Scheduling reserved traffic in input-queued switches: new delay bounds via probabilistic techniques

We consider the problem of providing delay bounds to reserved traffic in high-speed input-queued switches. We assume that the matrix of bandwidth demands is known, and we use the now standard approach of decomposing this matrix into a convex combination of permutation matrices. Our problem, therefore, reduces to the problem of constructing a schedule for these permutation matrices. We derive delay bounds for four algorithms that are based on probabilistic techniques. For each algorithm, we first place tokens randomly in continuous time for each permutation matrix. If the nth token that appears corresponds to permutation matrix M/sub k/, then we schedule matrix M/sub k/ in the nth time slot. The algorithms differ in how the random token processes are defined. For two of the algorithms, we are able to perform a derandomization so as to obtain deterministic schedules. We show through numerical computation that in many situations the resulting delay bounds are smaller than the previously best-known delay bounds of Chang et al. (see Proc. IEEE IWQoS, London, U.K., 1999 and Proc. IEEE INFOCOM, Tel-Aviv, Israel, Mar 2000).     

On the stability of input-queued switches with speed-up

We consider cell-based switch and router architectures whose internal switching matrix does not provide enough speed to avoid input buffering. These architectures require a scheduling algorithm to select at each slot a subset of input buffered cells which can be transferred toward output ports. We propose several classes of scheduling algorithms whose stability properties are studied using analytical techniques mainly based upon Lyapunov functions. Original stability conditions are also derived for scheduling algorithms that are being used today in high-performance switch and router architectures     

Achieving stability in networks of input-queued switches

Research has generated many interesting results on scheduling input-queued switches. However, most of this work focuses on a single switch in isolation. We study the problem of scheduling a network of input-queued switches. We consider the longest-queue-first and longest-port-first scheduling policies that are stable for a single switch, and show that they can be unstable even for a fixed traffic pattern in a simple network of eight input-queued switches. Moreover, this result holds regardless of how the traffic sharing the same port-pair is scheduled at each switch. On the positive side, we present a policy, longest-in-network, that is stable in networks of input-queued switches. This result holds even if the traffic pattern is allowed to change over time.     

Captured-frame eligibility and round-robin matching for input-queued packet switches

A variety of matching schemes for input-queued (IQ) switches that deliver high throughput under traffic with uniform distributions has been proposed. However, there is a need of matching schemes that provide high throughput under several admissible traffic patterns, including those with nonuniform distributions, while keeping implementation complexity low. In this letter, first, we introduce the captured frame concept for matching schemes in IQ switches. Second, we propose a round-robin based matching scheme, uFORM, which uses the proposed concept for cell matching eligibility. We show via simulation that our matching scheme delivers high throughput under several nonuniform traffic patterns, and retains the high performance under uniform traffic that round-robin matching schemes are known to offer.     

Throughput analysis of bifurcated input-queued packet switches withrestricted contention

An input-queueing scheme is suggested in which a buffer is divided into several smaller buffer blocks for enhancement of the limited throughput of the ordinary input-queued switch. The scheme is analysed and compared with respect to the performance of the scheme with free contention     

Analysis model of multiple input-queued switches with PIMscheduling algorithm

In this letter, we propose a new analysis model of multiple input-queued switches that use the parallel iterative matching (PIM) scheduling algorithm under i.i.d Bernoulli traffic. Compared to the previous analysis models, our approach incurs very low computational complexity while maintaining good accuracy by employing a simple queueing model. Specifically, we model an input queue of the switch as a synchronous Geom/Geom/1/B queue with a service rate which is directly obtained from a PIM scheduling algorithm. We perform the simulation and verify the accuracy of our model     

Multicast traffic in input-queued switches: optimal scheduling and maximum throughput

The paper studies input-queued packet switches loaded with both unicast and multicast traffic. The packet switch architecture is assumed to comprise a switching fabric with multicast (and broadcast) capabilities, operating in a synchronous slotted fashion. Fixed-size data units, called cells, are transferred from each switch input to any set of outputs in one time slot, according to the decisions of the switch scheduler, that identifies at each time slot a set of nonconflicting cells, i.e., cells neither coming from the same input, nor directed to the same output. First, multicast traffic admissibility conditions are discussed, and a simple counterexample is presented, showing intrinsic performance losses of input-queued with respect to output-queued switch architectures. Second, the optimal scheduling discipline to transfer multicast packets from inputs to outputs is defined. This discipline is rather complex, requires a queuing architecture that probably is not implementable, and does not guarantee in-sequence delivery of data. However, from the definition of the optimal multicast scheduling discipline, the formal characterization of the sustainable multicast traffic region naturally follows. Then, several theorems showing intrinsic performance losses of input-queued with respect to output-queued switch architectures are proved. In particular, we prove that, when using per multicast flow FIFO queueing architectures, the internal speedup that guarantees 100% throughput under admissible traffic grows with the number of switch ports.     

Per-source mean cell delay and mean buffer contents in ATM queues

Most performance studies of ATM cell buffers so far have been limited to global performance characteristics such as the total mean buffer contents and the global mean cell delay. The authors present an analytical technique which allows the derivation of performance measures for single sources     

Performance evaluation of multiple input-queued ATM switches withPIM scheduling under bursty traffic

In this letter, we analyze the performance of multiple input-queued asynchronous transfer mode (ATM) switches that use parallel iterative matching (PIM) for scheduling the transmission of head-of-line cells in the input queues. A queueing model of the switch is developed under independently, identically distributed, two-state Markov modulated Bernoulli processes bursty traffic. The underlying Markov chain of the queueing model is a quasi-birth-death (QBD) chain. The QBD chain is solved using an iterative computing method. Interesting performance metrics of the ATM switch such as the throughput, the mean cell delay, and the cell loss probability can be derived from the model. Numerical results from both the analytical model and simulation are presented, and the accuracy of the analysis is briefly discussed     

Packet loss and delay performance of feedback and feed-forwardarrayed-waveguide gratings-based optical packet switches with WDMinputs-outputs

This paper analyzes the packet loss and delay performance of an arrayed-waveguide-grating-based (AWG) optical packet switch developed within the EPSRC-funded project WASPNET (wavelength switched packet network). Two node designs are proposed based on feedback and feed-forward strategies, using sharing among multiple wavelengths to assist in contention resolution. The feedback configuration allows packet priority routing at the expense of using a larger AWG. An analytical framework has been established to compute the packet loss probability and delay under Bernoulli traffic, justified by simulation. A packet loss probability of less than 10^-9 was obtained with a buffer depth per wavelength of 10 for a switch size of 16 inputs-outputs, four wavelengths per input at a uniform Bernoulli traffic load of 0.8 per wavelength. The mean delay is less than 0.5 timeslots at the same buffer depth per wavelength     

切换时延不为零的光交换调度算法

文章针对切换时延不为零的光交换调度提出了一种新算法--2近似启发算法.算法由两部分组成:选择匹配和决策权重.其中,选择匹配是确定光交叉阵列的切换次数,由贪心算法完成;决策权重是决定各个配置的持续时长,它是通过选择一个值以使剩下的业务矩阵的开销估计最优.2近似启发算法的近似因子为2,时间复杂度为O(N2logN).仿真表明这种调度算法更接近最优调度,比DOUBLE[1]和ADJUST[2]算法更能自适应传送来的不同业务模式.     

The turn-on delay time of silicon p-n-p-n switches

The turn-on delay time of silicon p-n-p-n switches has been experimentally shown to be inversely proportional to gate currents in excess of the threshold value. Based on the measurements of bidirectional p-n-p-n switches, it is demonstrated that p-n-p-n structures with remote gating have inherently longer turn-on delay times than those of the conventional construction having the gate lead attached to a base region.     

Evaluation and comparison of cell loss and delay models for ATM multiplexers

Among several models that are available to represent the aggregate cell flow generated by on–off sources at an ATM multiplexer (either at an access or a switching node), the Interrupted Bernoulli Process (IBP) is characterized by particular simplicity and analytical tractability. The superposition of sources individually modeled as an IBP, whose cells enter a common buffer, is considered in this paper. The main goal is to compute approximations of two basic Quality of Service (QoS) indicators, namely, cell loss rate, whose analytical computation has been already presented in previous works, and the rate of cells exceeding a specified delay, whose presentation constitutes the theoretical novelty of the paper. Analytical expressions of these two quantities are given for homogeneous sources, i.e., possessing the same statistical parameters and QoS requirements. The analytical formulation is carefully evaluated by comparing the results obtained with others presented in the literature and with simulation results; in the latter, the actual cell arrival process is generated by means of a Markov Modulated Deterministic Process (MMDP) model of the on–off sources. Several comparisons are performed for different offered loads and by varying the buffer length, which show the effectiveness and the limits of the technique under investigation.     

Derivation of Craig's formula for Gaussian probability function

A recent work provides two proofs for Craig's formula, which is an integral formula for the Gaussian probability density function. It also highlights the fact that the original proof of the Craig formula is somewhat unclear. The authors of the work provide two proofs, one based on the Stieltjes transform of a Gaussian pulse and another based on the moment generation function (MGF) of a unit Gaussian random variable (GRV). Another integral formula for Q(x) based on the characteristic function (CHF) of a unit GRV is also provided. This formula can be applied to the analysis of coherent predetection equal-gain combining diversity receivers     

ATM cell delay and loss for best-effort TCP in the presence ofisochronous traffic

This paper reports the findings of a simulation study of the queueing behavior of “best-effort” traffic in the presence of constant bit-rate and variable bit-rate isochronous traffic. In this study, best-effort traffic refers to ATM cells that support communications between host end systems executing various applications and exchanging information using TCP/IP. The performance measures considered are TCP cell loss, TCP packet loss, mean cell queueing delay, and mean cell queue length. Our simulation results show that, under certain conditions, best-effort TCP traffic may experience as much as 2% cell loss. Our results also show that the probability of cell and packet loss decreases logarithmically with increased buffer size     

Accurate approximation of cell loss probability for self-similartraffic in ATM networks

Recently, self-similar (or fractal) stochastic processes have been regarded as more accurate models of certain categories of traffic (e.g. LAN traffic) which will be transported in ATM networks. The authors propose a method for estimating the cell loss probability in an ATM multiplexer fed by a self-similar arrival process. The packet arrivals are generated by a fractional Brownian motion process and the service process is deterministic. The approach is based on theory for large deviations, and simulation tests show that it is more accurate than the existing approximation result     

业务穿越ATM-PON的延时和延时变化研究

ATM-PON是光纤接入网的重要技术。文章研究了业务穿越ATM-PON接入网的延时和延时变化性能，着重分析媒体接入控制协议对业务延时和延时变化性能的影响。研究结论对ATM-PON媒体接入控制协议的合理设计有很大的帮助。     

IPv6 delay and loss performance evolution

Although packet delay and loss are two important parameters of the Internet performance, to the best of our knowledge, the evolution of large‐scale IPv6 delay and loss performance has previously not been studied. In this paper, we analyze more than 600 end‐to‐end IPv6 paths between about 26 testboxes of RIPE Network Coordination Centre over two years, and compare the delay and loss performance over time with their IPv4 counterparts. We present and discuss the measurement methodologies and show that IPv6 paths have a higher delay and loss than their IPv4 counterparts. The main reason for the worse performance stems from IPv6‐in‐IPv4 tunnels rather than from native IPv6 paths and such tunnels are still widely used today. Copyright © 2007 John Wiley & Sons, Ltd.     

Relationship between the slowing and loss in optical delay lines

In this paper, we demonstrate the relation between the amount of slowing and the amount of insertion loss in an optical slow wave structure when the material used has finite absorption. The delay properties are calculated as a function of wavelength for a single Fabry-Perot resonator and a delay line consisting of multiple coupled resonators. In all of these delay lines, if the amount of delay increases, the insertion loss of the line likewise increases. For low material loss, the normalized increase in delay is equal to the normalized increase in insertion loss. We also compare a coupled resonator delay line to a simple waveguide made of the same material and with the same amount of delay. The simple waveguide always has less insertion loss than the coupled resonator line because of the unavoidable reflection from the coupled resonator line. Even in the case of an asymmetric mirror delay line with zero reflection at the input, the simple waveguide has less insertion loss.