Investigating dependence in packet queues with the index of dispersion for work

Fendick, Kerry W.; Saksena, V.R.; Whitt, Ward

doi:10.1109/26.134013

Cited by 31 publications

(28 citation statements)

References 21 publications

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“…The dependence in inter-arrival times is either completely ignored by the SI approximation or fully accounted for by the ASY approximation; Albin(1984) and Whitt(1981Whitt( , 1982. This dependence is sometimes critical in queueing performance analysis; Fendick et al(1989Fendick et al( , 1991, and Sriram and Whitt(1986). Moreover, its effect is dependent on traffic intensity at a station; that is, traffic intensity determines the range of relevant lag of autocorrelations.…”

Section: Decomposition Approximation and The Variability Functionmentioning

confidence: 99%

“…However, using SCV as a single measure of the variability of a non-renewal process may result in significant error in the approximation of performance measure. It is shown that the two-moment parametrization that does not account for the autocorrelation is subject to a serious under-approximation of waiting time especially at a bottleneck station in a network with highly variable arrival process or highly variable service process; Fendick, Saksena, and Whitt(1989Whitt( , 1991, Jageman et. al.…”

Section: Introductionmentioning

confidence: 99%

“…This paper proposes a method to refine the variability function with an ad hoc approach to approximate the index of dispersion for intervals(IDI) sequence, i.e. -interval SCV discussed in Fendick et al(1989Fendick et al( , 1991, Sriram and Whitt(1986), and Whitt(1995). Two different cases of tandem networks considered in Whitt (1990a, 1990b) are used for the regression analysis of the variability function queueing formula.…”

Section: Introductionmentioning

confidence: 99%

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A Simulation Study on the Variability Function of the Arrival Process in Queueing Networks

Kim

2011

Journal of the Korea Society for Simulation

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In queueing network analysis, arrival processes are usually modeled as renewal processes by matching mean and variance. The renewal approximation simplifies the analysis and provides reasonably good estimate for the performance measures of the queueing systems under moderate conditions. However, high variability in arrival process or in service process requires more sophisticated approximation procedures for the variability parameter of departure/arrival processes. In this paper, we propose an heuristic approach to refine Whitt's variability function with the -interval squared coefficient of variation also known as the index of dispersion for intervals(IDI). Regression analysis is used to establish an empirical relationships between the IDI of arrival process and the IDI of departure process of a queueing system.

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Section: Decomposition Approximation and The Variability Functionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A Simulation Study on the Variability Function of the Arrival Process in Queueing Networks

Kim

2011

Journal of the Korea Society for Simulation

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“…Since the appearance of QNA there have been important thrusts dealing with autocorrelated interarrival times [9,10,35,36,43] and deterministic routing [2,42]. The present paper, like [17], deals with correlations between different streams, rather than autocorrelations.…”

Section: Introductionmentioning

confidence: 96%

Taking Account of Correlations Between Streams in Queueing Network Approximations

2005

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In this paper we describe a new variation on QNA, the Queueing Network Analyzer (Whitt [38]). QNA calculates approximate congestion measures for a network of queues. The variant proposed here allows us to relax QNA's assumption that certain counts of events in the network are uncorrelated. Following QNA, the network is approximated in terms of three basic operations on streams, namely, queueing, splitting and superposition, and random quantities of interest are characterized approximately by two moments. The approach differs from QNA in that instead of expressing the network operations as transformations applied to two-moment characterizations of the inputs, it expresses these operations as regression relations between counts in the output streams and the input streams. In essence, we substitute approximate regression relationships between random variables for QNA's approximate moment relationships. This device allows us to enhance QNA's moment relationships with information about correlations between the streams. We compare the performance of the proposed approach with QNA on a simple feed-forward network to demonstrate the need for taking account of correlation. We also discuss some of the limitations of this approach, particularly its difficulty in handling feedback, and give some ideas to improve accuracy.

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“…Bitran and Tirupati [4] modeled the interference between different arrival classes under deterministic routing which Whitt [21] and Kim [11] refined subsequently. As a key issue in decomposition approximation, the high variability and burstiness due to autocorrelation in arrival processes have been modeled in many different ways mostly by the index of dispersion for counts (IDC) and the index of dispersion for intervals (IDI) as described in Fendick et al [5,6]. Whitt [22] proposed the variability function to explain the heavy traffic bottleneck phenomenon discussed in Suresh and Whitt [18] as a means of overcoming the limitation of twomoment two-parameter decomposition approximations.…”

Section: Introductionmentioning

confidence: 99%

The two-moment three-parameter decomposition approximation of queueing networks with exponential residual renewal processes

Kim

2011

Queueing Syst

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We propose a two-moment three-parameter decomposition approximation of general open queueing networks by which both autocorrelation and cross correlation are accounted for. Each arrival process is approximated as an exponential residual (ER) renewal process that is characterized by three parameters: intensity, residue, and decrement. While the ER renewal process is adopted for modeling autocorrelated processes, the innovations method is used for modeling the cross correlation between randomly split streams. As the interarrival times of an ER renewal process follow a two-stage mixed generalized Erlang distribution, viz., MGE(2), each station is analyzed as an MGE(2)/G/1 system for the approximate mean waiting time. Variability functions are also used in network equations for a more accurate modeling of the propagation of cross correlations in queueing networks. Since an ER renewal process is a special case of a Markovian arrival process (MAP), the value of the variability function is determined by a MAP/MAP/1 approximation of the departure process. Numerical results show that our proposed approach greatly improves the performance of the parametric decomposition approximation of open queueing networks.

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Investigating dependence in packet queues with the index of dispersion for work

Cited by 31 publications

References 21 publications

A Simulation Study on the Variability Function of the Arrival Process in Queueing Networks

A Simulation Study on the Variability Function of the Arrival Process in Queueing Networks

Taking Account of Correlations Between Streams in Queueing Network Approximations

The two-moment three-parameter decomposition approximation of queueing networks with exponential residual renewal processes

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