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Buffer Stopping Time Analysis in Data Center Networks

IEEE COMMUNICATIONS LETTERS 2014年第10期18卷 1739-1742页

作者： Luan, Gan Beijing Univ Posts & Telecommun State Key Lab Networking & Switching Technol Beijing 100876 Peoples R China

This letter investigates buffer behavior in data center networks (DCNs). An analytical framework to model a switch buffer in a DCN is proposed. Based on a martingale perspective, we derive the expectation of the stopping time, and we provide explicit expression for the relationship between overflow probability of the stopping time and buffer size. Simulations are given to validate the analysis. In addition, an example is provided to explain how the method can be applied to switch design.

关键词： Buffer size data center network stopping time overflow probability

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Router Buffer Behavior Analysis for Aggregate Traffic Based on Martingale Method

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IEEE COMMUNICATIONS LETTERS 2018年第10期22卷 2040-2043页

作者： Sun, Hongliang Chi, Xuefen Nan, Zhufen Jilin Univ Dept Commun Engn Changchun 130012 Jilin Peoples R China

The buffer behavior of routers has an important influence on the quality of service of network services. Exploring theory and methods to analyze the characteristics of the buffer is an interesting job, especially when aggregate traffic is transmitted. This letter investigates the buffer behavior of a single server queuing system with multiple arrival flows, which models the operations of a router. A martingale analytical framework is proposed, which could evaluate buffer performance for aggregate traffic arrivals with different distributions. We use the processes of arrival and service to construct martingales, and analyze the queuing system with heterogeneous arrivals in martingale domain. Applying the stopping time theory of martingale, the transient performance of queue buffer is presented. The probability of buffer overflow and the expectation of buffer stopping time are derived together in this model. The simulations are given to validate the analytical results. This investigation provides a valuable reference for router buffer design.

关键词： Aggregate traffic martingale theory queuing system overflow probability stopping time

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Network decomposition: Theory and practice

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IEEE-ACM TRANSACTIONS ON NETWORKING 2005年第3期13卷 526-539页

作者： Eun, DY Shroff, NB N Carolina State Univ Dept Elect & Comp Engn Raleigh NC 27695 USA Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47905 USA

We show that significant simplicities can be obtained for the analysis of a network when link capacities are large enough to carry many flows. We develop a network decomposition approach in which network analysis can be greatly simplified. We prove that the queue length at the downstream queue converges to that of a single queue obtained by removing the upstream queue, as the capacity and the number of flows at the upstream queue increase. The precise modes of convergence vary depending on the type of input traffic, i.e., from regulated traffic arrivals to point process inputs. Our results thus help simplify network analysis by decomposing the original network into a simplified network in which all the nodes with large capacity have been eliminated. By means of extensive numerical investigation under various network scenarios, we demonstrate different aspects and implications of our network decomposition approach. Some of our findings are that our techniques perform well especially for the cases when: i) many flows are multiplexed as they enter the queue and/or ii) departing flows are routed to different downstream nodes, i.e., no single flow dominates at any node.

关键词： aggregation many-sources-asymptotic network decomposition overflow probability performance analysis

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A measurement-analytic approach for QoS estimation in a network based on the dominant time scale

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IEEE-ACM TRANSACTIONS ON NETWORKING 2003年第2期11卷 222-235页

作者： Eun, DY Shroff, NB Purdue Univ Sch Elect & Comp Engn W Lafayette IN 47907 USA

In this paper, we describe a measurement-analytic approach for estimating the overflow probability, an important measure of the quality of service (QoS), at a given multiplexing point in the network. A multiplexing point in the network could be a multiplexer or an output port of a switch or router where resources such as bandwidth and buffers are shared. Our approach impinges on using the notion of the dominant time scale (DTS), which corresponds to the most probable time scale over which overflow occurs. The DTS provides us with a measurement window for the statistics of the traffic, but is in fact itself defined in terms of the statistics of the traffic over all time. This, in essence, results in a chicken-and-egg type of unresolved problem. For the DTS to be useful for on-line measurements, we need to be able to break this chicken-and-egg cycle, and to estimate the DTS with only a bounded window of time over which the statistics of the traffic are to be measured. In this paper, we present a stopping criterion to successfully break this cycle and find a bound on the DTS. Thus, the result has significant implications for network measurements. Our approach is quite different from other works in the literature that require off-line measurements of the entire trace of the traffic. In our case, we need to measure only the statistics of the traffic up to a bound. on the DTS. We also investigate the characteristics of this upper bound on the DTS, and provide numerical results to illustrate the utility of our measurement analytic approach.

关键词： dominant time scale (DTS) Gaussian processes measurements overflow probability stopping criterion

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A loss network model with overflow for capacity planning of a neonatal unit

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ANNALS OF OPERATIONS RESEARCH 2010年第1期178卷 67-76页

作者： Asaduzzaman, Md Chaussalet, Thierry J. Robertson, Nicola J. Univ Westminster Hlth & Social Care Modelling Grp HSCMG Sch Informat London W1W 6UW England UCL UCL Elizabeth Garrett Inst Womens Hlth London W1T 7DN England

The main aim of this paper is to derive a solution to the capacity problem faced by many perinatal networks in the United Kingdom. We propose a queueing model to determine the number of cots at all care units for any desired overflow and rejection probability in a neonatal unit. The model formulation is developed, being motivated by overflow models in telecommunication systems. Exact expressions for the overflow and rejection probabilities are derived. The model is then applied to a neonatal unit of a perinatal network in the UK.

关键词： Neonatal unit overflow probability Rejection probability Queueing network OR in health care

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BOUNDS ON BUFFER overflow PROBABILITIES IN COMMUNICATION-SYSTEMS

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PERFORMANCE EVALUATION 1982年第3期2卷 149-160页

作者： GEIHS, K KOBAYASHI, H TH DARMSTADT DEPT COMP SCID-6100 DARMSTADTFED REP GER IBM JAPAN LTD INST SCIMINATO KUTOKYO 106JAPAN

A model to analyze the buffer behaviour in a multiplexor is derived, based on the analogy between the buffer occupancy in a discrete time model of multiplexing and the waiting time of a GI/G/1 queueing system. The bounding techniques developed earlier by Kingman and Ross are extended to the discrete time model. Simple and useful bounds are obtained for the buffer overflow probabilities under general assumptions concerning incoming message traffic characteristics. Numerical examples are presented and compared with other methods.

关键词： Buffer overflow Concentrator GI/G/1 Queue Multiplexor overflow probability Kingman-Ross Bounds Sequential Analysis Wald's Identity IFR DFR

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Cell loss probability for M/G/1 and time-slotted queues

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JOURNAL OF APPLIED probability 2000年第4期37卷 1149-1156页

作者： McDonald, D Théberge, F Univ Ottawa Dept Math & Stat Ottawa ON K1N 6N5 Canada

It is common practice to approximate the cell loss probability (CLP) of cells entering a finite buffer by the overflow probability (OVFL) of a corresponding infinite buffer queue, since the CLP is typically harder to estimate. We obtain exact asymptotic results for CLP and OVFL, for time-slotted queues where block arrivals in different time slots are i.i.d. and one cell is served per time slot. In this case the ratio of CLP to OVFL is asymptotically (1 - rho)/rho, where rho is the use or, equivalently, the mean arrival rate per time slot. Analogous asymptotic results are obtained for continuous time M/G/1 queues. In this case the ratio of CLP to OVFL is asymptotically 1 - rho.

关键词： CBR cell loss probability M/G/1 overflow probability

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BUFFER BEHAVIOR FOR POISSON ARRIVALS AND MULTIPLE SYNCHRONOUS CONSTANT OUTPUTS

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IEEE TRANSACTIONS ON COMPUTERS 1970年第6期C 19卷 530-&页

作者： CHU, WW IEEE Abstract Authors References Cited By Keywords Metrics Similar Download Citation Email Print Request Permissions

A queuing model with a limited waiting room (buffer), Poisson arrivals, multiple synchronous servers (synchronous transmission channels), and constant services is studied. Using traffic intensity and number of transmission lines as parameters, the relationships among overflow probabilities, buffer size, and expected queuing delay due to buffering are obtained. These relationships are represented in graphs which are provided as a guide to the design of buffer systems. An example is given to illustrate the use of these results in buffer design problems. In addition, the procedure to design an optimal buffer system in the sense of minimal cost (tradeoff between buffer cost and transmission cost) is discussed.

关键词： Asynchronous time division multiplexing buffer design multiplexor design overflow probability queuing delay queuing theory.

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Admission control with long-range dependence traffic input

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Journal of Harbin Institute of Technology(New Series) 2005年第4期12卷 396-399页

作者：饶云华邹雪城 School of Electronics Information Wuhan University Wuhan 430079 China Dept. of Electronics Science and Technology Huazhong Univ. of Science and Technology Wuhan 430074 China

The admission control scheme is investigated for a FIFO self-similar queuing system with Quality of Service (QoS) performance guarantees. Since the self-similar queuing system performance analysis is often carried out under the condition of infinite buffer, it is difficult to deduce the upper boundary of buffer overflow probability. To overcome this shortcoming, a simple overflow condition is proposed, which defines a buffer overflow occurrence whenever the arrival rate exceeds the service rate. The analytic formula for the buffer overflow probability upper boundary is easily obtained under this condition. The required bandwidth upper boundary with long-range dependence input and determined overflow probability is then derived from this formula. Based on the above analytic formulas, the upper boundaries of the admission control regions for homogeneous and heterogeneous long-range dependence traffic sources are separately obtained. Finally, an effective admission control scheme for long-range dependence input is proposed. Simulation studies with real traffic have confirmed the validity of these results.

关键词： long-range dependence queuing system overflow probability admission control

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Exact overflow asymptotics for queues with many Gaussian inputs

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JOURNAL OF APPLIED probability 2003年第3期40卷 704-720页

作者： Debicki, K Mandjes, M Univ Wroclaw Inst Math PL-50384 Wroclaw Poland CWI NL-1090 GB Amsterdam Netherlands

In this paper we consider a queue fed by a large number of independent continuous-time Gaussian processes with stationary increments. After scaling the buffer exceedance threshold and the (constant) service capacity by the number of sources, we present asymptotically exact results for the probability that the buffer threshold is exceeded. We consider both the stationary overflow probability and the (transient) probability of overflow at a finite time horizon. We give detailed results for the practically important cases in which the inputs are fractional Brownian motion processes or integrated Gaussian processes.

关键词： Gaussian process fluid queue extremes overflow probability exact asymptotics integrated Gaussian process fractional Brownian motion

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