Kotikalapudi Sriram and Ward Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, SAC4 (6):833--846, September 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the emergence voice over IP, i.e. the emulation of telephony service on a packet network that is based on the Internet protocol. It is not hard to see that the number of packets per burst is typically not very large: activity periods can be thought of as of the order of 0.5 s, cf. 22, p. 26] and [25], while packets in IP are of the order of a few hundred bytes. For example, with a peak rate of 32 kbit s this leads to a burst size of 5 to 10 packets. As the number of packets per burst is small, fluid models (that ignore the packet nature of the streams) are not very accurate consequently ....

....and a burst scale they distinguish a call scale, i.e. the time scale on which customers enter and leave. In our study the number of customers is held fixed. Literature. Combined packet burst models attracted attention in the context of ATM networks, in the late 1980s and the early 1990s see [19, 25] and the references therein. With the advent of voice over IP the subject regained relevance [9] particularly because fluid approximations tend to be not very accurate (due to the larger packet size in IP compared to ATM) The key performance measure is the overflow probability, which we will ....

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$. SRIRAM AND W. WHITT. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, 4:833 - 846, 1986.

....explanation of the material presented; see for instance [15] The main reference for the MMPP process is K. Meier s thesis [11] which includes formal tests of fit, but references [6, 12, 17] are also informative. The analysis of arrival processes using indices of dispersions is proposed in [5, 9, 20]. These studies, however, deal for the most part with processes measured in the context of telephone communication, i.e. packetized voice data. Heffes and Lucantoni [9] propose a fitting procedure for the superposition of packetized voice processes to an MMPP process. Their characterization ....

Sriram, K. and W. Whitt, Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data, IEEE Journal on Selected Areas in Communications SAC-4, 7 (September 1986), 833-846.

....1. VolP System A. Components of the VolP system Speech is an analog signal that varies slowly in time (with bandwidth not exceeding 4KHz) The speech signal alternates between talkspurts and silence periods, which are typically considered to be exponentially distributed; Sriram and Whitt in [2] used mean 352 ms for talkspurts and 650 ms for silences. For the purpose of transmission over networks, the speech analog signal is converted into a digital signal at the sender; the reverse process is performed at the receiver. In an interactive conversation, the participating parties switch ....

K. Sriram, W. Whitt, 'Characterizing superposition arrival processes in packet multiplexers for voice and data", IEEE Journal on Selected Areas on Communications, SAC-4(6): 833-846, September 1986.

....where the authors show, after exhaustive measurements on an Ethernet network at Bellcore (NJ, USA) that the nature of the traffic is self similar or fractal . The main characteristic of this traffic is the presence of correlation over a wide range of time scales. Although Sriram and Whitt [29] had already observed an exceptional positive long term correlation in the aggregated traffic, and obtained delays much higher than the predicted with Poisson models, we must note that the importance of the self similar models is due to their capacity of exhibiting long range dependence over all ....

K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, 4:833--846, 1986.

....and receivers are assumed to be negligible. We assume that voice silence suppression is activated in the codecs and, therefore, each voice source in the simulations can be modeled as a simple two state variable bit rate ON OFF source, a traffic model extensively used in standard voice sources [19]. This source generates audio frames of size and in the ON (active) and OFF (idle) state, respectively. We let the ON and OFF state durations be distributed exponentially with means 352 ms and 650 ms, which are commonly used values in modeling phone calls [20] The frame generating instants of ....

K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE J. Select. Areas Commun., vol. SAC-4, pp. 833--846, Sept. 1986.

....that possesses high bit rate fluctuations over relatively short time frames. It has been reported in [11] that VBR traffic is highly bursty, non stationary and correlated. Compared to a Poisson process which has a small squared coefficient of variation, C, the VBR traffic has been reported in [10] to have C = 18.1 for a packet arrival process due to a single voice source. Considering the fact that the typical VBR traffic will consist of a superposition of N voice sources[20] we can therefore expect that for the short term, this superposition will resemble very much a Poisson process. In ....

K. Siriram, and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for 1986

.... Network (B ISDN) has led to an intense concentration of research efforts on technologies which allow for traffic multiplexing, such as the Asynchronous Transfer Mode (ATM) Performance evaluation of statistical multiplexers under a variety of input processes and or service policies (see [1] [2], 3] 4] 5] 6] and the references therein) has been essential in determining the achievable effectiveness of statistical multiplexing. The development of efficient congestion control and call admission procedures is an area in which multiplexing analysis and network traffic characterization ....

K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Select. Areas Commun., Sept. 1986.

....not developed for Gaussian inputs. We then consider non Gaussian input sources and compare our MVA approximation for loss with other approximations in the literature. Specifically, we consider MMF sources which have been used as representative of voice tra#c in many different papers (e.g. 34] [35]) and also consider JPEG and MPEG video sources that have been used in other papers in the literature (e.g. 20] 36] A. Gaussian Processes We begin by considering the simple case when the input is a Gaussian Autoregressive (AR) process with autocovariance C # (l) 258 0.9 l (note that ....

....in [39] Ave Peak, the analytical technique developed in [24] Hybrid, and the famous e#ective bandwidth scheme Effective BW [40] We now consider the practically important case of multiplexed voice sources. The input MMF process, which has widely been used to model voice tra#c source [34] [35], has the following state transition matrix and rate vector: State transition matrix : 0.9833 0.0167 0.025 0.975 Input rate vector : 0 cells slot 0.85 cells slot These values are chosen for a 45 Mbps ATM link with 10 msec time slot and 53 byte ATM cell. In this example, we assume ....

K. Sriram and W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexer for Voice and Data," IEEE Journal on Selected Areas in Communications, vol. 4, pp. 833-- 846, Sep. 1986.

....an ATM environment. The problem of characterizing the superposition process of a set of arrival processes has been addressed extensively in the literature. One approach for obtaining the superposition process is to approximate it by a renewal process, see Albin [1] Whitt [27] Sriram and Whitt [22], and also Perros and Onvural [19] An insightful discussion of the various time scales affecting the accuracy of the approximate superposition of packet voice sources (modeled as a variant of IBP) was provided in [22] Heffes and Lucantoni [10] considered the superposition process of packet voice ....

.... approximate it by a renewal process, see Albin [1] Whitt [27] Sriram and Whitt [22] and also Perros and Onvural [19] An insightful discussion of the various time scales affecting the accuracy of the approximate superposition of packet voice sources (modeled as a variant of IBP) was provided in [22]. Heffes and Lucantoni [10] considered the superposition process of packet voice sources modeled as an IBP where arrivals occur periodically. They approximate the superposition by a Markov Modulated Poisson Process (MMPP) The accuracy of the superposition is reasonable when the average delay in ....

K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, 6:833--846, 1986.

....real traffic stream. We also point out that it it is not practical to seek a perfect model and that a consensus around a model such as the M Pareto is important. 1 Introduction Over the past two decades there were many proposals for broadband and or multimedia traffic models (see, for example [2, 5, 6, 7, 8, 9, 11, 14, 15] and references therein) Despite the extensive effort to find a perfect model, there is still no consensus on a traffic model which is used by all practitioners for analysis and performance evaluation of new products and protocols, and for network dimensioning. There is no model which fills the ....

K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, Vol. SAC-4, No. 6, September 1986, pp 833-- 846.

....detector output. We are mainly interested in how much bandwidth utilization gain can be achieved by multiplexing, and what packet loss rate is introduced by the multiplexer for a particular utilization gain. Previous studies on the performance of voice traffic multiplexers [5] 15] 7] 11] [20] assume that the length of spurts and gaps follow an exponential distribution [2] 3] 4] Since most of these speech measurements are based on either analog or simple digital silence detectors [2] This work is supported by research grants from Hewlett Packard Labs [3] 4] 8] we suspected ....

....mean spurt and gap length can fall into two regions. If T is 0 or very small, mean spurt is around 200 to 400 ms, and the mean gap is around 500 to 700 ms. If T is around 200 ms, most short gaps are eliminated, and both the mean spurt and gap will be on the order of 1 to 2 sec. Sriram and Whitt [20] quote 1 a mean spurt of 352 ms and a mean gap of 650 ms. Apparently this correspond to 0 or a small hangover. The ITU P.59 [12] recommendation specifies an artificial on off model for generating human speech. It specifies a mean spurt of 227ms and a mean gap of 596 ms without hangover, and a ....

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Kotikalapudi Sriram and Ward Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, SAC-4(6):833--846, September 1986.

....an ATM environment. The problem of characterizing the superposition process of a set of arrival processes has been addressed extensively in the literature. One approach for obtaining the superposition process is to approximate it by a renewal process, see Albin [1] Whitt [16] Sriram and Whitt [12], and also Perros and Onvural [11] An insightful discussion of the various time scales affecting the accuracy of the approximate superposition of packet voice sources (modeled as a variant of IBP) was provided in [12] Heffes and Lucantoni [6] considered the superposition process of packet voice ....

.... approximate it by a renewal process, see Albin [1] Whitt [16] Sriram and Whitt [12] and also Perros and Onvural [11] An insightful discussion of the various time scales affecting the accuracy of the approximate superposition of packet voice sources (modeled as a variant of IBP) was provided in [12]. Heffes and Lucantoni [6] considered the superposition process of packet voice sources modeled as an IBP where arrivals occur periodically. They approximate the superposition by a Markov Modulated Poisson Process (MMPP) The accuracy of the superposition is reasonable when the average delay in ....

K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, 6:833--846, 1986.

....that p = n 1 n . This fact implies that the ON periods have a expected value of = nT , where n is the expected value of the number of packets in a talk spurt. We assume that the OFF periods are exponentially distributed with mean , which is well documentedand discussed by Sriram and Whitt [15]. A voice source may be viewed as a two state birth death process with birth rate and death rate . The OFF state represents the idle periods and the ON state represents the talk spurts. While in a talk spurt, packets are generated with a rate of 1 T packets per second. IPTEL2001 5 Exp(1 T) ....

....simply add the intensities of the sources that are currently in a talk spurt and receive a new Poisson process for the superposition. To validate the accuracy of approximating with a MMPP process, we calculated the index of dispersion of intervals (IDI) using a formula from Sriram and Whitt [15]. The IDI, also called the squared coefficient of variation, gives us some measure of how similar the traffic is in terms of burstiness. A value of 1 shows the traffic is as bursty as Poisson traffic, whereas a value as 18 is the burstiness of a single voice source. The high value accounts for the ....

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Kotikalapudi Sriram and Ward Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, SAC-4(6):833--846, September 1986.

....I [A i 2k] 6 Numerical Example Consider trac from a number of 13 Kb s voice sources traversing a TDMA based wireless downlink. Each voice source is modeled statistically using a two state Markov chain with a voice activity factor of 40 . This voice source model is derived from the model in [13] for 32 Kb s packetized voice by scaling down the peak rate in the active state of the source. The nominal channel model for all connections is the Rayleigh model for frequency non selective fading with a (maximum) Doppler frequency of 50 Hz. We assume packetized transmission in terms of ATM ....

K. Sriram and W. Whitt, \Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE J. Select. Areas Commun., vol. SAC-4, no. 6, pp. 833-846, September 1986. 23

....we only need to check whether PfXn 0j Delta; Q 0 g a:s: Kn Gamma(1 ffi) for all n MQ ff 0 on fQ 0 x 0 g. For simplicity of illustration, we first check the two state MMF on off processes (these processes have widely been used to model voice traffic sources in telecommunication systems [8, 20], and are hence important in their own right) Without loss of generality, let r 1 = 0 and r 2 = 1. Since the process is stationary and ergodic, it has a unique stationary distribution, i.e. for each fixed j, the (i; j) th element of A n converges to the same value for all i. Then, 0 a ii 1 ....

Sriram, K. and Whitt, W. (1986). Characterizing Superposition Arrival Processes in Packet Multiplexer for Voice and Data. IEEE Journal on Selected Areas in Communications 4, 833--846.

....and Var[rs(m) respectively, and are evaluated for increasing values of m. The ratio of the variance and the expectation of rs(m) is referred to as the index of dispersion for counts. This is a second order descriptor that has been used to capture the burstiness properties of arrival processes [29]. It allows one to quantify the deviation of the source traffic from being a Poisson or a renewal process. A comparison of the results from the simulation and the measured data is depicted in Figures 6 and 7. Figures 6 show the QQ plots and Figures 7 depict the variations of E[rs(m) and ....

K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE J. Select. Areas Commun., vol.6, p833-846, 1986.

....that distribution. However, in practice the peak to mean ratio and the squared coefficient of variation are the most frequently used first order measures in the teletraffic literature [5, 18] Measures expressing second order properties of the traffic are more complex. The indices of dispersion [7, 20] and the generalized peakedness [2, 3] are the most well known measures from this class. The indices of dispersion measures include the correlation properties of the traffic and can be very informative [7] The generalized peakedness measure, which gives a complete second order characterization of ....

K. Srivam, W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE Journal on Selected Areas in Communications , Vol. 4, No. 6, September, 1986.

....time distribution. In practice the peak to mean ratio and the squared coefficient of variation are the most frequently used first order measures [13, 15] Measures expressing second order properties of the traffic are more complex. The autocorrelation function, the indices of dispersion [4, 18] and the generalized peakedness [2, 3] are the most well known measures from this class. c flIFIP 1996. Published by Chapman Hall 2 Peakedness Characterization in Teletraffic Moreover, there are a number of burstiness measures based on different concepts, e.g. we can use burst length measures ....

K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers fo voice and data. IEEE Journal on Selected Areas in Communications, 4(6), September 1986.

....of that distribution. However, in practice the peak to mean ratio and the squared coefficient of variation are the most frequently used first order measures in the teletraffic literature [4, 15] Measures expressing second order properties of the traffic are more complex. The indices of dispersion [6, 17] and the generalized peakedness [2] are the most well known measures from this class. The indices of dispersion measures includes the correlation properties of the traffic and can be very informative [6] The generalized peakedness measure, which gives a complete second order characterization of ....

K. Srivam, W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE Journal on Selected Areas in Communications , Vol. 4, No. 6, September, 1986.

....on the link is high and the number of streams multiplexed on the link low. On the other hand, 9] 21] and [29] found that in the case of lightly utilized high speed links, where the utilization is low and the number of streams multiplexed exceeds 100, and yield similar results. [31] studied the effect of Speech Activity Detection (SAD) that is, silence suppression) on voice delay: it was found that the increase in traffic variability that results from the inclusion of SAD in the encoding process hinders the advantage that is obtained from the reduction in average ....

....protocol layers, the rate of the packetized voice stream remains in the order of tens of Kilobits per second, which is much lower than the data rates that correspond to typical video and data traffic. In addition, speech consists of an alternation of talk spurts and silence More specifically, [31] found that the queuing delay resulting from an model in which the rate of the incoming (Poisson) process is set equal to the average incoming rate of voice traffic heavily underestimates the delay incurred by voice traffic in the network. Fig. 1. End to end delay components for voice ....

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K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE Journal on Selected Areas in Communications, Vol. SAC-4, No. 6, pp. 833-46, Sept. 1986.

....on the model presented in the paper for all models and provide diagrams on the performance parameters. 5 Numerical Example The models are demonstrated on an ATM multiplexer with ON OFF type voice input channels with mean talkspurt duration 1 =352ms and mean silence duration 1 =650ms [12]. The output channel is assumed to be T1 line with a rate of 1.536Mbps. Taking into account that each ON source generates data with rate 64kbps and each 47 Byte should be encapsulated into 53 Byte cell by AAL1, the source speed will be 72,17kbps and thus C=21. With these values the time unit is ....

K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Selected Areas on Communications, SAC4 (6):833-846, 1986.

....4 Numerical example Begain et al. demonstrated the calculation of the performance parameters on the following example [1] They examined an ATM multiplexer, to which voice transmission input lines were connected. The mean talkspurt time was chosen to be 352 ms, while the mean silence time 650 ms [6]. In this paper the optimal and pessimal cell arrival schedules and the corresponding performance parameters are calculated for the parameter values C = 10, N = 12; 15; 18; 21, for various bu er lengths. These values are less than the ones used by Begain et al. because the same parameter value ....

K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Selected Areas on Communications, SAC-4(6):833-846, 1986. 10

....a source which is either in an on state, transmitting at its peak rate, or in an off state, transmitting at zero bit rate. The durations of the on and the off states are assumed to be exponentially distributed random variables. When this model is used to describe a packet voice source [19, 20, 21, 22], the source will stay in the on state for an average of 352 msec, transmitting at 32 Kbps, or stay in the off state for an average of 650 msec, transmitting at zero bits per second. Based on this two state fluid flow model, a traffic source can be described by three parameters: its peak rate, ....

K. Sriram and W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data," IEEE Journal on Selected Areas in Communications, vol. 4, pp. 833--846, September 1986.

....a source which is either in an on state, transmitting at its peak rate, or in an off state, transmitting at zero bit rate. The durations of the on and the off states are assumed to be exponentially distributed random variables. When this model is used to describe a packet voice source [27, 46, 65, 78], the source will stay in the on state for an average of 352 msec, transmitting at 32 Kbps, or stay in the off state for an average of 650 msec, transmitting at zero bit rate. Based on this two state fluid flow model, a traffic source can be described by three parameters: its peak rate, r ....

Sriram, K. and Whitt, W. Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, 4:833--846, September 1986.

....detector output. We are mainly interested in how much bandwidth utilization gain can be achieved by multiplexing, and what packet loss rate is introduced by the multiplexer for a particular utilization gain. Previous studies on the performance of voice traffic multiplexers [5] 15] 7] 11] [20] assume that the length of spurts and gaps follow an exponential distribution [2] 3] 4] Since most of these speech measurements are based on either analog or simple digital silence detectors [2] This work is supported by research grants from Hewlett Packard Labs [3] 4] 8] we suspected ....

....mean spurt and gap length can fall into two regions. If # is 0 or very small, mean spurt is around 200 to 400 ms, and the mean gap is around 500 to 700 ms. If # is around 200ms, most short gaps are eliminated, and both the mean spurt and gap will be on the order of 1 to 2 sec. Sriram and Whitt [20] quote 1 a mean spurt of 352 ms and a mean gap of 650ms. Apparently this correspond to 0 or a small hangover. The ITU P.59 [12] recommendation specifies an artificial on off model for generating human speech. It specifies a mean spurt of 227 ms and a mean gap of 596 ms without hangover, and a ....

[Article contains additional citation context not shown here]

Kotikalapudi Sriram and Ward Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, SAC-4(6):833--846, September 1986.

....coefficient of variation, c X , since they take into account the autocorrelation function, ae X (j) as well. In fact, for renewal traffic, JX (n) j JX = I X = c 2 X . Moreover, these indices of dispersion may be usefully applied to the study of the effect of an offered load on a server system [16, 4, 7]. In practical queueing studies, one uses the indices of dispersion, JX (n) and I X (t) and especially the simpler common limit JX = I X , by estimating their values from empirical observations and then fitting a suitable traffic model, such as a Markov modulated Poisson process (MMPP) which is ....

Sriram, K. and Whitt, W. (1986) "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE J. on Selected Areas in Communications 4(6), 833--846.

....0.050 0.060 Probability of End to End Dynamic Failure DBP M EDF (b) End to End Dynamic Failure Figure 5: Comparison of the EDF and DBP M policies for a voice application. 5. 1 Voice Application The primary voice stream is modeled using a bursty ON OFF model with standard parameters [8, 9]. Specifically, the ON and the OFF times are exponentially distributed with means 352 ms and 650 ms respectively. When a stream is in the ON state the time between packets is 8 ms. When in the OFF state no packets are generated. The packet transmission time is fixed at 1 3 ms to correspond to the ....

S. Kotikalapudi and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE Journal on Selected Areas in Communications, vol. SAC-4, pp. 833--846, September 1986.

....Much queueing theoretic work has been published recently [19,20,21, 22, 23, 24] showing that packet voice is significantly more bursty and ill behaved than Poisson sources. The queueing analysis is also more difficult, and efforts havebeenmadetoshow where simpler models maybeused effectively [25, 26, 27]. These analyses tend to measure performance in terms of expected delayor probability of loss byoverflowing a finite, FIFO buffer. A rich theory exists for these performance measures mainly because they are appropriate for evaluating data networks or arrival of voice calls to a circuit switch. ....

K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE J. Sel. Areas in Commun.,vol. 4, pp. 833--46, September 1986.

....untractable. Therefore, it is necessary to capture its most significant characteristics. Two very important properties are the correlation between the number of cells in the output process in successive slots and the correlation between interdeparture times. Many studies (Heffes Lucantoni 1986, Sriram Whitt 1986) have confirmed the impact of the autocovariance sum on the queueing performance. In particular these studies stress the importance of the Index of Dispersion for Counts (IDC) and the Index of Dispersion for Intervals (IDI) together with their limits. In this paper we study a particular class of ....

....j ) kE[X 1 ] It is also well known that for a process for which the number of arrivals in a slot is renewal, C(k) c 2 1 , for all k 1, where c 2 1 is the squared coefficient of variation of the number of arrivals in a slot. In particular for a Bernoulli process, C(k) 1 p (Sriram Whitt 1986), where p is the probability of generating an arrival in a slot. In contrast to the limit of the correlation of the arraval process of a D MAP, the limit of the IDC is not dependent on the periodicity of the transition matrix D 0 D 1 . The limit of the IDC has a unique value. We give an ....

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Sriram, K. & Whitt, W. (1986), `Characterizing superposition arrival processes in packet multiplexers for voice and data', J. on Selected Areas in Communications SAC-4(6), 833--846.

....sources. This is theoretically supported by the classical limit theorem stating that superpositions of arrival processes, suitably scaled, converge to a Poisson process as the number of component arrival processes increases; e.g. see C , inlar [19] See Heffes and Lucantoni [30] Sriram and Whitt [43] and Fendick, Saksena and Whitt [25] for related performance studies. In contrast, with the effectivebandwidth approximation, the burstiness of n superposed independent and identically distributed sources is the same as for a single source (e.g. see p. 76 of [45] This implies that the ....

....a single source (e.g. see p. 76 of [45] This implies that the effective bandwidth approximation will predict greater congestion for any fixed arrival rate than it should. Nevertheless, there is a case for the effective bandwidths, because previous teletraffic analysis (such as in [25] 30] [43]) did not focus on extremely small loss probabilities such as 10 9 . Such very small loss probabilities naturally suggest that appropriate asymptotics should provide what we want. And the asymptotic analysis associated with effective bandwidths indicates no traffic smoothing. The question, ....

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K. Sriram and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Sel. Areas. Commun. SAC-4 (1986) 833-846.

....when the sources are scaled to keep the total arrival rate fixed. Hence, when the arrival process is a superposition of a large number of independent processes, the asymptotic decay rate alone often does not yield good approximations for tail probabilities. As in previous work on steadystate means [16,20,39], more intricate approximations are evidently needed. Example 6.3 To illustrate how the results extend beyond BMAP arrival processes, we consider the G 0.5 G 2 1 queue, which has G 2 E 2 service times independent of a G 1 2 renewal arrival process. Since the G 1 2 distribution does not have a ....

Sriram, K. and W. Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE J. Sel. Areas Commun., SAC-4 (1986) 833-846.

.... the fact that typically the stationary interval method dictates that c a 2 1, while the asymptotic method can dictate something very different (e.g. c a 2 20) and the actual appropriate value is somewhere in between; see Whitt (1982, 1983, 1985) Albin (1982, 1984) Newell (1984) Sriram and Whitt (1986), Heffes and Lucantoni (1986) Fendick, Saksena and Whitt (1989, 1991) and Fendick and Whitt (1989) Hence, if a given external arrival process to which we wish to assign a variability parameter happens to be such a superposition of non Poisson processes, then it is quite likely to have ....

....4.3 of Whitt (1983) except that c ai 2 (r) and c a 2 (r) in (3) are allowed to depend on r. For superpositions of renewal processes at a single queue, the method here coincides with Whitt (1983) This approximation has already been studied quite extensively; e.g. see Albin (1982, 1984) and Sriram and Whitt (1986). 2.2 Independent Splitting Since independent splitting of a renewal process is exactly a renewal process, it is natural to use the exact formula for the SCV, as in Section 4.4 of Whitt (1983) In particular, if a stream with variability function c 2 (r) is split into n streams, with each ....

Sriram, K. and W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data," IEEE J. Sel. Areas. Commun., SAR-4 (1986), 833-846.

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Kotikalapudi Sriram and Ward Whitt. Characterizing superposition arrival processes in packet multiplexers for voice and data. IEEE Journal on Selected Areas in Communications, SAC4 (6):833--846, September 1986.

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Kotikalapudi Sriram, Ward Whitt, \Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data" IEEE J. Selec. Areas Commun. Vol. SAC-4, NO. 6, September 1986.

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K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data. IEEE Journal on Selected Areas in Communications, 6:833--846, 1986.

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K. Sriram and W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE Journal on Selected Areas in Communications, Vol. SAC-4, No. 6, September, 1986.

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K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexors for Voice and Data. In IEEE J. Select. Areas Commun., volume 4, pages 833--846, 1986.

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K. Sriram and W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data," IEEE Journal on Selected Areas in Communications, vol. 4, no. 6, pp. 833--846, 1986.

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K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE J. Select. Areas Commun., vol. SAC-4, pp. 833--846, Sept. 1986.

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K. Sriram and W. Whitt. Characterizing Superposition Arrival Processes in Packet Multiplexors for Voice and Data. In IEEE J. Select. Areas Commun., volume 4, pages 833--846, 1986.

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Kotikalapudi Sriram, Ward Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", Intergrated Broadband Networks, pp.172

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K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data", IEEE Journal on Selected Areas of Communication, pages 833-846, September 1986,

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K. Sriram, W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE Journal on Selected Areas in Communications, SAC-4(6):833--846, September 1986.

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K. Sriram, W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data", IEEE Journal on selected areas in communications, Vol. SAC- No. 6, September 1986. 13

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K. Sriram, W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data", IEEE JSAC, vol. 4, (6):833-846, Sept.1986.

No context found.

K. Sriram and W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data," IEEE Journal on SelectedAreas in Comm. sac-4, pp. 833#846, 1986.

No context found.

Sriram, K. and Whitt, W. (1986). Characterizing superposition arrival pro- cesses in packet multiplexers for voice and data. IEEE J. Selected Areas Commun., 4, 833-846.

No context found.

K. Sriram, W. Whitt, "Characterizing superposition arrival processes in packet multiplexers for voice and data", IEEE JSAC, vol. 4, (6):833-846, Sept.1986.

No context found.

K. Sriram, W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE J. Select. Areas Commun. , Sept. 1986, pp. 833-846.

No context found.

K. Sriram, W. Whitt, "Characterizing Superposition Arrival Processes in Packet Multiplexers for Voice and Data", IEEE Journal on Select. Areas in Commun., Vol. SAC 4, No. 6, Sept. 1986.

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