Optical Passive Star Research Articles

Reconfigurable optical star network architecture for multicast media production data centres

Passive optical star networks have attractive properties for multicast traffic in data centres, but are limited in transmission bandwidth per node due to sharing a finite total throughput capacity. By adding reconfigurable switching elements to the core of an optical star topology, simulations show that the expected transmission rate per node can be increased by 26–40% (at 90% and 70% network load respectively). The proposed architecture shows no loss of multicast functionality compared to a single passive optical star, and only 7.1% increase in power consumption. Network throughput is shown to be highly dependent on the network traffic pattern, with simulations of multicast zonal media production traffic showing 6 times greater throughput than random or hotspot traffic models.

Optimal hypercube simulation on the partitioned optical passive stars network

Partitioned Optimal Passive Stars network, POPS(d,g), is an optical interconnection network of N processors (N=dg) with g 2 optical passive star couplers. In this network, there are g groups of d processors each and the g 2 couplers are used for connecting each group with each of the groups, including itself. In this paper, we present a technique for optimally simulating a frequently arising hypercube communication pattern on this network for all combinations of values of d and g. Specifically, we show that one-hop movements on the hypercube along the same dimension can be simulated on the POPS(d,g) network in $\lceil \frac{d}{g}\rceil$ slots for d?g and in 2 slots for d=g.

Online Permutation Routing in Partitioned Optical Passive Star Networks

This paper establishes the state of the art in both deterministic and randomized online permutation routing in the POPS network. Indeed, we show that any permutation can be routed online on a {\rm POPS}(d, g) network either with O({\frac{d}{g}}\log g) deterministic slots, or, with high probability, with 5c\lceil d/g \rceil + o(d/g) + O(\log\log g) randomized slots, where constant c = \exp (1 + e^{-1}) \approx 3.927. When d = \Theta(g), which we claim to be the "interesting” case, the randomized algorithm is exponentially faster than any other algorithm in the literature, both deterministic and randomized ones. This is true in practice as well. Indeed, experiments show that it outperforms its rivals even starting from as small a network as a POPS(2, 2) and the gap grows exponentially with the size of the network. We can also show that, under proper hypothesis, no deterministic algorithm can asymptotically match its performance.

Hypercube computations on partitioned optical passive stars networks

This paper shows that an n=2k processor partitioned optical passive stars (POPS) network with g groups and d processors per group can simulate every bidirectional move of an n processor hypercube using one slot when d g. Moreover, the same POPS network can simulate every monodirectional move of a processor hypercube using one slot when d=g. All these results are shown to be optimal. Our simulations improve on the literature whenever dneg and directly yield several important consequences. For example, as a direct consequence of our simulations, a POPS network, n=dg and d<g, can compute the prefix sums of n data values in log2n slots. This is faster than the best previously known ad hoc algorithm and is actually optimal. Similarly, we improve on the best POPS network algorithms for both the prefix sums problem on general POPS networks and the fundamental online permutation routing problem, among others

Packet routing and selection on the POPS network

Partitioned optical passive stars (POPS) network has been proposed recently as a desirable model of parallel computing. Many papers have been published that address fundamental problems on these networks. Packet routing is one such important problem. We present a randomized algorithm in this paper that performs better than the best prior algorithms. We also present a randomized algorithm for selection on the POPS network.

RANDOMIZED SORTING ON THE POPS NETWORK

Partitioned Optical Passive Stars (POPS) network has been presented recently as a desirable model of parallel computation. Several papers have been published that address fundamental problems on this architecture. The algorithms presented in this paper are valid for POPS(d,g) where d&gt;g and use randomization. We present an algorithm that solves the problem of sparse enumeration sorting of d∊ keys in [Formula: see text] time and hence performs better than previous algorithms. We also present algorithms that allow us to do stable sorting of integers in the range [1, log n] and [Formula: see text] in [Formula: see text] time. When g=n∊, for any constant 0&lt;∊&lt;½ this allows us to do sorting of integers in the range [1,n] in [Formula: see text] time. We finally use these algorithms to solve the problem of multiple binary search in the case where we have d∊ keys in [Formula: see text] time and in the case where we have integer keys in the range [1,n] in [Formula: see text] time, when g=n∊, for some constant 0&lt;∊&lt;½.

A Reservation-Based Multicast Protocol for WDM Optical Star Networks

In this paper, we present a reservation-based medium access control (MAC) protocol with multicast support for wavelength-division multiplexing networks. Our system is based on the single-hop, passive optical star architecture. Of the available wavelengths (channels), one channel is designated as a control channel, and the remaining channels are used for data transmission. Each node is equipped with a pair of fixed transceiver to access the control channel, and a fixed transmitter and a tunable receiver to access data channels. For easy implementation of the protocol in hardware and for precisely computing the protocol's processing overhead, we give a register-transfer model of the protocol. We simulate the protocol to study its throughput behavior, and present its analytic model. For a node to be able to send data packets in successive data slots with no time gap between them, in spite of the situation that the protocol's execution time may be longer than data transmission time, we propose the idea of multiple MAC units at each node. Unicast throughput of our protocol reaches the theoretically possible maximum throughput for MAC protocols with distributed control, and the multicast throughput is at least as good as, and even better than, those delivered by existing MAC protocols with distributed control.

A Multilayer Optical Packet Switching Network Based on the Kautz Graph and Optical Passive Star Couplers

The multihop optical network is the most appropriate solution to satisfy the increasing applications of Internet services. This paper extends the regular Kautz graph to one with multiple layers in order to produce more architectural variations. The connectivity between adjacent layers utilizes the systematic connection patterns of a regular Kautz graph. A routing algorithm based on its property is presented. Optical passive star (OPS) couplers are adopted to implement our new topologies. Three scheduling criteria that can solve the contention problem in the intermediate nodes are evaluated and compared in terms of their capability to improve the accessibility.

Summation and routing on a partitioned optical passive stars network with large group size

In a partitioned optical passive stars (POPS) network, n=dg processors are divided into g groups of d processors each, and such a POPS network is denoted by POPS(d,g). There is an optical passive star (OPS) coupler between every pair of groups. Hence, a POPS(d,g) requires g/sup 2/ couplers. It is likely that, in a practical system, the number of couplers will be less than the number of processors, i.e., d>/spl radic/n>g and the number of groups will be smaller than the number of processors in a group. Hence, it is important to design fast algorithms for basic operations on such POPS networks with large group size. We present fast algorithms for data sum, prefix sum, and permutation routing on a POPS(d,g) such that d>/spl radic/n>g. Our data sum and prefix sum algorithms improve upon the best known algorithms for these problems designed by Sahni (2000). Permutation routing can be solved on a POPS network by simulating a hypercube sorting algorithm. Our algorithm for permutation routing is more efficient compared to this simulated hypercube sorting algorithm.

Routing permutations in Partitioned Optical Passive Stars Networks

It is shown that a Partitioned Optical Passive Stars (POPS) network with g groups and d processors per group can route any permutation among the n= dg processors in one slot when d=1 and 2⌈ d/ g⌉ slots when d>1. The number of slots used is optimal in the worst case, and is at most the double of the optimum for all permutations π such that π( i)≠ i, for all i.

Transmission schedules for hypercube interconnection in WDM optical passive star networks

This paper is concerned with optimal transmission schedules for a hypercube interconnection using wavelength division multiplexed (WDM) optical passive star network. Our model of the network consists of a set V of N nodes with N tunable transmitters and N fixed-tuned receivers (where each node is assigned a transmitter–receiver pair), k (=2 b for an integer b ) wavelengths (each wavelength is shared by N / k receivers where N / k is an integer), and tuning time δ >0 (in units of time slot, for transmitters to tune from one wavelength to another). We assume that N is equal to the number of nodes in the hypercube, and that at any given time slot at most one transmission can be done per wavelength. An optimal transmission schedule for a hypercube interconnection is defined to be the one that schedules transmissions such that for each node v of the hypercube, v transmits once to each of its neighboring nodes within a repeating cycle of minimum length. In this paper, we first show that the n -dimensional hypercube Q n can be embedded in V such that for any node of Q n , its n neighboring nodes are evenly partitioned into b groups where each group shares a wavelength. Under this embedding, we then present an optimal transmission schedule for each tuning time.

MODELS AND ALGORITHMS FOR OPTICAL AND OPTOELECTRONIC PARALLEL COMPUTERS

This paper briefly reviews some of the more popular parallel-computer models-pipelined optical bus, optical transpose interconnect system (OTIS), and partitioned optical passive stars (POPS) network-that employ optical interconnect. The interconnect topology and some simple algorithms for each model are also described.

Scheduling of real-time messages in optical broadcast-and-select networks

In this paper, we consider broadcast-and-select networks based on optical passive stars. In these single-hop networks, communicating pairs can exchange messages directly, without the need to store information at intermediate nodes for later forwarding. Messages are transmitted in a packetized way, and each message has an associated deadline. In order to guarantee the message reception timeliness, we ask that all the messages are received within their corresponding deadline. We show that this scheduling problem is strong NP-complete, even in a very restricted case. Then, we turn our attention to fast approximating heuristics. We present four of them, assess their average performance by means of computer simulation, and give their worst-case performance bounds. Such bounds can be effectively used to test the success of the schedule before generating it.

A MAC Protocol for IP Differentiated Services in a WDM Metropolitan Area Network

This paper presents a Media Access Control (MAC) protocol for a WDM passive optical star. The protocol supports scalable service differentiation for Internet traffic in the spirit of the IETF's Diffserv architecture. We describe the functional elements of the protocol (signaling, arbitration, service disciplines and buffer management techniques) and the way they interact to support the Diffserv's Expedited Forwarding (EF) PHB and Assured Forwarding (AF) PHB group, where PHB stands for Per-Hop-Behavior. Extensive simulation results give quantitative estimations of the performance of the protocol under combined EF/AF traffic.

A multihop multi-OPS optical interconnection network

In this paper, we study the design of regular multicast networks implemented with optical passive star (OPS) couplers. We focus on an architecture based on both Kautz graphs and stack-graphs, and show that it is very cost-effective with respect to its resources requirements, namely the number of OPS couplers, power budget, scalability and number of transceivers, and presents a large ratio number-of-nodes/diameter. The important issue of medium access control is also addressed and control protocol for accessing the optical couplers are given and analyzed. Finally, we show through simulation that these control protocols efficiently implement shortest path routing on these networks.

The partitioned optical passive stars network: simulations and fundamental operations

We show how a multiprocessor computer interconnected by a partitioned optical passive stars network (POPS) can simulate hypercube and mesh-connected computers. POPS algorithms for data sum, prefix sum, rank, adjacent sum, consecutive sum, concentrate, distribute, and generalize are also developed. These fundamental operations form the building blocks of parallel algorithms for many applications.

Matrix multiplication of data routing using a partitioned optical passive stars network

We develop optimal or near optimal algorithms to multiply matrices and perform commonly occurring data permutations and BPC permutations on multiprocessor computers interconnected by a partitioned optical passive stars network.

Topologies for optical interconnection networks based on the optical transpose interconnection system

Many results exist in the literature describing technological and theoretical advances in optical network topologies and design. However, an essential effort has yet to be made in linking those results together. We propose a step in this direction by giving optical layouts for several graph-theoretical topologies studied in the literature, using the optical transpose interconnection system (OTIS) architecture. These topologies include the family of partitioned optical passive star (POPS) and stack-Kautz networks as well as a generalization of the Kautz and the de Bruijn digraphs.

Self-Simulation for the Passive Optical Star

Optical technology offers simple interconnection schemes with straightforward layouts that support complex logical interconnection patterns. The passive optical star (pos), in which communication takes place via optical wavelengths agreed upon between senders and receivers, is often suggested as a platform for implementing the optical network: Logically it offers an all-to-all broadcast capability. We investigate the use of pos optical technology as the communication medium for parallel computing, focusing on the scalability or self-simulation issue, which is a fundamental concern of great importance to the simplicity of algorithm design and program portability. A family of parallel machines is scalable or self-simulating if any member of the family can simulate any larger member with k times as many processors with a slowdown close to k; i.e., scalability states that if a certain efficiency is achievable on a large machine, then it is achievable on any smaller machine as well. A pos is balanced if the number of available wavelengths equals the number of processors. We show that the balanced pos is highly scalable by presenting a universal randomized simulation of a kn-processor balanced pos on an n-processor balanced pos, for arbitrary integers n,k≥1, with an expected slowdown of O(k+log*n). We also describe a deterministic simulation with a slowdown of O(min{k2,k+logn}) and show that a slowdown of O(k) is achievable if the communication pattern of each step is known in advance and available for preprocessing. For a certain restricted class of self-simulations we establish matching upper and lower bounds of Θ(k2). We also show that the balanced pos is equivalent to a balanced version of the well-known collision crcw pram, where we now take the balance condition to mean that the number of shared memory cells is the same as the number of processors.

Optimal transmission schedules for lightwave networks embedded with de Bruijn graphs

We 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.