Clos Network Research Articles

On 3-Stage Clos Networks with Different Nonblocking Requirements on Two Types of Calls

Hwang and Lin introduced a new nonblocking requirement for 2-cast traffic which imposes different requirements on different types of coexisting calls. The requirement is strictly nonblocking for point-to-point calls among the 2-cast traffic, and is rearrangeable for genuine 2-cast calls. They conjectured that the 3-stage Clos network C(n,n,r,r,2n) satisfies the above requirement. We prove that C(n,n,4,r,2n) satisfies the above requirement.

A Unifying Approach to Determine the Necessary and Sufficient Conditions for Nonblocking Multicast Three-Stage Clos Networks

A parallel between Reed-Solomon codes in the complex field and multicarrier transmission using orthogonal frequency-division multi- plexing (OFDM) is first presented. This shows that when the signal is sent over some channel composed of Gaussian plus impulse noise, the impulse noise can be removed by a procedure similar to channel coding decoding, using information carried by the syndrome. The result is first derived in a simple situation (oversampled discrete multitone, additive channel), which is merely of theoretical interest. In any case, consecutive zeros, in the output of the OFDM modulator, do not correspond to real subcarriers. Pilot tones are emitted for synchronization or channel-estimation purposes. These pilot tones are generally scattered among the information ones. Our approach is to see these pilot tones as syndromes, in order to correct impulse noise. We show that the correction capacity is conditioned by the position of these pilot tones in the emitted sequence. A protection subsystem is in- troduced after the decoding operation in order to detect malfunction of this decoder. Efficiency of this technique is corroborated with simulations in the slightly modified Hiperlan2 context. Other extensions are then provided in order to increase the practical usefulness of the method. Abstract—In this paper, we propose a serial concatenated trellis-coded modulation system using one or more inner rate-1 accumulate codes and a mapping to a higher order, Gray-labeled signal constellation. As outer codes, we consider repeat codes, single parity-check codes, and convolu- tional codes. We show that under maximum-likelihood decoding, there ex- ists a signal-to-noise ratio threshold beyond which the bit-error probability goes to zero as the blocklength goes to infinity. We then evaluate the perfor- mance for finite blocklengths using a modified union bound. Computer sim- ulations demonstrate that the proposed system, despite its use of a simple rate-1 inner code, achieves performance in additive white Gaussian noise and Rayleigh fading that is comparable to, or better than, that of more complex systems suggested in the literature.

On Evil-Twin Routing in Clos Networks

The evil twin randomized routing algorithm is successfully applied to three-stage Clos networks in packet-switching platforms. Here we show the essence of evil twin permutations and how to construct evil twin permutations. The concept of evil twin permutations is also generalized in this letter.

A fault-tolerant rearrangeable permutation network

As optical communication becomes a promising networking choice, the well-known Clos network has regained much attention recently from optical switch designers/manufacturers and cluster computing community. There has been much work on the Clos network in the literature due to its uses as optical crossconnects (OXCs) in optical networks and high-speed interconnects in parallel/distributed computing systems. However, little attention has been paid to its fault tolerance capability, an indispensable requirement for any practical high-performance networks. We analyze the fault tolerance capability of the three-stage rearrangeable Clos network. We first establish a fault model on losing-contact faults in the switches of the network. Then, under this model, we analyze the fault tolerance capability of the Clos network when multiple such faults present in switches in the input stage, middle stage, and/or output stage of the network. Our results show that the rearrangeable condition on the number of middle stage switches for a fault-free rearrangeable Clos network still holds in the presence of a substantial amount of faults, while a more expensive crossbar network cannot tolerate any single such fault. In particular, we obtain that, for an N/spl times/N Clos network C(m,n,r), where N = nr and m/spl ges/n, it can tolerate any m - 1 losing-contact faults arbitrarily located in input/output stage switches, or any m - n losing-contact faults arbitrarily located in middle stage switches, when realizing any permutations. We also demonstrate that, for a given permutation, the network usually can tolerate much more such faults. We then present a necessary and sufficient condition on the losing-contact faults a Clos network can tolerate for any given permutation. We also develop an efficient fault-tolerant routing algorithm for a rearrangeable Clos network based on these results.

Wide-sense nonblocking for symmetric or asymmetric 3-stage Clos networks under various routing strategies

Beneš established the notion of wide-sense nonblocking by constructing an example on the symmetric 3-stage Clos network under packing which requires less hardware compared to strict nonblocking. This has remained the only example of a wide-sense non-blocking 3-stage Clos network which is not strictly nonblocking. In this paper, we study packing as well as several other routing strategies which have been studied in the literature and proved that no other example exists for the symmetric 3-stage Clos network. We then extend the study to asymmetric 3-stage Clos network for the first time. In particular, we extend Beneš example to asymmetric 3-stage Clos network and show that these are the only two possible examples for the strategies under study.

Rearrangeability of multicast Clos networks with middle-stage fan-out

The sufficient and necessary conditions under which a three-stage Clos network is rearrangeable for multicast connections are given. It is assumed that only switches of the middle stage have the fan-out property. Such an assumption is valid for some practical switching systems, e.g., high-speed crossconnects.

Strictly nonblocking three-stage clos networks with some rearrangeable multicast capability

F.K. Hwang and S.C. Liaw (see IEEE/ACM Trans. Networking, vol.8, p.535-9, 2000) introduced a new nonblocking requirement for 2-cast traffic which imposes different requirements on different types of coexisting calls. The requirement is strictly nonblocking for point-to-point calls among the 2-cast traffic, and is rearrangeable for genuine 2-cast calls. We generalize the 2-cast calls to multicast calls and give a sufficient condition for such networks when the number of multicast calls is upper bounded.

Multirate clos networks

Clos networks are a class of multistage switching network topologies that provide alternate paths between inputs and outputs, making it possible to minimize or eliminate the blocking that can otherwise occur in such networks. In his seminal paper in the Bell System Technical Journal in 1953, Charles Clos showed how these networks could be configured to make them nonblocking and effectively launched the systematic study of switching system performance, a field that has developed a rich technical literature, and continues to be very active and of continuing practical importance. This article describes how Clos' results have been generalized to systems that support connections with varying bandwidth requirements. These generalizations have extended the application of Clos networks well beyond their original technological context and have led to a number of interesting new results, especially in connection with systems that support multicast communication.

50th anniversary of clos networks - nonblocking, repackable, and rearrangeable clos networks: fifty years, of the theory evolution

The article gives an overview of major theoretical issues associated with a switching network structure proposed by C. Clos (1953). The concepts of strict-sense and wide-sense nonblocking as well as repackable and rearrangeable networks are described, showing the development of major research areas. A taxonomy of Clos switching networks and some important results for the basic network structure are given and discussed. Other research issues are enumerated.

A survey of noriblocking multicast three-stage clos networks

The author gave a survey on multicast nonblocking multistage interconnection networks in his 1998 book. Here he focuses on the three-stage Clos network and its recursive extensions. Not only does this article bring the literature up to date, but it also provides some fresh viewpoints to either clarify or simplify some issues.

Matching algorithms for three-stage bufferless clos network switches

Three-stage Clos network switches are an attractive solution for future broadband packet routers due to their modularity and scalability. Most three-stage Clos network switches assume either all modules are space switches without memory (bufferless), or employ shared memory modules in the first and third stages (buffered). The former is also referred to as the space-space-space (S/sup 3/) Clos network switch, while the latter is referred to as the memory-space-memory (MSM) Clos network switch. We provide a survey of recent literature concerning switching schemes in the S/sup 3/ Clos network switch. The switching problem in the S/sup 3/ Clos network switch can be divided into two major parts, namely port-to-port matching (scheduling) and route assignment between the first and third stages. Traditionally, researchers have proposed algorithms to solve these issues separately. Recently, a new class of switching algorithms, called matching algorithms for Clos (MAC), has been proposed to solve scheduling and route assignment simultaneously. We focus on the MAC schemes and show that the new class of algorithms can achieve high performance and maintain good scalability.

A new routing algorithm for multirate rearrangeable Clos networks

In this paper, we study the problem of finding routing algorithms on the multirate rearrangeable Clos networks which use as few number of middle-stage switches as possible. We propose a new routing algorithm called the “grouping algorithm”. This is a simple algorithm which uses fewer middle-stage switches than all known strategies, given that the number of input-stage switches and output-stage switches are relatively small compared to the size of input and output switches. In particular, the grouping algorithm implies that m=2n+⌈(n−1)/2k⌉ is a sufficient number of middle-stage switches for the symmetric three-stage Clos network C(n,m,r) to be multirate rearrangeable, where k is any positive integer and r⩽n/(2k−1).

Multirate Rearrangeable Clos Networks and a Generalized Edge-Coloring Problem on Bipartite Graphs

Chung and Ross [SIAM J. Comput., 20 (1991), pp. 726--736] conjectured that the minimum number m(n,r) of middle-stage switches for the symmetric 3-stage Clos network C(n,m(n,r),r) to be rearrangeable in the multirate environment is at most 2n-1. This problem is equivalent to a generalized version of the bipartite graph edge-coloring problem. The best bounds known so far on this function m(n,r) are $11n/9 \leq m(n,r) \leq 41n/16 + O(1)$, for $n, r \geq 2$, derived by Du et al. [SIAM J. Comput., 28 (1999), pp. 464--471]. In this paper, we make several contributions. First, we give evidence to show that even a stronger result might hold. In particular, we give a coloring algorithm to show that $m(n,r) \leq \lceil (r+1)n/2 \rceil$, which implies $m(n,2) \leq \lceil 3n/2 \rceil$---stronger than the conjectured value of 2n-1. Second, we derive that m(2,r) = 3 by an elegant argument. Last, we improve both the best upper and lower bounds given above: $\lceil 5n/4 \rceil \leq m(n,r) \leq 2n-1+\lceil (r-1)/2 \rceil$, where the upper bound is an improvement over $41n/16$ when r is relatively small compared to n. We also conjecture that $m(n,r) \leq \lfloor 2n(1-1/2^r) \rfloor$.

Parallel routing algorithms in Benes-Clos networks

A new parallel algorithm for route assignments in Benes-Clos (1962, 1953) networks is studied. Most known sequential route assignment algorithms, such as the looping algorithm, are designed for circuit switching systems where the switching configuration can be rearranged at relatively low speed. In packet switching systems, switch fabrics must be able to provide internally conflict-free paths simultaneously, and accommodate packets requesting connections in real time as they arrive at the inputs. In this paper, we develop a parallel routing algorithm for Benes networks by solving a set of Boolean equations which are derived from the connection requests and the symmetric structure of the networks. Our approach can handle partial permutations easily. The time complexity of our algorithm is O(log/sup 2/ N), where N is the network size. We also extend the algorithm and show that it can be applied to the Clos networks if the number of central modules is M=2/sup m/, where m is a positive integer. The time complexity is O(log N/spl times/log M) in this case.

A traffic control algorithm for Clos network type ATM switches

This paper presents a new traffic control algorithm for asynchronous transfer mode (ATM) switches composed of Clos network type switch fabric. In most traffic control algorithms previously proposed, an ATM switch has been considered as a single node, although the switch fabric of an ATM switch is usually of a network type. In this paper, we suggest a new control algorithm that is designed not only for the ATM network but also for the switch fabric and that can maintain high speed even in cases where buffer capacity of the switch fabric is limited. Main modules of the suggested algorithm are a traffic status detection mechanism based on non-parametric statistical tests, a cell-loss detection mechanism, and a cluster-based fair share computation procedure. Results of simulation experiments show that the suggested algorithm satisfactorily adjusts traffic rate of available bit rate services according to changes in traffic rate used by quality of service (QoS) guaranteed services. The results also show that the algorithm prevents cell losses relatively well and keeps the delay time of QoS guaranteed services short enough.

Split-connection rearrangeably nonblocking operation of three-stage multirate Clos networks

In this paper, we study the rearrangeably nonblocking (RNB) operation of asymmetrical three-stage Clos switching networks in the multirate environment. In order to achieve RNB operation in a Clos network, we must find a way to route any given traffic load through the middle-stage switches, possibly rearranging existing connections. The model under consideration assumes that a single connection can be routed through more than one middle-stage switch ( split-connection model). To solve the routing problem, we develop a network model and solve it using a maximum flow-based algorithm. We also derive sufficient conditions on the number of middle-stage switches needed to achieve the RNB operation.

Architectural design for multistage 2-D MEMS optical switches

Next-generation wavelength routing optical networks requiring optical cross connects (OXC) in the network have the ability to direct optical signals from any input interface to suitable output interfaces by configuring their internal embedded optical switch matrices. Microelectromechanical systems (MEMS) switches are regarded as the most promising technology to achieve such functionality. We consider the construction of a multistage MEMS switch network with single two-dimensional (2-D) MEMS switch blocks. A power loss model is developed that calls on a single MEMS block that is then used to develop the model for a three-stage Clos network. An effective model for maximum loss difference between calls is also developed. Based on these, the paper also proposes three connection patterns [Max + Min greedy (MMG), compressed extended generalized shuffle 1 (C-EGS-1), and compressed extended generalized shuffle 2 (C-EGS-2)] to connect outlet ports and inlet ports between two neighboring stages in a three-stage Clos network. These connection patterns are proved to be optimal and efficient enough to reach the minimums of both the maximum power loss of calls and the maximum loss difference between calls.

Efficient architectures and algorithms for multicasting data in computer communication networks

This paper presents two network architectures with associated routing and multicast algorithms for improved performance under multicasting traffic conditions. A conditionally nonblocking network, referred to as a Clos network, forms the basis for the development of efficient multicast communication networks. The Clos network is first analyzed under multicast traffic conditions for blocking and multicast overflow probability. The analysis determines the overflow probability under two different multicast distribution assumptions. The first distribution assumes all packets request the same number of copies and the second distribution uses a random number of requested copies. An analysis of an extension of the presented network to multiplexed parallel planes of a network shows a significant improvement on the network performance and particularly on the carried traffic load when compared with previously published multicast architectures using different buffering strategies.

Providing per-session deterministic quality of service guarantees in cross-path packet switch

Recently, a quasi-static routing scheme called path switching was proposed for large-scale packet switch systems. The path-switched Clos network is called a cross-path switch. Cross-path switch is capable of supporting multirate and multicast traffic. In this paper, we develop a general framework for it to handle multimedia traffic. We obtain upper bounds on the delay and backlog at the cross-path switch on a per-session basis, wherein no packet lost or delay bound violation is allowed. Our results show that these bounds much depend on the way of token assignment at the central stage. To understand such dependence, we quantify the effect of the token assignment on the switch performance. From these results, we design an effective token assignment scheme to achieve better performance guarantees in the switch. We show that cross-path switch with such token assignments always provides near-optimal performance guarantees to each data session.

Multirate multicast switching networks

This paper investigates multirate multicast Clos switching networks which are nonblocking in a wide sense, where a compatible multicast request is guaranteed to be routed without disturbing the existing networks if all requests have conformed to a given routing scheme. The routing strategy discovers (2.875n−1) min(k+r 1/k)+1 middle switches are sufficient for any multirate multicast requests, whereas strictly nonblocking multirate switching networks requires infinite number of middle switches if the range of weights is widely distributed. This paper also shows that Yang and Masson's nonblocking multicast Clos network for pure circuit switching is rearrangeable for multirate multicast communication if each weight is chosen from a given finite set of integer multiplicity. Note that a general rearrangeability of multirate Clos network even for point-to-point communications has not been known yet. In our work, the number of middle switches only depends on the configuration of the switch itself but not on the patterns of connection requests, which is advisable to construct large-scale switching networks.