Efficient simulation of queues in heavy traffic

Wang, Chia-Li; Wolff, Ronald W.

doi:10.1145/778553.778556

Cited by 7 publications

(5 citation statements)

References 13 publications

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“…These estimators are based on a way of generating equilibrium idle periods that was motivated by ideas in Section 2. For estimating d, variance reduction over known alternatives, by a factor of about 20 in some runs, is reported in [11].…”

Section: Introductionmentioning

confidence: 99%

Idle period approximations and bounds for the GI/G/1 queue

Wolff¹,

Wang²

2003

Advances in Applied Probability

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The average delay for the GI/G/1 queue is often approximated as a function of the first two moments of interarrival and service times. For highly irregular arrivals, however, it varies widely among queues with the same first two moments, even in moderately heavy traffic. Empirically, it decreases as the interarrival time third moment increases. For GI/M/1 queues, a heavy-traffic expression for the average delay with this property has been previously obtained. The method, however, sheds little light on why the third moment arises. We analyze the equilibrium idle-period distribution in heavy traffic using real-variable methods. For GI/M/1 queues, we derive the above heavy-traffic result and also obtain conditions under which it is either an upper or lower bound. Our approach provides an intuitive explanation for the result and also strongly suggests that similar results should hold for general service. This is supported by empirical evidence. For any given service distribution, it has been conjectured that the expected delay under pure-batch arrivals, where interarrival times are scaled Bernoulli random variables, is an upper bound on the average delay over all interarrival distributions with the same first two moments. We investigate this conjecture and show, among other things, that pure-batch arrivals have the smallest third moment. We obtain conditions under which this conjecture is true and present a counterexample where it fails. Arrivals that arise as overflows from other queues can be highly irregular. We show that interoverflow distributions in a certain class have decreasing failure rate.

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Section: Introductionmentioning

confidence: 99%

Idle period approximations and bounds for the GI/G/1 queue

Wolff¹,

Wang²

2003

Advances in Applied Probability

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“…The precision is defined as the percentage error in the estimated mean which is equal to CI half length divided by the estimated mean. It is noted that very low loads and high loads contribute to a longer CI, as the simulation becomes less stable and the estimators converge very slowly to their true values, especially when traffic is irregular [59]. The length of the CI of the other performance metrics exhibited the same characteristics.…”

Section: Impact Of Bursty Trafficmentioning

confidence: 82%

Performance analysis and comparison of interrupt-handling schemes in gigabit networks

Salah

Elbadawi

Haidari

2007

Computer Communications

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Interrupt processing can be a major bottleneck in the end-to-end performance of Gigabit networks. The performance of Gigabit network end hosts or servers can be severely degraded due to interrupt overhead caused by heavy incoming traffic. In particular, excessive latency and significant degradation in system throughput can be encountered. Also, user applications may livelock as the CPU power gets mostly consumed by interrupt handling and protocol processing. A number of interrupt handling schemes has been proposed and employed to mitigate the interrupt overhead and improve OS performance. Among the most popular interrupt handling schemes are normal interruption, polling, interrupt coalescing, and disabling and enabling of interrupts. In previous work, we presented a preliminary analytical study and models of normal interruption and interrupt coalescing. In this article, we extend our analysis and modeling to include polling and the scheme of interrupt disabling and enabling. For polling, we study both pure (or FreeBSD-style) polling and Linux NAPI polling.The performances for all these schemes are compared using both mathematical analysis and discrete-event simulation. The performance is studied in terms of three key performance indictors: throughput, system latency, and the residual CPU bandwidth available for user applications. As opposed to our previous work, we consider not only Poisson traffic, but also bursty traffic with empirical packet size distribution. Our analysis and simulation work gives insight into predicting the system performance and behavior when employing a certain interrupt handling scheme. It is concluded that no single interrupt handling scheme outperforms all other schemes under all traffic conditions. Based on obtained results, we propose and discuss a novel hybrid scheme of interrupt disabling-enabling and pure polling in order to attain peak performance under low and heavy traffic loads.

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“…Suppose that Ô Ø ´Øµ Ü ´Øµ Þ ¡ µ´ µ (17) We will represent the normal random variable which Ô Ø´Ê´Øµ Üµ converges to in terms of and . Similarly to (16), it can be shown that…”

Section: Lemma 1 (A Clt Version Of the Response Time Law)mentioning

confidence: 90%

“…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%

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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Efficient simulation of queues in heavy traffic

Cited by 7 publications

References 13 publications

Idle period approximations and bounds for the GI/G/1 queue

Idle period approximations and bounds for the GI/G/1 queue

Performance analysis and comparison of interrupt-handling schemes in gigabit networks

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

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