BENNET, C.V., SCOTT, E.P., and KOLNER, B.H.: ‘Temporal magnification and reversal of lOOGbis optical data with an upconversion time microscope’, Appl. Phys. Lett., 1994, 65, (20), pp. 2513-251 5 5 COPPINGER, F., BHUSHAN, A.S., and JALALI, B.: ‘Time magnification of electrical signal using chirped optical pulse’, Electron. Lett., 1998, 34, (4), pp. 399-400
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ABR performance in presence of bursty TCP traffic J.R. Vidal, J. Martinez and L. Guijarro The available bit rate (ABR)service class is a solution for the integration of data traffic in asynchronous transfer mode networks. Many algorithms have been proposed to implement ABR services. The authors present simulation results showing poor performance by a common ABR algorithm when supporting TCP bursty traffic. As a solution to this problem, the authors propose time averaging of the parameters calculated by the ABR
algorithms.
Introduction: Asynchronous transfer mode (ATM) is the generally accepted switching technology for the support of broadband integrated services digital networks. One of the services to be integrated is data service, which conveys random and bursty traffic. To efficiently manage data traffic in ATM networks, the ATM Forum has proposed two service categories: UBR (unspecified bit rate) and ABR (available bit rate) [l]. ABR is currently considered the most promising solution because of its ability to share the changing available network bandwidth with a low cell loss rate. Nevertheless, it is not proven that ABR is the best choice for data applications because it has not yet been tested in completely realistic environments. ABR performs congestion control by means of a closed loop of resource management (RM) cells. This loop starts at the source, goes forward to the destination along the virtual connection path, and returns to the source. Returning RM cells collect information about the network state. Depending on this information, the source must limit its cell rate emission, according to a standard protocol. Several algorithms have been proposed to compute the information to be written into the RM cells for the switches [2]. ABR performance has been evaluated under different conditions, including persistent and modulated sources, as well as TCP sources [3]. For every traffic burst, an ABR connection operates in two phases: open loop and closed loop. The loop is open from the start of transmission until the first RM cell arrives at the source. From this moment, the connection is in closed loop. ABR algorithms are designed and tested to operate in closed loop, but the assumption that ABR connections will remain in closed loop most of the time is not always realistic. If an ABR connection conveys traffic bursts with a shorter transmission time than the connection round trip time (RTT), then it will operate in open loop. With this kind of traffic, ABR algorithm behaviour may be very different from that seen in closed loop, with its performance worse, as we show below.
a loss segment is detected, and opens it gradually after the reception of new ACKs. In the slow start phase, TCP generates short traffic bursts with RTT millisecond periodicity.
ABR instability: During the open loop phase, an ABR source has no information about the network state. Thus, if some connections operate for a long time in open loop, the ABR algorithm can become unstable. This situation arises when sources emit bursty traffic, as TCP sources do during the slow start phase. If the bursts are shorter than RTT, then when a source receives RM cells, the burst has already ended. According to the ABR source behaviour, however, this information can be used erroneously in the next burst. This is what causes instability, because this information does not refer to the present state of the network. This instability can be observed in the simulation results shown below. They correspond to a configuration of two switches, connected by a l O O k m trunk link at 150Mbit/s, and five terminals connected to each switch by lOOkm links. At the terminals, TCP is running and using ABR connections. There is a TCP connection between each pair of terminals on one side and the other. All of these connections convey unidirectional data traffic. The TCP transmission window is set to equal the product delay bandwidth, so the transmission rate is limited only by the link rate. In the switch, ABR is implemented by the ERICA algorithm [4]. This algorithm computes the arrival cell rate to each output port (ZR),measuring the arriving time of 60 cells, and counts the number of active connections N. A target rate TR of 90% of available bandwidth is defined. For each port, it calculates an ‘overload factor’ of = ZRITR, and a ‘fair cell rate’ CR, = T N N . When a backward RM cell arrives, then its explicit rate information is clipped to the maximum of CCRiof and CR, CCR is the connection current cell rate, carried by the forward RM cells. This algorithm leads, in most situations, to an accurate fair sharing of the target rate between the active connections. I5t
Fig. 1 Link cell rate filtering without parameters _ _ _ _ filteringwith parameters
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ABR with TCP traffic: The bursty profile of data traffic can be caused not only by the application demand patterns, but also by congestion control mechanisms in the upper layer protocols running in most legacy nets. In particular, TCP can cause this bursty traffic, leading the ABR connection to operate mostly in open loop. TCP uses a window mechanism to control flow and avoid congestion. It does not use the network state information from lower layers, but obtains an estimation of the network state from ACK messages. Thus, network congestion is perceived by TCP only when packets are lost, which means a delay of at least one RTT. To cope with this uncertainty about the current network state, TCP implements a number of preventive mechanisms. The most important of these from the point of view of ABR, is the slow start mechanism. Slow start closes the transmission window when
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In the simulations shown, the five connections sharing the link are in steady state until t = 500ms. At this time, the link capacity is reduced to one half, as seen in Fig. 1. This causes a transitory in
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the ABR control mechanism, filling the output port queue, as seen in Fig. 2. To study the performance with cell losses, the queue is limited to 100 cells. So, during the transient period, cells are discarded. In Fig. 3, the traffic emitted by one of the sources is plotted as a solid line. After the queue overflow at t = 500ms, the source emits persistent trafic for some milliseconds, until it detects a packet loss. Then TCP enters in slow start phase, emitting a traffic burst every RTT (3ms). The early bursts are shorter than the RTT, causing the instability described above. The result is that, after some RTTs, the queue overflows again (Fig. 2), and TCP retransmits, repeating a similar traffic pattem. Because the fair rate calculated at the switch is inaccurate, the system cannot stabilise using this queue capacity. In Fig. 1, the solid line shows that the traffic link is under-used.
References 1 Technical Committee ATM-Forum. Traffic Management Specification. Version 4.0. Technical Specification, ATM Forum, 1996 2 ARULAMBALAN, A., and CHEN, x : ‘Allocating fair rates for available bit rate service in ATM networks’, IEEE Commun. Mag., November 1996, pp. 92-100 3 HASEGAWA, G , OHSAKI, H , MURATA, M , and MIYAHARA, H : ‘Performance of TCP over ABR service class’. GLOBECOM’96, 1996 4 JAIN, R : ‘ERICA switch algorithm: A complete description’. Contribution AF/96-01172,ATM Forum, 1996
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Asymptotically exact computation of differential cepstrum using FFT approach
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A new concept of the differential cepstrum calculation is presented which uses the FFT with interpolation in the frequency domain. The algorithm assures asymptotically exact values, without cepstral aliasing. It completely separates the causal and the anticausal part of the cepstrum and it does not suffer from signal singularities, i.e. zeros on the unit circle in the z-plane. The algorithm’s computational complexity i s at least four times lower than for any other cepstral aliasing reduction method, while no extended memory signal buffer is required.
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ABR parameter Jiltering: The effect described above occurs because, when the traffic is bursty, the instantaneous measurement obtained by the ABR switch algorithm is too random to be significant. Therefore, the exact fair rate cannot be calculated for a time shorter than the RTT. The effect of t h s indetennince is the oscillation of port parameters of and ER, To solve this problem, we propose extension of the measurement interval to longer than RTT ms. This can be achieved by time-averaging the port parameters. In the simulations shown here, we have implemented this time-average function by filtering both parameters with the function y[z]= (1 a)y[i 11 + ax[z] (0 < a < 1). The a factor chosen is low enough to eliminate at least those frequency components higher than 1RTT Hz. The dashed lines in Figs. 1 and 3 show the result of a simulation of the former scenario, fdtering with a = 0.1. Fig. 3 shows that, after the queue overflow at t = 500ms, the sources restart transmitting in bursts. In this case, however, the system stabilises after the slow start phase, resulting in a better use of the available bandwidth, as seen in Fig. 1. ~
Introduction: Many practical problems are known where solutions in the cepstral domain have proved beneficial, e.g. echo cancellation, image deblurring [2], deconvolution of basic building blocks in geophysics, sonar, speech [2, 11, biomedical engineering [5], and, lately, also in system identification [4]. From a computational point of view, the differential cepstrum is the most convenient for signal transforms to the cepstral domain. However, its inherent cepstral aliasing caused by the FFT calculation algorithm may, in reality, totally ruin the results. So far, the only way to reduce cepstral aliasing has been by prolongation of the processed signals to multiples of their lengths by padding them with zeros. In this Letter, we introduce a new concept of the differential cepstrum.
~
Conclusions: With the ABR service class, traffic congestion control is effective only while the RM cell loop is closed. However, TCP data traffic can consist of short bursts, causing ABR to work in open loop. This results in a loss of performance. In the simulations shown here, the ERICA algorithm is used, but these results could be generalised to all ABR switch algorithms which try to calculate the exact fair cell rate in a short measurement interval, and pass this information quickly to the sources. To cope with the burstiness of data traffic, these algorithms should fdter their estimations in some way, and send more conservative values to the sources. As the traffic pattems described here are likely to be common in real systems, a filtering of the estimations similar to that described in this paper is necessary.
Differential cepstrum with interpolation: Let x(n) be an exponential sequence of the moving-average (MA)type, and X(z) its factorised z-transform:
where A denotes a scale factor, KO
IT (-L)
A =~ ( 0 )
bk
k=l
r denotes a delay, r = %, and ak and b,, denote inner and K , outer zeros, respectively (la,l, lbkl all < 1). We showed in [3] that a deconvolution of two signals carried out with their interpolated frequency-domain samples only, exhibits several advantages. The sequence of interpolated samples is obtained via the time-domain where i denotes the interpolation operation, x,,,(n) = x(n) level and m stands for the sample location inside the interpolation intervals in the frequency domain. Such a sequence enables a new definition of the so-called interpolated dfierential cepstrum [6]:
wr,
Acknowledgment: This work has been supported by CICYT, TIC 96-0680. 0 IEE 1998 27 February 1998 Electronics Letters Online No: 19980635 J.R. Vidal, J. Martinez and L. Guijarro (Departamento de Comunicaciones, Universidad PolitCcnica de Valencia, Cami de Vera S/ N 46071, Valencia, Spain)
Practically feasible computation will be carried out by the D I T in the following way:
E-mail:
[email protected]
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