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High timeresolution measurement and analysis of LAN traffic: Implications for LAN interconnection
, 1991
"... The interconnection of local area networks is increasingly important, but little data are available on the characteristics of the aggregate traffic that LANs will be submitting to the interconnection media. In order to understand the interactions between LANs and the proposed interconnection network ..."
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Cited by 104 (1 self)
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The interconnection of local area networks is increasingly important, but little data are available on the characteristics of the aggregate traffic that LANs will be submitting to the interconnection media. In order to understand the interactions between LANs and the proposed interconnection networks (MANs, WANs, and BISDN networks), it is necessary to study the behavior of this external LAN traffic over many time scales – from milliseconds to hundreds of seconds. We present a high timeresolution hardware monitor for Ethernet LANs that avoids the shortcomings of previous monitoring tools, such as traffic burst clipping and timestamp jitter. Using data recorded by our monitor for several hundred million Ethernet packets, we present an overview of the shortrange time correlations in external LAN traffic. Our analysis shows that LAN traffic is extremely bursty across time domains spanning six orders of magnitude. We compare this behavior with simple formal traffic models and employ the data in a tracedriven simulation of the LANBISDN interface proposed for the SMDS SM service. Our results suggest that the pronounced shortterm traffic correlations, together with the extensive time regime of traffic burstiness, strongly influence the patterns of loss and delay induced by LAN interconnection. 1.
Characterizing the Variability of Arrival Processes with Indices of Dispersion
 IEEE Journal on Selected Areas in Communications
, 1990
"... We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indic ..."
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Cited by 69 (0 self)
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We propose to characterize the burstiness of packet arrival processes with indices of dispersion for intervals and for counts. These indices, which are functions of the variance of intervals and counts, are relatively straightforward to estimate and convey much more information than simpler indices, such as the coefficient of variation, that are often used to describe burstiness quantitatively.
Heavytraffic asymptotic expansions for the asymptotic decay rates
 in the BMAP/G/1 queue. Stochastic Models
, 1994
"... versatile Markovian point process, tail probabilities in queues, asymptotic decay rate, PerronFrobenius eigenvalue, asymptotic expansion, caudal characteristic curve, heavy traffic In great generality, the basic steadystate distributions in the BMAP / G /1 queue have asymptotically exponential tai ..."
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Cited by 15 (10 self)
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versatile Markovian point process, tail probabilities in queues, asymptotic decay rate, PerronFrobenius eigenvalue, asymptotic expansion, caudal characteristic curve, heavy traffic In great generality, the basic steadystate distributions in the BMAP / G /1 queue have asymptotically exponential tails. Here we develop asymptotic expansions for the asymptotic decay rates of these tail probabilities in powers of one minus the traffic intensity. The first term coincides with the decay rate of the exponential distribution arising in the standard heavytraffic limit. The coefficients of these heavytraffic expansions depend on the moments of the servicetime distribution and the derivatives of the PerronFrobenius eigenvalue δ(z) of the BMAP matrix generating function D(z) at z = 1. We give recursive formulas for the derivatives δ (k) ( 1). The asymptotic expansions provide the basis for efficiently computing the asymptotic decay rates as functions of the traffic intensity, i.e., the caudal characteristic curves. The asymptotic expansions also reveal what features of the model the asymptotic decay rates primarily depend upon. In particular, δ(z) coincides with the limiting timeaverage of the factorial cumulant generating function (the logarithm of the generating function) of the arrival counting process, and the derivatives δ (k) ( 1) coincide with the asymptotic factorial cumulants of the arrival counting process. This insight is important for admission control schemes in multiservice networks based in part on asymptotic decay rates. The interpretation helps identify appropriate statistics to compute from network traffic data in order to predict performance. 1.
Variability Functions for ParametricDecomposition Approximations of Queueing Networks
 Management Sci
, 1995
"... We propose an enhancement to the parametricdecomposition method for calculating approximate steadystate performance measures of open queueing networks with nonPoisson arrival processes and nonexponential servicetime distributions. Instead of using a variability parameter c a 2 for each arrival ..."
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Cited by 10 (3 self)
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We propose an enhancement to the parametricdecomposition method for calculating approximate steadystate performance measures of open queueing networks with nonPoisson arrival processes and nonexponential servicetime distributions. Instead of using a variability parameter c a 2 for each arrival process, we suggest using a variability function c a 2 (ρ) , 0 < ρ < 1, for each arrival process; i.e., the variability parameter should be regarded as a function of the traffic intensity ρ of a queue to which the arrival process might go. Variability functions provide a convenient representation of different levels of variability in different time scales for arrival processes that are not nearly renewal processes. Variability functions enable the approximations to account for longrange effects in queueing networks that cannot be addressed by variability parameters. For example, the variability functions provide a way to address the heavytraffic bottleneck phenomenon, in which exceptional variability (either high or low) in the input has little impact in a series of queues with lowtomoderate traffic intensities, and then has a big impact when it reaches a later queue with a relatively high traffic intensity. The variability functions also enable the approximations to characterize irregular periodic deterministic external arrival processes in a reasonable way; i.e., if there are no batches, then c a 2 (ρ) should be 0 for ρ near 0 or 1, but c a 2 (ρ) can assume arbitrarily large values for appropriate intermediate ρ. We present a full network algorithm with variability functions, showing that the idea is implementable. We also show how simulations of single queues can be effectively exploited to determine variability functions for difficult external arrival processes. Key words: queueing networks, tandem queues, approximations, parametricdecomposition approximations, twomoment approximations, heavy traffic, squared coefficient of variation.
A multiclass fluid model for a contact center with skillbased routing
, 1997
"... A multiclass deterministic fluid model is proposed to describe and improve the performance of a customer contact center with skillbased routing. The fluid model can be regarded as an approximation for a stochastic queueing system with multiple customer classes and multiple server groups, with cust ..."
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Cited by 6 (3 self)
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A multiclass deterministic fluid model is proposed to describe and improve the performance of a customer contact center with skillbased routing. The fluid model can be regarded as an approximation for a stochastic queueing system with multiple customer classes and multiple server groups, with customer abandonment and nonexponential servicetime and timetoabandon distributions. The fluid model is attractive to provide a rough analysis of large systems, with high arrival rate and many servers. Even though the fluid model evolves deterministically, the servicetime distributions and timetoabandon distributions beyond their means play a critical role. The fluid model can be used for staffing, routing and system design, because it is possible to formulate tractable optimization problems.
Determining Priority Queue Performance from Second Moment Traffic Characterizations
, 1996
"... A crucial problem to the efficient design and management of integrated services networks is how to best allocate and reserve network resources for heterogeneous and bursty traffic streams in multiplexers that support prioritized service disciplines. In this paper, we introduce a new approach for det ..."
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A crucial problem to the efficient design and management of integrated services networks is how to best allocate and reserve network resources for heterogeneous and bursty traffic streams in multiplexers that support prioritized service disciplines. In this paper, we introduce a new approach for determining perconnection QoS parameters such as delaybound violation probability and loss probability in multiservice networks. The approach utilizes a traffic characterization that consists of the variances of a stream's rate distribution over multiple interval lengths, which captures its burstiness properties and autocorrelation structure. The resource allocation scheme is based on application of the Central Limit Theorem over intervals, together with use of stochastic delaybounding techniques; it results in simple and efficient algorithms for determining QoS parameters. We perform experiments with long traces of MPEGcompressed video and show that the new scheme is accurate enough to ca...
ARRANGING QUEUES IN SERIES
, 1988
"... For given external arrival process and given servicetime distributions, the object is to determine the order of infinitecapacity singleserver queues in series that minimizes the longrun average sojourn time per customer. We gain additional insight into this queueing design problem, and congestio ..."
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For given external arrival process and given servicetime distributions, the object is to determine the order of infinitecapacity singleserver queues in series that minimizes the longrun average sojourn time per customer. We gain additional insight into this queueing design problem, and congestion in open queueing networks more generally, primarily by performing simulation experiments. We develop a new parametricdecomposition approximation for departure processes, which can be used in general queueing network algorithms as well as in this design problem. For this design problem, we conclude that the key issue is variability: The order tends to matter when the servicetime distributions have significantly different variability, and not otherwise. The order also matters less in light traffic, even with a relative difference criterion. Arranging the queues in order of increasing servicetime variability, using the squared coefficient of variation as a partial characterization of variability, seems to be an effective simple heuristic. In all cases of two queues in series, the simulation results indicate that the same order is optimal for all combinations of the traffic intensities, suggesting that the lighttraffic asymptotics in Greenberg and Wolff (1988) should usually be effective for identifying the best order. Comparisons with simulations for two queues also indicate that the parametricdecomposition approximations provide quite accurate quantitative estimates of the expected sojourn time with each order. However, for more than two queues, the approximations need not properly describe the congestion at a bottleneck queue. Key Words: queueing networks; tandem queues; departure processes; queueing system design; simulation; variance reduction; common random numbers; approximations; parametricdecomposition approximations.