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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. ...

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

2017
*
Aequationes Mathematicae
*

We hope that in this way we will make it easier to take some steps forward

doi:10.1007/s00010-017-0471-1
fatcat:p3hcuqlapfgf3aitz33n7stie4
*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. ...##
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Analytic Root Clustering: A Complete Algorithm Using Soft Zero Tests
[chapter]

2013
*
Lecture Notes in Computer Science
*

A challenge to current

doi:10.1007/978-3-642-39053-1_51
fatcat:zxgpk2iqw5f5xeocnd6w5eb4pm
*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]

2020
*
arXiv
*
pre-print

To obtain

arXiv:2001.08959v3
fatcat:5wy3n2qfefaxjdeenp7xohqphy
*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

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

1997
*
Journal of Applied Mathematics and Stochastic Analysis
*

Explicit solutions are discussed

doi:10.1155/s1048953397000464
fatcat:umdb2h625vgb7oc45owy6zpppe
*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

2005
*
Queueing systems
*

While in general this is true

doi:10.1007/s11134-005-0402-z
fatcat:kegbjcfdz5g7phyejefwpzsmjm
*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]

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

1996
*
Journal of the Operational Research Society
*

accessing publications that users recognise and abide by

doi:10.2307/3010589
fatcat:tcksxcmoprh77gohr3ugs4o6sq
*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

2015
*
Transportation Science
*

A Markov chain embedded in

doi:10.1287/trsc.2014.0537
fatcat:aj2pghl5jfgytbu4jnj6v54ps4
*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

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. ...

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

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

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]

2017
*
arXiv
*
pre-print

In this paper, we analyze

arXiv:1604.00103v3
fatcat:vcyt2gzkyzd4digth5jb42buwm
*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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