torus networks

This paper consists of two parts. In the first part, a new algorithm for deadlock- and livelock-free routing for the n-dimensional torus network is presented. This algo- rithm, called *-Channels, is fully-adaptive minimal, i.e. all paths with a minimal number of hops from source to destination are available for routing. *-Channels works for messages of unknown size, thus yielding new rout- ing techniques for both packet-switched and worm-hole models. *.Channels differs radically from the packetswitched fully-adaptive minimal methods presented in SPAA '91 by Pifarr6, Gravano, Felperin, and Sanz [PGFS91]. In particular, the packet-based techniques in [PGFS91] do not work for worm-hole routing as dead- lock situations can be constructed

Analysis of wormhole routings in cayley graphs of permutation groups.

Over a decade, a new class of switching technology, called wormhole routing, has been investigated in the multicomputer interconnection network field. Several classes of wormhole routing algorithms have been proposed. Most of the algorithms have been centered on the traditional binary hypercube, k-ary n-cube mesh, and torus networks. In the design of a wormhole routing algorithm, deadlock avoidance scheme is the main concern. Recently, new classes of networks called Cayley graphs of permutation groups are considered very promising alternatives. Although proposed Cayley networks have superior topological properties over the traditional network topologies, the design of the deadlock-free wormhole routing algorithm in these networks is not simple. In this dissertation, we investigate deadlock free wormhole routing algorithms in the several classes of Cayley networks, such as complete-transposition and star networks. We evaluate several classes of routing algorithms on these networks, and compare the performance of each algorithm to the simulation study. Also, the performances of these networks are compared to the traditional networks. Through extensive simulation we found that adaptive algorithm outperformed deterministic algorithm in general with more virtual channels. On the network performance comparison, the complete transposition network showed the best performance among the similar sized networks, and the binary hypercube performed better compared to the star graph

GridHub: a grid-based, high-density material handling system.

In the past twenty years, the share of e-commerce has increased (FRED, 2019). Since more and more activities, such as picking and sorting customers’ orders, are done in warehouses, high efficiency warehouses are in demand. Furthermore, the efficiency of warehouses is related to customer satisfaction (Colla and Lapoule, 2012). Storage systems are key components in warehouses, which are related to the efficiency of warehouse operations. In this dissertation, we address an automatic puzzle-based storage system under decentralized control. We call this system GridHub. GridHub meets standards of Industry 4.0 (Lasi et al., 2014), and it features high throughput with parallel order processing. In the first part of this research, we describe a GridHub which can handle unit-sized items; that is, one box only occupies one conveyor module. The GridHub is capable of moving boxes in all cardinal directions. It can complete multiple material handling tasks, such as sorting, sequencing, retrieving, and storing without changing the control algorithms. To move the active boxes to their targets, we developed a decentralized control algorithm to arrange box movements. The algorithms are executed by conveyor modules cyclically, and all actions in the execution process are one iteration of the algorithm. There are three phases in one iteration (assess, negotiation and convey), and several steps consist of one phase. The conveyor modules execute the algorithm simultaneously and synchronize at every step. The goal of the control algorithms is to move active boxes into their immediate destinations, and the key idea of the algorithm is to move away other boxes for the active boxes through message passing process. Negotiation behaviors are patterns of action generated by the conveyor modules while executing the algorithms. We describe these behaviors and explain how they affect the transfer process of active boxes. Some of those behaviors and other actions, which can prevent the transferring processes of boxes, are listed and discussed. These actions are related to deadlock and livelock in the GridHub. We prove that GridHub is deadlock free, and it is also livelock free under certain conditions. In the second part of this research, we extend the unit-sized GridHub by enabling it to handle non-unit-sized boxes meaning every box can occupy more than one conveyor module. We name the new GridHub the NU GridHub. The control algorithms of the NU GridHub are developed based on the unit-sized GridHub’s algorithms by adding new rules. Performance of the NU GridHub is also measured and discussed. GridHub is the first grid-based material handling system to offer four-way movement of stored items with a rich set of material handling task – storage, retrieval, sorting, and sequencing. GridHub is also the first grid-based system to implement a decentralized control algorithm based on “nested attempts,” a feature the guarantee deadlock free operation. Finally, the NU GridHub is the first grid-based solution to handle bigger boxes, which have not been done for a grid-based system under the virtual aisle method

Performance evaluation of distributed crossbar switch hypermesh

The interconnection network is one of the most crucial components in any multicomputer as it greatly influences the overall system performance. Several recent studies have suggested that hypergraph networks, such as the Distributed Crossbar Switch Hypermesh (DCSH), exhibit superior topological and performance characteristics over many traditional graph networks, e.g. k-ary n-cubes. Previous work on the DCSH has focused on issues related to implementation and performance comparisons with existing networks. These comparisons have so far been confined to deterministic routing and unicast (one-to-one) communication. Using analytical models validated through simulation experiments, this thesis extends that analysis to include adaptive routing and broadcast communication. The study concentrates on wormhole switching, which has been widely adopted in practical multicomputers, thanks to its low buffering requirement and the reduced dependence of latency on distance under low traffic. Adaptive routing has recently been proposed as a means of improving network performance, but while the comparative evaluation of adaptive and deterministic routing has been widely reported in the literature, the focus has been on graph networks. The first part of this thesis deals with adaptive routing, developing an analytical model to measure latency in the DCSH, and which is used throughout the rest of the work for performance comparisons. Also, an investigation of different routing algorithms in this network is presented. Conventional k-ary n-cubes have been the underlying topology of contemporary multicomputers, but it is only recently that adaptive routing has been incorporated into such systems. The thesis studies the relative performance merits of the DCSH and k-ary n-cubes under adaptive routing strategy. The analysis takes into consideration real-world factors, such as router complexity and bandwidth constraints imposed by implementation technology. However, in any network, the routing of unicast messages is not the only factor in traffic control. In many situations (for example, parallel iterative algorithms, memory update and invalidation procedures in shared memory systems, global notification of network errors), there is a significant requirement for broadcast traffic. The DCSH, by virtue of its use of hypergraph links, can implement broadcast operations particularly efficiently. The second part of the thesis examines how the DCSH and k-ary n-cube performance is affected by the presence of a broadcast traffic component. In general, these studies demonstrate that because of their relatively high diameter, k-ary n-cubes perform poorly when message lengths are short. This is consistent with earlier more simplistic analyses which led to the proposal for the express-cube, an enhancement of the basic k-ary n-cube structure, which provides additional express channels, allowing messages to bypass groups of nodes along their paths. The final part of the thesis investigates whether this "partial bypassing" can compete with the "total bypassing" capability provided inherently by the DCSH topology