Achieving 100% throughput in an input-queued switch

It is well known that head-of-line blocking limits the throughput of an input-queued switch with first-in-first-out (FIFO) queues. Under certain conditions, the throughput can be shown to be limited to approximately 58.6%. It is also known that if non-FIFO queueing policies are used, the throughput can be increased. However, it has not been previously shown that if a suitable queueing policy and scheduling algorithm are used, then it is possible to achieve 100% throughput for all independent arrival processes. In this paper we prove this to be the case using a simple linear programming argument and quadratic Lyapunov function. In particular, we assume that each input maintains a separate FIFO queue for each output and that the switch is scheduled using a maximum weight bipartite matching algorithm. We introduce two maximum weight matching algorithms: longest queue first (LQF) and oldest cell first (OCF). Both algorithms achieve 100% throughput for all independent arrival processes. LQF favors queues with larger occupancy, ensuring that larger queues will eventually be served. However, we find that LQF can lead to the permanent starvation of short queues. OCF overcomes this limitation by favoring cells with large waiting times     

NN based ATM cell scheduling with queue length-based priorityscheme

The asynchronous transfer mode (ATM) is the choice of transport mode for broadband integrated service digital networks (B-ISDNs). We propose a window-based contention resolution algorithm to achieve higher throughput for nonblocking switches in ATM environments. In a nonblocking switch with input queues, significant loss of throughput can occur due to head-of-line (HOL) blocking when first-in first-out (FIFO) queueing is employed. To resolve this problem, we employ bypass queueing and present a cell scheduling algorithm which maximizes the switch throughput. We also employ a queue length based priority scheme to reduce the cell delay variations and cell loss probabilities. With the employed priority scheme, the variance of cell delay is also significantly reduced under nonuniform traffic, resulting in lower cell loss rates (CLRs) at a given buffer size. As the cell scheduling controller, we propose a neural network (NN) model which uses a high degree of parallelism. Due to higher switch throughput achieved with our cell scheduling, the cell loss probabilities and the buffer sizes necessary to guarantee a given CLR become smaller than those of other approaches based on sequential input window scheduling or output queueing     

Nonuniform traffic analysis on a nonblocking space-division packetswitch

The nonuniform traffic performance on a nonblocking space division packet switch is studied. When an output link is simultaneously contended by multiple input packets, only one can succeed, and the rest will be buffered in the queues associated with each input link. given the condition that the traffic on each output is not dominated by individual inputs, this study indicates that the output contention involved by packets at the head of input queues can be viewed as an independent phase-type process for a sufficiently large size of the switch. Therefore, each input queue can be modeled by an independent Geom/PH/1 queueing process. Once the relative input traffic intensities and their output address assignment functions are defined, a general formulation can be developed for the maximum throughput of the switch in saturation. The result indicates under what condition the input queue will saturate. A general solution technique for the evaluation of the queue length distribution is proposed. The numerical study based on this analysis agrees well with simulation results     

On Guaranteed Smooth Switching for Buffered Crossbar Switches

Scalability considerations drive the evolution of switch design from output queueing to input queueing and further to combined input and crosspoint queueing (CICQ). However, CICQ switches with credit-based flow control face new challenges of scalability and predictability. In this paper, we propose a novel approach of rate-based smoothed switching, and design a CICQ switch called the smoothed buffered crossbar or sBUX. First, the concept of smoothness is developed from two complementary perspectives of covering and spacing, which, commonly known as fairness and jitter, are unified in the same model. Second, a smoothed multiplexer sMUX is designed that allocates bandwidth among competing flows sharing a link and guarantees almost ideal smoothness for each flow. Third, the buffered crossbar sBUX is designed that uses the scheduler sMUX at each input and output, and a two-cell buffer at each crosspoint. It is proved that sBUX guarantees 100% throughput for real-time services and almost ideal smoothness for each flow. Fourth, an on-line bandwidth regulator is designed that periodically estimates bandwidth demand and generates admissible allocations, which enables sBUX to support best-effort services. Simulation shows almost 100% throughput and multi-microsecond average delay. In particular, neither credit-based flow control or speed-up is used, and arbitrary fabric-internal latency is allowed between line cards and the switch core, simplifying the switch implementation.     

The single-queue switch: a building block for switches withprogrammable scheduling

We introduce a new approach to ATM switching. We propose an ATM switch architecture which uses only a single shift-register-type buffering element to store and queue cells, and within the same (physical) queue, switches the cells by organizing them in logical queues destined for different output lines. The buffer is also a sequencer which allows flexible ordering of the cells in each logical queue to achieve any appropriate scheduling algorithm. This switch is proposed for use as the building block of large-stale multistage ATM switches because of low hardware complexity and flexibility in providing (per-VC) scheduling among the cells. The switch can also be used as scheduler/controller for RAM-based switches. The single-queue switch implements output queueing and performs full buffer sharing. The hardware complexity is low. The number of input and output lines can vary independently without affecting the switch core. The size of the buffering space can be increased simply by cascading the buffering elements     

Input Versus Output Queueing on a Space-Division Packet Switch

Two simple models of queueing on anN times Nspace-division packet switch are examined. The switch operates synchronously with fixed-length packets; during each time slot, packets may arrive on any inputs addressed to any outputs. Because packet arrivals to the switch are unscheduled, more than one packet may arrive for the same output during the same time slot, making queueing unavoidable. Mean queue lengths are always greater for queueing on inputs than for queueing on outputs, and the output queues saturate only as the utilization approaches unity. Input queues, on the other hand, saturate at a utilization that depends onN, but is approximately(2 -sqrt{2}) = 0.586whenNis large. If output trunk utilization is the primary consideration, it is possible to slightly increase utilization of the output trunks-upto(1 - e^{-1}) = 0.632asN rightarrow infty-by dropping interfering packets at the end of each time slot, rather than storing them in the input queues. This improvement is possible, however, only when the utilization of the input trunks exceeds a second critical threshold-approximatelyln (1 +sqrt{2}) = 0.881for largeN.     

The Tera project: a hybrid queueing ATM switch architecture for LAN

The Tera ATM LAN project at Carnegie Mellon University addresses the interconnection of hundreds of workstations in the Electrical and Computer Engineering Department via an ATM-based network. The Tera network architecture consists of switched Ethernet clusters that are interconnected using an ATM network. This paper presents the Tera network architecture, including an Ethernet/ATM network interface, the Tera ATM switch, and its performance analysis. The Tera switch architecture for asynchronous transfer mode (ATM) local area networks (LAN's) incorporates a scalable nonblocking switching element with hybrid queueing discipline. The hybrid queueing strategy includes a global first-in first-out (FIFO) queue that is shared by all switch inputs and dedicated output queues with small speedup. Due to hybrid queueing, switch performance is comparable to output queueing switches. The shared input queue design is scalable since it is based on a Banyan network and N FIFO memories. The Tera switch incorporates an optimal throughput multicast stage that is also based on a Banyan network. Switch performance is evaluated using queueing analysis and simulation under various traffic patterns     

The performance analysis and implementation of an input accessscheme in a high-speed packet switch

The performance analysis of an input access scheme in a high-speed packet switch for broadband ISDN is presented. In this switch, each input port maintains a separate queue for each of the outputs, thus n ² input queues in an (n×n) switch. Using synchronous operation, at most one packet per input and output will be transferred in any slot. We derive lower and upper bounds for the throughput which show close to optimal performance. The bounds are very tight and approach to unity for switch sizes on the order of a hundred under any traffic load, which is a significant result by itself. Then the mean packet delay is derived and its variance is bounded. A neural network implementation of this input access scheme is given. The energy function of the network, its optimized parameters and the connection matrix are determined. Simulation results of the neural network fall between the theoretical throughput bounds     

On achieving throughput in an input-queued switch

We establish some lower bounds on the speedup required to achieve throughput for some classes of switching algorithms in a input-queued switch with virtual output queues (VOQs). We use a weak notion of throughput, which will only strengthen the results, since an algorithm that cannot achieve weak throughput cannot achieve stronger notions of throughput. We focus on priority switching algorithms, i.e., algorithms that assign priorities to VOQs and forward packets of high priority first. We show a lower bound on the speedup for two fairly general classes of priority switching algorithms: input priority switching algorithms and output priority switching algorithms. An input priority scheme prioritizes the VOQs based on the state of the input queues, while an output priority scheme prioritizes the VOQs based on their output ports. We first show that, for output priority switching algorithms, a speedup S/spl ges/2 is required to achieve weak throughput. From this, we deduce that both maximal and maximum size matching switching algorithms do not imply weak throughput unless S/spl ges/2. The bound of S/spl ges/2 is tight in all cases above, based on a result in Dai et al. Finally, we show that a speedup S/spl ges/3/2 is required for the class of input priority switching algorithms to achieve weak throughput.     

Analysis of input and output queueing for nonblocking ATM switches

A switch model for ATM networks is analyzed. Its interconnection network is internally nonblocking and is provided with dedicated input and output queues, one per switch inlet and one per switch outlet. The switch operates with an internal speed-up: more than one packet per slot can be transferred from the head-of-line positions of the input queues to each output queue by the interconnection network. Two different operation modes are considered for the interaction between input and output queues: backpressure mode and queue loss mode. The analytical model developed for the evaluation of the switch performance under random traffic assumes an infinite size for the switch, arbitrary values for input and output queue size, as well as for the speed-up factor. Switch throughput, packet delay and loss performance are evaluated and the analytical model accuracy is assessed using computer simulation results     

Performance analysis of the multiple input-queued packet switch with the restricted rule

The multiple input-queued (MIQ) switch is the switch which manages multiple (m) queues in each input port, each of which is dedicated to a group of output ports. Since each input port can switch up to m cells in a time slot, one from each queue, it hardly suffers from the head-of-line (HOL) blocking which is known to be the decisive factor limiting the throughput of the single input-queued (SIQ) switch. As a result, the MIQ switch guarantees enhanced performance characteristics as the number of queues m in an input increases. However, the service of multiple cells from an input could cause internal speedup or expansion of the switch fabric, diluting the merit of high-speed operation in the conventional SIQ scheme. The restricted rule is contrived to circumvent this side effect by regulating the number of cells switched from an input port. We analyze the performance of the MIQ switch employing the restricted rule. For the switch using the restricted rule, the closed formulas for the throughput bound, the mean cell delay and average queue length, and the cell loss bound of the switch are derived as functions of m, by generalizing the analysis for the SIQ switch by J.Y. Hui and E. Arthurs (see IEEE J. Select. Areas Commun., vol.SAC-5, p.1262-73, 1987).     

Nonpreemptive Scheduling of Optical Switches

Many high-speed routers today use input-queuing (IQ) architectures with a crossbar switching fabric based on optical technology. Packets in the input queues are divided into cells of unit length, and the goal is to find a schedule of minimum makespan that forwards all packets to the output ports. The problem is complicated since, in optical switches, so-called configuration delay, that is the time required to reconfigure the switching fabric, is non-negligible with respect to the cell transmission time. We aim to design a scheduler whose complexity does not depend on the number of packets in the input queues. Thus, we focus on the nonpreemptive bipartite scheduling (NPBS) problem, where each input queue is connected to each output port in at most one configuration. We demonstrate that the NPBS problem is NP-hard for any value of the configuration delay, and approximation within a ratio smaller than 7/6 is NP-hard as well. For the offline version of the NPBS problem, we show that a simple greedy algorithm achieves an approximation factor of 2 for arbitrary configuration delay. Then, we consider the online version of the NPBS problem, where the switch gathers the incoming traffic periodically and then schedules the accumulated batches. We propose a scheduling algorithm that guarantees strict delay for any admissible traffic, provided that the switch has a moderate speed-up of two. Finally, we extend our results to the nonbipartite scheduling problem.     

Performance study of an input and output queueing ATM switch with a window scheme and a speed constraint

In this paper, we study the performance of an input and output queueing switch with a window scheme and a speed constraint. The performance of a non-blocking ATM switch can usually be improved by increasing the switching speed. Also, the performance of a switch can be improved using a window scheme by relaxing the first-in-firstout (FIFO) queueing discipline in the input queue. Thus, one can expect that a combined scheme of windowing and a speed constraint can improve further the performance of the packet switch. Here, we analyze the maximum throughput of the input and output queueing switch with a speed constraint combined with windowing, and show that it is possible to obtain high throughput with a small increment of speed-up and window size. For analysis, we model the HOL queueing system as a virtual queueing system. By analyzing the dynamics of HOL packets in this virtual queueing model, we obtain the service probability of the HOL server as a function of output contention capabilities. Using the result, we apply the flow conservation relation to this model and obtain the maximum throughput. The analytical results are verified by simulation.     

A multistage ATM switch with interstage buffers

Asynchronous transfer mode (ATM) is the transport technique for the broadband ISDN recommended by CCITT (I.121). Many switches have been proposed to accommodate the ATM that requires fast packet switching capability.^1-8 The proposed switches for the broadband ISDN can be classified as being of input queueing or output queueing type. Those of the input queueing type have a throughput performance which is approximately 58 per cent that of the output queueing type. However, output queueing networks require larger amounts of hardware than input queueing networks. In this paper, we propose a new multistage switch with internal buffering that approaches a maximum throughput of 100 per cent as the buffering is increased. The switch is capable of broadcasting and self-routeing. It consists of two switching planes which consist of packet processors, 2 x 2 switching elements, distributors and buffers located between stages and in the output ports. The internal data rate of the proposed switch is the same as that of the arriving information stream. In this sense, the switch does not require speed-up. The switch has log₂ N stages that forward packets in a store-and-forward fashion, thus incurring a latency of log₂ N time periods. Performance analysis shows that the additional delay is small.     

Switching using parallel input-output queued switches with no speedup

We propose an efficient parallel switching architecture that requires no speedup and guarantees bounded delay. Our architecture consists of k input-output-queued switches with first-in-first-out queues, operating at the line speed in parallel under the control of a single scheduler, with k being independent of the number N of inputs and outputs. Arriving traffic is demultiplexed (spread) over the k identical switches, switched to the correct output, and multiplexed (combined) before departing from the parallel switch. We show that by using an appropriate demultiplexing strategy at the inputs and by applying the same matching at each of the k parallel switches during each cell slot, our scheme guarantees a way for cells of a flow to be read in order from the output queues of the switches, thus, eliminating the need for cell resequencing. Further, by allowing the scheduler to examine the state of only the first of the k parallel switches, our scheme also reduces considerably the amount of state information required by the scheduler. The switching algorithms that we develop are based on existing practical switching algorithms for input-queued switches, and have an additional communication complexity that is optimal up to a constant factor.     

Head of the line arbitration of packet switches with combined input and output queueing

A single-stage non-blocking N × N packet switch is considered. Data units may be stored before switching at the inputs as well as after switching at the outputs. Some output buffering capacity is intended to achieve high throughput, whereas an additional input buffering capacity keeps losses due to input-buffer overflow reasonably low. The paper studies the impact on performance of the head of the line arbitration policy, i.e. the sequence which is used to transfer data units from the heads of input queues to each output queue. The investigation is based on two performance measures: the average delay and the maximum throughput of the switch. Closed-form expressions for the FCFS, LCFS and the ROS policies are obtained. The result of the average delay with the FCFS policy leads to a lower bound, and that with the LCFS policy to an upper bound for the average delay, corresponding to an arbitrary symmetric policy which does not use information related to the state of the input queues. It is shown that the maximum throughput does not depend on the head of the line arbitration policy. It depends only on the output-buffer size and the packet-size distribution. The cases of fixed and exponentially distributed packet sizes are studied. The effects of asymmetric policies which result in different behaviours of some of the input queues is also considered.     

Bifurcated queueing for throughput enhancement in input-queuedswitches

We propose a bifurcated queueing approach to breaking the well-known 0.586 barrier for the throughput of input queued switches with head-of-line blocking. Each input line maintains a small number k of parallel queues, one for each of a set of k mutually exclusive subsets of the set of output-port addresses. We generalize the analysis of Karol et al. (1987) and show that the upper bound on throughput is (1+k)-√1+k², k=1, 2, 3, .... We point out that even for k=2, there is a significant improvement in throughput and that as k increases, the throughput approaches one     

Derivation of the mean cell delay and cell loss probability formultiple input-queued switches

The multiple input-queued (MIQ) asynchronous transfer mode (ATM) switch has drawn much interest as a promising candidate for a high-speed and high-performance packet switch. The most conspicuous feature of the switch is that each input port is equipped with m(1⩽m⩽N) distinct queues, each for a group of output ports. Since the MIQ switch has multiple queues, an input can serve up to m cells in a time slot, leading to an enhanced performance. We derive the average queue length, mean cell delay, and cell loss probability for the MIQ switch in terms of the number of queues in an input port (m) and input load. The results include a special case of the single input-queued (SIQ) switch (m=1), which is analyzed by Hui et al. (1987)     

Performance of an input-queued ATM switch with even/odd switchingplanes

A switch architecture is proposed for alleviating the HOL blocking by employing even/odd dual FIFO queues at each input and even/odd dual switching planes dedicated to each even/odd queue. Under random traffic, it gives 76.4% throughput without output expansion and 100% with output expansion r=2, with the same amount of crosspoints as for the ordinary output expansion scheme     

Analysis of packet switches with input and output queuing

A single-stage nonblocking N*N packet switch with both output and input queuing is considered. The limited queuing at the output ports resolves output port contention partially. Overflow at the output queues is prevented by a backpressure mechanism and additional queuing at the input ports. The impact of the backpressure effect on the switch performance for arbitrary output buffer sizes and for N to infinity is studied. Two different switch models are considered: an asynchronous model with Poisson arrivals and a synchronous model with Bernoulli arrivals. The investigation is based on the average delay and the maximum throughput of the switch. Closed-form expressions for these performance measures are derived for operation with fixed size packets. The results demonstrate that a modest amount of output queuing, in conjunction with appropriate switch speedup, provides significant delay and throughput improvements over pure input queuing. The maximum throughput is the same for the synchronous and the asynchronous switch model, although the delay is different.<>