Technical Note—Simulating the <i>GI</i>/<i>G</i>/1 Queue in Heavy Traffic

Minh, Do Le; Sorli, Ronald M.

doi:10.1287/opre.31.5.966

Cited by 15 publications

(11 citation statements)

References 8 publications

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“…The mean delay in the GI/G/1 queue can be expressed as a sum of the mean equilibrium idle period and a quantity that can be calculated from the service time and the interarrival time distributions [17]. Minh and Sorli show that, under heavy traffic, it is more efficient to estimate the mean delay in a GI/G/1 queue by estimating the mean equilibrium idle period and calculating the mean delay via the relationship between the delay and the idle period than directly estimating the mean delay [11]. The mean equilibrium idle period is estimated by the first two sample moments of the idle period in [11].…”

Section: ½º½ ê ð ø ûóömentioning

confidence: 99%

“…Minh and Sorli show that, under heavy traffic, it is more efficient to estimate the mean delay in a GI/G/1 queue by estimating the mean equilibrium idle period and calculating the mean delay via the relationship between the delay and the idle period than directly estimating the mean delay [11]. The mean equilibrium idle period is estimated by the first two sample moments of the idle period in [11]. Recently, Wang and Wolff propose a superior method to estimate the mean equilibrium idle period directly [16].…”

Section: ½º½ ê ð ø ûóömentioning

confidence: 99%

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Relations in the Central Limit Theorem Version of the Response Time Law

Foumeau

2007

Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)

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We study the accuracy of the estimators of mean response time and throughput in closed interactive systems such as Web systems. The response time law allows us to calculate the throughput from the mean response time and vice versa. However, we find that the accuracy of the two estimators can be quite different. We refine the response time law using the central limit theorem and study the asymptotic accuracy of the estimators when the measurement time approaches infinity. Based on the asymptotic accuracy of the estimators, we derive rules of thumb for the accuracy of the measured mean response time and measured throughput. Extensive simulation study suggests that the rules of thumb are often valid under realistic measurement time.

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Section: ½º½ ê ð ø ûóömentioning

confidence: 99%

Section: ½º½ ê ð ø ûóömentioning

confidence: 99%

Relations in the Central Limit Theorem Version of the Response Time Law

Foumeau

2007

Fourth International Conference on the Quantitative Evaluation of Systems (QEST 2007)

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“…Recently Minh and Sori [50] have proposed using a simulation to find the moments of I and then using the above equation to find the average waiting time.…”

Section: Hybrid Modeling Of Computer Systemsmentioning

confidence: 99%

A Packet Communication Network Synthesis and Analysis System.

Shanmugan¹,

Frost²,

Minden³

et al. 1986

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“…The first proposal to do this may also be in Minh and Sorli [1983], however, a similar proposal appears on page 181 of Kollerstrom [1981].…”

Section: Introductionmentioning

confidence: 99%

“…In heavy traffic, it was shown empirically in Minh and Sorli [1983] that this estimator, which we call DI, is more efficient, often by a very large factor, than estimating d directly. The first proposal to do this may also be in Minh and Sorli [1983], however, a similar proposal appears on page 181 of Kollerstrom [1981].…”

Section: Introductionmentioning

confidence: 99%

Efficient simulation of queues in heavy traffic

Wang

Wolff

2003

ACM Trans. Model. Comput. Simul.

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When simulating queues in heavy traffic, estimators of quantities such as average delay in queue d converge slowly to their true values. This problem is exacerbated when interarrival and service distributions are irregular. For the GI/G/1 queue, delay moments can be expressed in terms of moments of idle period I . Instead of estimating d directly by a standard regenerative estimator that we call DD, a method we call DI estimates d from estimated moments of I . DI was investigated some time ago and shown to be much more efficient than DD in heavy traffic. We measure efficiency as the factor by which variance is reduced. For the GI/G/1 queue, we show how to generate a sequence of realized values of the equilibrium idle period, I e , that are not independent and identically distributed, but have the correct statistical properties in the long run. We show how to use this sequence to construct a new estimator of d , called DE, and of higher moments of delay as well. When arrivals are irregular, we show that DE is more efficient than DI, in some cases by a large factor, independent of the traffic intensity. Comparing DE with DD, these factors multiply.For GI/G/c, we construct a control-variates estimator of average delay in queue d c that is efficient in heavy traffic. It uses DE to estimate the average delay for the corresponding fast single server. We compare the efficiency of this method with another method in the literature. For M/G/c, we use insensitivity to construct another control-variates estimator of d c . We compare the efficiency of this estimator with the two c-server estimators above.

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Technical Note—Simulating the GI/G/1 Queue in Heavy Traffic

Cited by 15 publications

References 8 publications

Relations in the Central Limit Theorem Version of the Response Time Law

Relations in the Central Limit Theorem Version of the Response Time Law

A Packet Communication Network Synthesis and Analysis System.

Efficient simulation of queues in heavy traffic

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