K. W. Fendick, V. R. Saksena and W. Whitt. Investigating dependence in packet queues with the index of dispersion for work. IEEE Trans. Commun., 39 (1991) 1231-1244.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by making a renewal assumption on message interarrival time. Limited studies are available in recent years for the queue response to second order input statistics, which is represented by three mutually equivalent functions: index of dispersion, autocorrelation and power spectrum [3] In [4], the index of dispersion is used to describe the dependence of interarrival time and service time, and hence to derive approximations for the performance of an average queue. The autocorrelation function is used to describe the strong time autocorrelation revealed in voice and video traffic, and ....

K.W. Fendick, V.R. Saksena, and W. W. Whitt, "Investigating Dependence in Packet Queues with the Index of Dispersion for Work", IEEE Trans. Commu., Vol. 39, No. 8, Aug. 1991, pp. 1231-1244.

....long range dependence and heavy tailed distributions) has practical implications for a wide range of network design and engineering problems. Traditional Markovian (or more general, short range dependent) input streams to queues are known to impact queueing performance (see for example, [6, 104, 113, 133, 134, 207, 240, 263, 264, 271, 351, 384, 400]) and a range of techniques (e.g. 101, 163, 251, 265, 317, 405] are by now available to quantify these impacts and their implications for network management and control. For example, considerable attention has been paid in the recent past to the problem of call admission control in high speed ....

K. W. Fendick, V. R. Saksena, and W. Whitt. Investigating dependence in packet queues with the index of dispersion for work. IEEE Transactions on Communications, 39:1231--1244, 1991.

.... 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 effective bandwidth approximation will ....

....same as for 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 ....

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K. W. Fendick, V. R. Saksena and W. Whitt. Investigating dependence in packet queues with the index of dispersion for work. IEEE Trans. Commun., 39 (1991) 1231-1244.

....that only approximation appears in the variability parameters. In many cases this aggregation step works quite well, but in some cases it does not. Difficulties with aggregation in the parametric decomposition approximations were noted by Bitran and Tirupati [5] and Fendick, Saksena and Whitt [9] [10]. Bitran and Tirupati point out difficulties with multiple classes and deterministic routing, especially in the low variability context common to manufacturing models. Fendick, Saksena and Whitt point out difficulties with multiple classes and highly variable (e.g. batch) arrival processes ....

....by having an arrival process variability parameter (squared coefficient of variation) c a 2 0.5 when r = 0.5 and c a 2 5.0 when r = 0.9. This difficulty is the motivation for the use of variability functions instead of variability parameters, e.g. the indices of dispersion in [9] [10] and references there (which we will not discuss further here) Whitt [37] shows that multiclass queueing networks with class dependent service times can exhibit relatively complex behavior. In particular, there can be unanticipated large fluctuations in the individual queue lengths due to the ....

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Fendick, K. W., Saksena, V. R. and Whitt, W., "Investigating Dependence in Packet Queues with the Index of Dispersion for Work," IEEE Trans-Commun. 39, 1231-1244 (1991). - R-2 -

....this problem here. We note that the Brownian model approximations in 2 Harrison and Nguyen (1990, 1993) and Dai, Nguyen and Reiman (1994) do directly address this problem. Another problem is properly treating different classes in multi class queueing networks; see Bitran and Tirupati (1988) Fendick, Saksena and Whitt (1989, 1991) and Whitt (1994) For the multi class case, we ideally should have parameters characterizing the arrival process of each class at each queue. We do not address this problem here either; here we consider only the aggregate arrival process at each queue. All two parameter approximation methods ....

.... 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 substantial dependence among its interarrival times. Moreover, even if all ....

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Fendick, K. W., V. R. Saksena and W. Whitt, "Investigating Dependence in Packet Queues with the Index of Dispersion for Work," IEEE Trans. Commun., 39 (1991), 1231-1244.

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K. W. Fendick, V. R. Saksena, W. Whitt, "Investigating Dependence in Packet Queues with the Index of Dispersion for Work", IEEE Trans. Communications 39, 1231-1244, 1991.

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