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Page 5633 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews
(BE-BEL-AMI; Minsk) On the modification of Rouche’s theorem for the queueing theory problems. (English summary) Queueing Syst. Theory Appl. 38 (2001), no. 4, 431-434.  ...  Rouché’s theorem cannot be applied when boundary conditions are violated on |z| = 1. The author proves the following useful result using the generalized principle of the argument: Let f(z)  ...

Page 696 of Mathematical Reviews Vol. 24, Issue 6A [page]

1962 Mathematical Reviews
For example, Rouché’s theorem of complex analysis serves often in determining certain parameters of the process.  ...  Also, the author discusses several modifications and restrictions on the usual one-server model ; for example, queues with balking, queues in tandom, etc.  ...

On the structure and solutions of functional equations arising from queueing models

El-sayed El-hady, Janusz Brzdęk, Hamed Nassar
2017 Aequationes Mathematicae
We hope that in this way we will make it easier to take some steps forward on the road towards a (more or less) general solving theory for this interesting class of equations.  ...  It is a survey on functional equations of a certain type, for functions in two complex variables, which often arise in queueing models.  ...  This scholarship was fully funded by the the Ministry of Higher Education and Scientific Research, Cairo, Egypt during the period January, 2013 till January, 2015.  ...

Analytic Root Clustering: A Complete Algorithm Using Soft Zero Tests [chapter]

Chee Yap, Michael Sagraloff, Vikram Sharma
2013 Lecture Notes in Computer Science
A challenge to current theories of computing in the continua is the proper treatment of the zero test. Such tests are critical for extracting geometric information.  ...  We address the basic problem of determining the geometry of the roots of a complex analytic function.  ...  of Rouché's Theorem, we conclude f k (z) and f (m + z) have the same number of roots inside the ball D 0 (r).  ...

Stationary analysis of certain Markov-modulated reflected random walks in the quarter plane [article]

Ioannis Dimitriou
2020 arXiv   pre-print
To obtain the stationary distribution, we apply the power series approximation method, and the theory of Riemann boundary value problems.  ...  The transition rates of the two-dimensional process depend on the state of a finite state Markovian background process.  ...  Acknowledgements The author would like to thank the Editor and the anonymous Reviewers for the careful reading of the manuscript and the insightful remarks and input, which helped to improve the original  ...

Application of Tauberian Theorem to the Exponential Decay of the Tail Probability of a Random Variable

Kenji Nakagawa
2007 IEEE Transactions on Information Theory
For the proof of the theorem, we extend and apply so-called a finite form of Ikehara's complex Tauberian theorem by Graham-Vaaler.  ...  We present a theorem, according to which if the abscissa of convergence of the LS transform is negative finite and the real point on the axis of convergence is a pole of the LS transform, then the tail  ...  See [8] for the survey of the history and recent developments of Tauberian theory. The following is a well-known Tauberian theorem.  ...

Queueing systems with renovation

A. Ya. Kreinin
1997 Journal of Applied Mathematics and Stochastic Analysis
Explicit solutions are discussed for the queues with Poisson input flow and for queues with general input and exponential service times.  ...  We study in this paper-single channel queueing systems with renovation. Such models are often encountered in computer science applications.  ...  By Rouche's theorem, the equation + .)z + 0 has only one root, z, E D. Therefore, the numerator of the fraction in (6) should be equal to 0 at z-z,.  ...

Analytic Computation Schemes for the Discrete-Time Bulk Service Queue

A. J. E. M. Janssen, J. S. H. van Leeuwaarden
2005 Queueing systems
While in general this is true for the moments of the stationary queue length, for determining the distribution itself, dependence on the roots might cause some problems, in particular for tail probabilities  ...  Chaudhry & Kim [7] used the same technique and presented some numerical work. The technique of finding roots to complete a transform has become a classic one in queueing theory.  ...  Acknowledgement The authors like to thank Onno J. Boxma for his help in proving Theorem 4.1. A Proof of Theorem 3.11 We have z(α) = z 0 (e iα ) where z 0 (w) is the solution of  ...

Reduction and decomposition of differential automata: Theory and applications [chapter]

Alexey S. Matveev, Andrey V. Savkin
1998 Lecture Notes in Computer Science
The argument princilple, Rouche's theorem, inverse function theorem.  ...  Action of the galois group on prime ideals.  ...

A Compensation Approach for Queueing Problems

Ben Atkinson, I. J. B. F. Adan
1996 Journal of the Operational Research Society
accessing publications that users recognise and abide by the legal requirements associated with these rights. • Users may download and print one copy of any publication from the public portal for the  ...  If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the "Taverne" license above, please follow below link for the End User Agreement: www.tue.nl/taverne  ...  In chapter 3 the symmetrie shortest queue problem is treated as an application of the theory in chapter 2.  ...

Models of Bus Queueing at Curbside Stops

Weihua Gu, Michael J. Cassidy, Yuwei Li
2015 Transportation Science
A Markov chain embedded in the bus queueing process is used to develop steady-state queueing models for two special cases of this stop type.  ...  The models further show why the proxy measure that is used for the delay target in other bus-stop studies is a poor one.  ...  Acknowledgements Funding for this work was provided by the University of California Transportation Center, by the Volvo Research and Educational Foundations, and by the Dwight David Eisenhower Transportation  ...

An exact root-free method for the expected queue length for a class of discrete-time queueing systems

A. Oblakova, A. Al Hanbali, R. J. Boucherie, J. C. W. van Ommeren, W. H. M. Zijm
2019 Queueing systems
For a class of discrete-time queueing systems, we present a new exact method of computing both the expectation and the distribution of the queue length.  ...  This allows us to derive a bound on the difference between the bulk-service and FCTL expected queue lengths, which turns out to be small in most of the realistic cases.  ...  Acknowledgements We would like to thank the anonymous reviewers and the associate editor for their valuable remarks and suggestions.  ...

ON THE OPTIMAL OPEN-LOOP CONTROL POLICY FOR DETERMINISTIC AND EXPONENTIAL POLLING SYSTEMS

Bruno Gaujal, Arie Hordijk, Dinard van der Laan
2007 Probability in the engineering and informational sciences (Print)
for the stochastic exponential case+  ...  + With two queues, we show that the best polling sequence is always periodic when the system is stable and forms a regular sequence+ The fraction of time spent by the server in the first queue is highly  ...  Acknowledgment This work was partially supported by the Van Gogh grant on discrete event systems+  ...

A modified HOL priority scheduling discipline: Performance analysis

Tom Maertens, Joris Walraevens, Herwig Bruneel
2007 European Journal of Operational Research
The modification is incorporated to cope with the so-called starvation problem of regular HOL priority queues.  ...  We show that the use of probability generating functions is suitable for analyzing the system contents and the packet delay.  ...  Acknowledgement The authors would like to thank the anonymous referees and the editor for their constructive suggestions, which led to a considerable improvement of this paper.  ...

Effect of Bitcoin fee on transaction-confirmation process [article]

Shoji Kasahara, Jun Kawahara
2017 arXiv   pre-print
In this paper, we analyze the transaction-confirmation time by queueing theory.  ...  We also consider the effect of the maximum block size on the transaction-confirmation time.  ...  Acknowledgment The first author would like to thank Prof. Tetsuya Takine of Osaka University for his valuable comment on the analysis of the queueing model in the paper.  ...
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