The maximum throughput of a nonblocking space-division packetswitch with correlated destinations

We propose a discrete-time queueing network model for space-division packet switches, in which the destinations of consecutive packets may be correlated, and different input traffic may have different destination distributions. We show that for switches under saturation, the steady-state probabilities have an approximate product-form solution. The solution is very accurate for real applications where the average packet sizes are often more than 10 times the number of bytes that can be transmitted in one time slot     

Performance of a nonblocking space-division packet switch withcorrelated input traffic

This work studies the performance of a nonblocking space-division packet switch in a correlated input traffic environment. In constructing the input traffic model, the author considers that each input is a time division multiaccess (TDM) link connecting to multiple sources. Every source on a link supports one call at a time. Each call experiences the alternation of ON and OFF periods, and generates packets periodically while in ON period. The stochastic property of each call does not have to be identical. Packets from each individual call are destined to the same output. The output address of each call is assumed to be uniformly assigned at random. The author derives both upper and lower bounds of the maximum throughput at system saturation. His study indicates that, if the source access rate is substantially lower than the link transmission rate, the effect of input traffic correlation on the output contentions can generally be ignored. Also, the analysis of each input queue becomes separable from the rest of the switch. The same study is carried out with nonuniform call address assignment     

Performance of a nonblocking space-division packet switch in a timevariant nonuniform traffic environment

The authors study the performance of a nonblocking space-division packet switch, given that the traffic intensities at the switch not only are nonuniform but also change as a function of time. A finite-state Markov chain is used as an underlying process to govern the time variation of traffic for the entire switch. The packet arrivals at each input form an independent Bernoulli process modulated by the underlying Markov chain. The output address of each packet is independently and randomly assigned with probability distributions, which are also modulated by the Markov chain. Provided that the traffic on each output is not dominated by individual inputs the service time of each output queue for sufficiently large switches can be characterized by an independent Markov modulated phase-type process. A matrix geometric solution for the resultant quasi-birth-death type queuing process is presented. The maximum throughput is obtained at the system saturation. The performance of the switch is numerically examined under various traffic conditions. A contention priority scheme to improve the switch performance is proposed     

Cell loss analysis and design trade-offs of nonblocking ATMswitches with nonuniform traffic

In practical ATM switch design, a proper dimensioning of buffer sizes and a cost effective selection of speed-up factor should be considered to guarantee a specified cell loss requirement for a given traffic. Although a larger speed-up factor provides better throughput for the switch, increasing the speed-up factor involves greater complexity and cost. Hence, it may not be cost effective to increase the speed-up factor for 100% throughput. Moreover, with a given buffer budget, an increase in the speed-up factor beyond a certain value only adds to the cell loss. The paper addresses design trade-offs existing between finite input/output buffer sizes and speed-up factor in a nonblocking ATM switch. Another important issue is the adverse effect on cell loss performance caused by nonuniform traffic (different traffic intensity and unevenly distributed routing). The paper analyzes cell loss performance of ATM switches with nonuniform traffic, and examines the effect of each nonuniform traffic parameter. The authors also provide an algorithm for effective buffer sharing that alleviates the performance degradation caused by traffic nonuniformity     

Markov-modulated flow model for the output queues of a packetswitch

The output queues of an M×N packet switch are studied using a Markov-modulated flow model. The switching element is a central server which sequentially routes packets from the inputs to the outputs. The focus is on systems in which the server speed is such that the bulk of the queuing takes place in the output queues. The conventional point process approach neglects the impact of switching and transmission time. An attempt is made to account for these finite system speeds by using a Markov-modulated continuous flow to approximate the arrival process to an output queue. This model captures the dependency between arrivals at different outputs and reflects the fact that packet arrivals and departures are not instantaneous. The output queue content distribution is obtained, for both infinite and finite buffer systems, from the spectral expansion of the solution of a system of differential equations. Numerical examples and comparisons with the results of an M/M/1 approximation are presented     

A strictly nonblocking network based on nonblocking 4×4 optical switches

Recently, the demand for communication has been growing rapidly. Hence, optical multistage network technologies are more appreciated nowadays. A double-layer network is a strictly nonblocking network, and it has the lowest system insertion loss of non-dilated networks. A Beneš network is a rearrangeably nonblocking network, and it has the same system insertion loss as a double-layer network. We have proposed the use of modified polarization selection elements (PSEs). The system insertion loss, number of drivers, and number of required components of a double-layer network could be reduced if it is constructed with modified PSEs. A nonblocking 4×4 optical switch with two stages of polarization selective elements has been presented in our previous study. Based on this nonblocking 4×4 optical switch, we propose a strictly nonblocking network structure which features even lower system insertion loss than those of a double-layer network and a Beneš network. The signal-to-noise ratio of the proposed network structure is a constant, and is higher than the constraint, although it is lower than that of the double-layer network. The number of major components of the proposed network is less than that of a double-layer network and larger than that of a Beneš network, since a Beneš network is rearrangeably nonblocking. We also offer a routing algorithm for the new proposed network; the time complexity of the routing algorithm is O(1).     

Performance analysis of nonblocking packet switch with input andoutput buffers

The performance of nonblocking packet switches such as the knockout switch and Batcher banyan switch for high-speed communication networks can be improved as the switching capacity L per output increases; the switching capacity per output refers to the maximum number of packets transferred to an output during a slot. The N×N switch with L=N was shown to attain the best possible performance by M.J. Karol et al. (1987). Here a N×N nonblocking packet switch with input and output buffers is analyzed for an arbitrary number of L such that 1⩽L⩽N. The maximum throughput and packet loss probability at input are obtained when N=∞     

Nonuniform sequential sampling for signal analysis

New electronic technologies for signal analysis raise the possibility of sampling very rapidly, with a time-varying density, and determining empirically both the sampling rate and the window width as the signal evolves in time. These opportunities also point to the possibility of sequentially sampling in a time-varying way in more traditional problems. Motivated by these ideas, we establish a sampling formula, valid in cases where both sampling rate and window width may be varied. The formula states that, in terms of the ways in which these quantities should alter with time, optimal performance is achieved when the window width is inversely proportional to squared sampling rate, and sampling rate is directly proportional to squared bias.     

Throughput analysis, optimal buffer allocation, and trafficimbalance study of a generic nonblocking packet switch

A general model is presented to study the performance of a family of space-domain packet switches, implementing both input and output queuing and varying degrees of speedup. Based on this model, the impact of the speedup factor on the switch performance is analyzed. In particular, the maximum switch throughput, and the average system delay for any given degree of speedup are obtained. The results demonstrate that the switch can achieve 99% throughput with a modest speedup factor of four. Packet blocking probability for systems with finite buffers can also be derived from this model, and the impact of buffer allocation on blocking probability is investigated. Given a fixed buffer budget, this analysis obtains an optimal placement of buffers among input and output ports to minimize the blocking probability. The model is also extended to cover a nonhomogeneous system, where traffic intensity at each input varies and destination distribution is not uniform. Using this model, the effect of traffic imbalance on the maximum switch throughput is studied. It is seen that input imbalance has a more adverse effect on throughput than output imbalance     

Wide-sense nonblocking multicast in a class of regular optical WDMnetworks

Multicast communication involves transmitting information from a single source node to multiple destination nodes, and is becoming an important requirement in high-performance networks. We study multicast communication in a class of optical WDM networks with regular topologies such as linear arrays, rings, meshes, tori and hypercubes. For each type of network, we derive the necessary and sufficient conditions on the minimum number of wavelengths required for a WDM network to be wide-sense nonblocking for multicast communication under some commonly used routing algorithms     

On the CNET: a rearrangeable nonblocking optical interconnection network

A planar, circular, rearrangeable nonblocking optical switching architecture using N(N-1) Ti:LiNbO/sub 3/ directional coupler switches is suggested. Various figures of merit such as the signal-to-crosstalk ratio (SXR), insertion loss and fault tolerance are presented. The outline for a distributed routing algorithm in O(N) time is given.<>     

Offiine traffic analysis system based on Hadoop

Offiine network traffic analysis is very important for an in-depth study upon the understanding of network conditions and characteristics, such as user behavior and abnormal traffic. With the rapid growth of the amount of information on the Intemet, the traditional stand-alone analysis tools face great challenges in storage capacity and computing efficiency, but which is the advantages for Hadoop cluster. In this paper, we designed an offiine traffic analysis system based on Hadoop （OTASH）, and proposed a MapReduce-based algorithm for TopN user statistics. In addition, we studied the computing performance and failure tolerance in OTASH. From the experiments we drew the conclusion that OTASH is suitable for handling large amounts of flow data, and are competent to calculate in the case of single node failure.     

基于IPFIX的网络流量日志系统

针对高速网络海量数据采集、存储和管理问题,分析了传统IPFIX流量日志系统在高速网络中的性能问题,提出了基于IPFIX协议的用户网络流量日志系统体系结构的优化设计,改进了数据聚类和存储算法,包括二元归并方式采集数据以及多层结构的散列算法存储数据。经校园网部署应用证明,可提供万兆链路下用户网络日志详单及准确上网流量计量值。     

Non-uniform traffic analysis on unbuffered banyan-type networks

Unbuffered banyan-type networks (BTNs) have been analysed in several studies with ad hoc models applicable only to the specific traffic pattern and BTN considered. The authors describe a generic model without such restrictions and show that the performance of topologically equivalent BTNs may differ significantly under non-uniform traffic     

Nonuniform currents on a wedge illuminated by a TE plane wave

Closed-form expressions for nonuniform currents on a perfectly conducting, infinite wedge illuminated by transverse electric (TE) plane wave are presented. These expressions are derived by requiring that they coincide with the current predicted by the asymptotic diffraction method far from the edge and, further, that they agree with the current predicted by the eigenfunction solution at the edge. The angle of incidence is arbitrary and our expressions remain valid even for glancing angles of incidence when either one or both faces of the wedge are in the vicinity of a geometric optic (GO) boundary. Formulas presented here are simple involving the well-known modified Fresnel functions but are not uniform. Exact expressions for nonuniform currents are available for the two special cases of half-plane and infinite plane. For these special cases, our solution reduces to the exact solution. Currents computed using the expressions developed here are compared with currents computed from the eigenfunction solution of the wedge. Good agreement is obtained throughout.     

Performance trade-offs in input/output buffer design for a non-blocking space-division packet switch

Performance trade-offs in buffer architecture design for a space-division packet switching system is studied. As described in Figure 1, the system is constructed by a non-blocking switch fabric and input/output buffers. The capacity of the non-blocking switch fabric is defined by the maximum number of packets, denoted by m, which can be simultaneously routed from multiple inputs to each output. The buffer size at each input is considered to be finite, equal to K. The emphasis here is placed on the input packet loss probability for systems constructed by different ms and Ks. From the performance point of view, we conclude:

• (a) choosing m = 3 or 4 is sufficient to exploit the maximum utilization of a non-blocking switch fabric
• (b) introducing input buffers of moderate size K significantly reduces the packet loss probability.

     

Studies on semiconductor optical amplifiers for line capacityexpansion in photonic space-division switching system

The problems associated with introducing traveling wave amplifiers (TWAs) to photonic space-division (SD) switching systems are examined. Experiments were carried out to clarify the TWA noise effect and interference between cascaded TWAs, using about 10-dB gain TWA modules. Possibility of a 128-line photonic SD switching system, using current polarization-independent LiNbO₃ 8×8 switch matrices, has been shown through the experiments. The possible line capacity value of the photonic SD switching system with TWAs is examined theoretically. It is shown that the expected line capacity value for such a switching system exceeds 10³     

NONUNIFORM CURRENTS ON A CONDUCTING WEDGE ILLUMINATED BY A TM PLANE WAVE

Closed-form expressions for nonuniform currents induced on a perfectly conductinginfinite wedge illuminated by a TM plane wave are presented.Results computed by using theseexpressions are in good agreement with ones of the eigenfunction solution of the wedge.     

Wavelet analysis of long-range-dependent traffic

A wavelet-based tool for the analysis of long-range dependence and a related semi-parametric estimator of the Hurst parameter is introduced. The estimator is shown to be unbiased under very general conditions, and efficient under Gaussian assumptions. It can be implemented very efficiently allowing the direct analysis of very large data sets, and is highly robust against the presence of deterministic trends, as well as allowing their detection and identification. Statistical, computational, and numerical comparisons are made against traditional estimators including that of Whittle. The estimator is used to perform a thorough analysis of the long-range dependence in Ethernet traffic traces. New features are found with important implications for the choice of valid models for performance evaluation. A study of mono versus multifractality is also performed, and a preliminary study of the stationarity with respect to the Hurst parameter and deterministic trends     

Mathematical framework towards the analysis of a generic traffic marker

DiffServ architecture has been widely adopted for the provision of QoS over the Internet. This makes the full understanding of its operation imperative. We believe that only mathematical analysis may have the power of such goal. As the heart of a DiffServ router is the token bucket algorithm, a generic one, with two‐colours marking, is to be considered here. A mathematical framework will be first developed for its analysis. Then, assuming an input traffic with Poisson arrivals and Exponential packet lengths, and a memoryless token bucket system, the two types of generated streams will be statistically characterized through their distributions and averages. This analysis will be carried out for two types of buckets, one with infinite size and a second with finite size. It will be shown how the derived equations will allow the prediction of the output traffic streams for given bucket and input traffic stream parameters. The paper will be then complemented by conclusions and suggestions. Copyright © 2006 John Wiley & Sons, Ltd.