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38th Symposium on Information Theory and its Applications (SITA)

作者： Saito, Shota Matsushima, Toshiyasu Waseda Univ Grad Sch Fundamental Sci & Engn Dept Pure & Appl Math Tokyo 1698555 Japan

We treat lossless fixed-to-variable length source coding under general sources for finite block length setting. We evaluate the threshold of the overflow probability for prefix and non-prefix codes in terms of the smooth max-entropy. We clarify the difference of the thresholds between prefix and non-prefix codes for finite block length. Further, we discuss our results under the asymptotic block length setting.

关键词： finite block length lossless fixed-to-variable length source coding overflow probability smooth max-entropy

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Evaluation of overflow probability of Bayes Code in Moderate Deviation Regime

Evaluation of Overflow Probability of Bayes Code in Moderate...

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39th Symposium on Information Theory and Its Applications (SITA)

作者： Saito, Shota Matsushima, Toshiyasu Waseda Univ Grad Sch Fundamental Sci & Engn Dept Pure & Appl Math Tokyo 1698555 Japan

This letter treats the problem of lossless fixed-to-variable length source coding in moderate deviation regime. We investigate the behavior of the overflow probability of the Bayes code. Our result clarifies that the behavior of the overflow probability of the Bayes code is similar to that of the optimal non-universal code for i.i.d. sources.

关键词： Bayes code lossless fixed-to-variable length source coding moderate deviation regime overflow probability

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The overflow probability Asymptotics in a Single-Class Retrial System with General Retrieve Time 24th

The Overflow Probability Asymptotics in a Single-Class Retri...

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24th International Conference on Distributed and Computer and Communication Networks, DCCN 2021

作者： Morozov, Evsey Zhukova, Ksenia Institute of Applied Mathematical Research Karelian Research Centre of the Russian Academy of Sciences Petrozavodsk Russia Petrozavodsk State University Petrozavodsk Russia Moscow Center for Fundamental and Applied Mathematics Moscow State University Moscow119991 Russia

ISBN: (纸本)9783030925062

We consider the logarithmic asymptotics of the large deviation probability in a single-server queue with Poisson input, where server, after completion of service, seeks a customer in a virtual orbit (retrial customer) for the next service, unless new arrival captures server. This system is described by a regenerative process, and under stability assumption, the logarithmic asymptotics of the stationary probability that the number of the customers in the system reaches a high threshold within a regeneration cycle is found. Some examples are given for particular retrieval time distributions. © 2021, Springer Nature Switzerland AG.

关键词： Large deviations Logarithmic asymptotics overflow probability Regenerative approach Retrial queue Stability conditions

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Optimum overflow Thresholds in Variable-Length Source Coding Allowing Non-Vanishing Error probability

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IEEE TRANSACTIONS ON INFORMATION THEORY 2019年第12期65卷 8213-8221页

作者： Nomura, Ryo Yagi, Hideki Waseda Univ Ctr Data Sci Tokyo 1620042 Japan Univ Electrocommun Dept Comp & Network Engn Koganei Tokyo 1848795 Japan

The variable-length source coding problem allowing the error probability up to some constant is considered for general sources. In this problem, the optimum mean codeword length of variable-length codes has already been determined. On the other hand, in this paper, we focus on the overflow (or excess codeword length) probability instead of the mean codeword length. The infimum of overflow thresholds under the constraint that both of the error probability and the overflow probability are smaller than or equal to some constant is called the optimum overflow threshold. In this paper, we first derive finite-length upper and lower bounds on these probabilities so as to analyze the optimum overflow thresholds. Then, by using these bounds, we determine the general formula of the optimum overflow thresholds in both of the first-order and second-order forms. Next, we consider another expression of the derived general formula so as to reveal the relationship with the optimum coding rate in the fixed-length source coding problem. Finally, we apply the general formula derived in this paper to the case of stationary memoryless sources.

关键词： Error probability general source overflow probability variable-length source coding

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The optimal overflow and underflow probabilities of variable-length coding for the general source

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IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES 2001年第10期E84A卷 2457-2465页

作者： Uchida, O Han, TS Kanagawa Inst Technol Dept Network Engn Atsugi Kanagawa 2430292 Japan Univ Electrocommun Grad Sch Informat Syst Chofu Tokyo 1828585 Japan

In variable-length coding, the probability of codeword length per source letter being above (resp. below) a prescribed threshold is called the overflow (resp. the underflow) probability. In this paper, we show that the infimum achievable threshold given the overflow probability exponent r always coincides with the infimum achievable fixed-length coding rate given the error exponent r, without any assumptions on the source. In the case of underflow probability, we also show the similar results. From these results, we can utilize various theorems and results on the fixed-length coding established by Han for the analysis of overflow and underflow probabilities. Moreover, we generalize the above results to the case with overflow and underflow probabilities of codeword cost.

关键词： overflow probability underflow probability general source variable-length source coding reliability function

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Importance sampling for a Markov modulated queuing network

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STOCHASTIC PROCESSES AND THEIR APPLICATIONS 2009年第2期119卷 491-517页

作者： Sezer, Ali Devin Middle E Tech Univ Inst Appl Math TR-06531 Ankara Turkey

Importance sampling (IS) is a variance reduction method for simulating rare events. A recent paper by Dupuis, Wang and Sezer [Paul Dupuis, Ali Devin Sezer, Hui Wang, Dynamic importance sampling for queueing networks, Annals of Applied probability 17 (4) (2007) 1306-1346] exploits connections between IS and stochastic games and optimal control problems to show how to design and analyze simple and efficient IS algorithms for various overflow events of tandem Jackson Networks. The present paper carries out a program parallel to the paper by Dupuis et al. for a two node tandem network whose arrival and service rates are modulated by in exogenous finite state Markov process. The overflow event we study is the following: the number of customers in the system reaches n without the system ever becoming empty, given that initially the system is empty. (C) 2008 Elsevier B.V. All rights reserved.

关键词： Dynamic importance sampling Rare event simulation Tandem queues Queuing networks Markov modulated Regime switch overflow probability Large deviations Isaacs equation Optimal control

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Long-range dependence and performance in telecom networks

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APPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY 2004年第4期20卷 305-321页

作者： Conti, PL Lijoi, A Ruggeri, F Univ Pavia Dipartimento Econ Polit & Methodi Quantitat I-27100 Pavia Italy Univ Roma La Sapienza Dipartimento Stat Probabil & Stat Applicate Rome Italy CNR Ist Matemat Appl & Tecnol Informat I-20133 Milan Italy

Telecommunications systems have recently undergone significant innovations. These call for suitable statistical models that can properly describe the behaviour of the input traffic in a network. Here we use fractional Brownian motion (FBM) to model cumulative traffic network, thus taking into account the possible presence of long-range dependence in the data. A Bayesian approach is devised in such a way that we are able to: (a) estimate the Hurst parameter H of the FBM;(b) estimate the overflow probability which is a parameter measuring the quality of service of a network: (c) develop a test for comparing the null hypothesis of long-range dependence in the data versus the alternative of short-range dependence. In order to achieve these inferential results, we elaborate an MCMC sampling scheme whose output enables us to obtain an approximation of the quantities of interest. An application to three real datasets, corresponding to three different levels of traffic, is finally considered. Copyright (C) 2004 John Wiley Sons, Ltd.

关键词： fractional Brownian motion long-range dependence overflow probability teletraffic data

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Fast simulation of overflow probabilities in a queue with Gaussian input

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ACM TRANSACTIONS ON MODELING AND COMPUTER SIMULATION 2006年第2期16卷 119-151页

作者： Dieker, A. B. Mandjes, M. CWI NL-1009 AB Amsterdam Netherlands Univ Twente NL-7500 AE Enschede Netherlands

In this article, we study a queue fed by a large number n of independent discrete-time Gaussian processes with stationary increments. We consider the many-sources asymptotic regime, that is, the buffer-exceedance threshold B and the service capacity C are scaled by the number of sources (B = nb and C = nc). We discuss four methods for simulating the steady-state probability that the buffer threshold is exceeded: the single-twist method (suggested by large deviation theory), the cut-and-twist method (simulating timeslot by timeslot), the random-twist method (the twist is sampled from a discrete distribution), and the sequential-twist method (simulating source by source). The asymptotic efficiency of these four methods is analytically investigated for n --> infinity. A necessary and sufficient condition is derived for the efficiency of the single-twist method, indicating that it is nearly always asymptotically inefficient. The other three methods, however, are asymptotically efficient. We numerically evaluate the four methods by performing a detailed simulation study where it is our main objective to compare the three efficient methods in practical situations.

关键词： algorithms performance asymptotic efficiency Gaussian processes importance sampling large deviations overflow probability queueing theory

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Efficient parallel multicast ATM switch

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IEE PROCEEDINGS-COMMUNICATIONS 2000年第2期147卷 123-132页

作者： Deng, YW Chen, WT Natl Tsing Hua Univ Dept Comp Sci Hsinchu 30043 Taiwan

A novel multicast snitch architecture with high throughput performance and low hardware complexity is proposed. The storage complexity of the translation tables required by the copy network is improved from O(N-2) to O(N). The throughput performance of the proposed switch architecture is very close to 100% when more than five multicast switching modules (MSMs) are used. The proposed multicast switch architecture is composed of multiple MSMs arranged in parallel. An MSM is composed of a copy network and a routing network. A multicast bounded-fanout principle is proposed which states that the overflow probability of a copy network can be reduced to an acceptable level if the output capacity of the copy network is properly expanded. Instead of building a very large expanded copy network, multiple small copy networks are arranged in parallel to effectively expand the aggregate output capacity of the copy networks. A simple copy network architecture is proposed which guarantees that all cell copies an generated at predefined outlets so that the storage complexity of the translation tables is of O(N). A Batcher-banyan based routing network is adopted to switch cell copies generated by the copy network. A 10(-9) cell loss probability can be achieved when twelve MSMs are used in the proposed switch.

关键词： multicast bounded-fanout principle Parallel architecture multistage interconnection networks computational complexity Batcher-banyan based routing network parallel architecture multicast communication routing network Communication switching translation tables high throughput performance Multiprocessor interconnection low hardware complexity parallel architectures ATM switch output capacity overflow probability Communication network design, planning and routing multicast switch architecture cell loss probability copy network telecommunication network routing storage complexity asynchronous transfer mode multicast switching modules

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A finite buffer fluid queue driven by a Markovian queue

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QUEUEING SYSTEMS 2001年第2期38卷 213-220页

作者： Sericola, B Inst Natl Rech Informat & Automat IRISA F-35042 Rennes France

We consider a finite buffer fluid queue receiving its input from the output of a Markovian queue with finite or infinite waiting room. The input flow into the fluid queue is thus characterized by a Markov modulated input rate process and we derive, for a wide class of such input processes, a procedure for the computation of the stationary buffer content of the fluid queue and the stationary overflow probability. This approach leads to a numerically stable algorithm for which the precision of the result can be specified in advance.

关键词： fluid queue Markovian queue Markov process overflow probability

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