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Multidimensional Transform Inversion with Applications to the Transient M/G/1 Queue

Gagan L. Choudhury, David M. Lucantoni, Ward Whitt
1994 The Annals of Applied Probability  
of the transient queue-length and workload distributions, in the M/G/1 queue.  ...  M/G/1 queue, transient distributions. 1980 AMS subject classification: 65D30, 60K25. workload and queue-length distributions in the M/G/1 queue; see Taka ´ cs (1962).  ...  We thank him for showing the way.  ... 
doi:10.1214/aoap/1177004968 fatcat:y723oy5zzjbvpmxlhvzbn4x6am

AN EXTENSION OF THE MATRIX-ANALYTIC METHOD FOR M/G/1-TYPE MARKOV PROCESSES

Yoshiaki Inoue, Tetsuya Takine
2015 Journal of the Operations Research Society of Japan  
The M/G/1-type Markov process was first introduced as a generalization of the workload process in the MAP/G/1 queue and its stationary distribution was analyzed under a strong assumption that the conditional  ...  We assume that U (t) (t ≥ 0) is skip-free to the left, and therefore we call it the M/G/1-type Markov process.  ...  As mentioned in Section 1, the M/G/1-type Markov process was first introduced as a continuous analog of the M/G/1 type Markov chain.  ... 
doi:10.15807/jorsj.58.376 fatcat:cvapr3i5fvdnjjw45j6vk7hlva

ON THE M/G/1 QUEUE WITH MULTIPLE VACATIONS AND GATED SERVICE DISCIPLINE

Tetsuya Takine, Toshiharu Hasegawa
1992 Journal of the Operations Research Society of Japan  
We first provide an alternative appreach to derive the Laplace-Stieltjes transfbrrn of the limiting waiting time distribution, which reveals the stochastic structure of the gated vacatien system.  ...  Next we discuss the regenerative cycle of the gated vacation system. Based on these considerations, we carry our a time-dependent analysis, from which various formulas are derived.  ...  Acknowledgment The authors would like to thank Dr, H. Takagi of IBM Tokyo Research Laboratory and the referees for their suggestions and comments.  ... 
doi:10.15807/jorsj.35.217 fatcat:gt76xipsxjaxbavyd4rldsoyaq

The rate of convergence to stationarity for M/G/1 models with admission controls via coupling [article]

Martin Kolb, Wolfgang Stadje, Achim Wübker
2012 arXiv   pre-print
We study the workload processes of two restricted M/G/1 queueing systems: in Model 1 any service requirement that would exceed a certain capacity threshold is truncated; in Model 2 new arrivals do not  ...  However, we prove that for the class of all Model 1 workload processes there is no uniform bound.  ...  Introduction In this paper we consider the long-run behavior of the workload processes V t of the two most important M/G/1 queueing systems with admission restrictions.  ... 
arXiv:1201.0532v1 fatcat:yjj5poi2cvbs5llfxzfqh7ekna

Toward Green Sensor Field by Optimizing Power Efficiency Using D-Policy M/G/1 Queuing Systems

Fuu-Cheng Jiang, Hsiang-Wei Wu, Fang-Yi Leu, Chao-Tung Yang
2013 Mobile Information Systems  
Making things different, in this article, we propose a novel optimization framework for alleviating power consumption of sensor node with the D-policy M/G/1 queuing approach.  ...  Toward green sensor field, the proposed power-saving technique can be applied to prolong the lifetime of ZSN economically and effectively.  ...  Acknowledgments This work was supported in part by the National Science Council, Taiwan ROC, under grant numbers NSC 101-2218-E-029-004, NSC 101-2221-E-029-014, and NSC 101-2622-E-029-008-CC3.  ... 
doi:10.1155/2013/642692 fatcat:x2qpbwt7abajzddq7u5ru5guta

A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues

Brian H. Fralix, Germán Riaño
2010 Journal of Applied Probability  
This new higher-moment law is then used to provide expressions for all moments of the number of customers in the system in an M/G/1 preemptive last-come-first-served queue at a time t > 0, for any initial  ...  What is especially novel about our approach is the use of Palm measures that are induced by nonstationary point processes, as these measures are not commonly found in the queueing literature.  ...  The authors would like to thank Yoni Nazarathy for stimulating discussions, which eventually led to the creation of this paper.  ... 
doi:10.1239/jap/1276784903 fatcat:uekvfgaqejbhlbmcimyozva65u

A new look at transient versions of Little's law, and M/G/1 preemptive last-come-first-served queues

Brian H. Fralix, Germán Riaño
2010 Journal of Applied Probability  
This new higher-moment law is then used to provide expressions for all moments of the number of customers in the system in an M/G/1 preemptive last-come-first-served queue at a time t > 0, for any initial  ...  What is especially novel about our approach is the use of Palm measures that are induced by nonstationary point processes, as these measures are not commonly found in the queueing literature.  ...  The authors would like to thank Yoni Nazarathy for stimulating discussions, which eventually led to the creation of this paper.  ... 
doi:10.1017/s0021900200006756 fatcat:et2ngeazbfffri6dgr7qdqp3da

Page 7483 of Mathematical Reviews Vol. , Issue 2002J [page]

2002 Mathematical Reviews  
The authors consider an M/G/1 queueing system having a finite workload capacity c.  ...  The authors present a new algorithm for the computation of the first passage matrix of M/G/1-type Markov chains.  ... 

Numerical Transform Inversion to Analyze Teletraffic Models [chapter]

Gagan L. Choudhury, David M. Lucantoni, Ward Whitt
1994 Teletraffic science and engineering  
The second combines numerical transform inversion (ordinary and multidimensional) and matrixanalytic methods to describe the transient behavior of the BMAP/G/1 queue (with a batch Markovian arrival process  ...  The first combines numerical transform inversion with numerical integration of Pollaczek's classical contour integrals to treat the general GI/G/1 queue.  ...  As shown in [37] , just as for the M/G/1 queue, it is possible to derive transforms of the transient distributions of the standard stochastic processes of interest in the BMAP/G/1 queue.  ... 
doi:10.1016/b978-0-444-82031-0.50107-4 fatcat:gpmywpzpmjhxnfhunt6fywpmoa

Page 433 of Mathematical Reviews Vol. , Issue 2004a [page]

2004 Mathematical Reviews  
In this significant contribution, the author identifies conditions for the Markov chains of M/G/1, GI/M/1 and matrix M/G/1 types with a tree structure to be positive recurrent, null recurrent, or transient  ...  ; Amsterdam) The asymptotic workload behavior of two coupled queues.  ... 

Page 2515 of Mathematical Reviews Vol. , Issue 97D [page]

1997 Mathematical Reviews  
The transform method developed in the article is supposed to be an alternative to the well known matrix-analytic method of the analysis of M/G/1-type Markov L. M.  ...  A. (1-MI; Ann Arbor, MI) Spectral analysis of M/G/1 and G/M/1 type Markov chains. (English summary) Adv. in Appl. Probab. 28 (1996), no. 1, 114-165.  ... 

Page 9199 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
The transient results obtained are applicable to almost any real life finite queuing system M/G/1/N.” 2002m:60186 60K25 Wang, Chia-Li An identity of the G//G/1 transient delay and its applications.  ...  We investigate its transient behavior by constructing a sample-path coupling of a transient and a general (delayed) process.  ... 

A Queueing System with Vacations after a Random Amount of Work

Ivo Adan, Onno Boxma, Dieter Claeys, Offer Kella
2018 SIAM Journal on Applied Mathematics  
This paper considers an M/G/1 queue with the following vacation discipline. The server takes a vacation as soon as it has served a certain amount of work since the end of the previous vacation.  ...  For the case the total amount of work till vacation is exponentially distributed, we derive the transforms of the steady-state workload at various epochs, busy period, waiting time, sojourn time, and queue  ...  The key idea was to exploit a link with a result from Cohen [5] about the transient behavior of the queue length at customer departure epochs in an ordinary M/G/1 queue and to apply contour integration  ... 
doi:10.1137/17m1142673 fatcat:vhcdlvly7zf27f4ftxjbho6mwm

Lévy processes with adaptable exponent

R. Bekker, O. J. Boxma, J. A. C. Resing
2009 Advances in Applied Probability  
In particular, we consider dam processes with a two-step release rule and M/G/1 queues in which the arrival rate, service speed, and/or jump size distribution may be adapted depending on whether the workload  ...  Feedback information about the level of the Lévy process ('workload level') may lead to adaptation of the Lévy exponent.  ...  Acknowledgements This research was done within the framework of the BRICKS project and the European Network of Excellence Euro-NGI.  ... 
doi:10.1017/s0001867800003189 fatcat:fa5nbwdodncmthum4xnkqhs2v4

Lévy processes with adaptable exponent

R. Bekker, O. J. Boxma, J. A. C. Resing
2009 Advances in Applied Probability  
In particular, we consider dam processes with a two-step release rule and M/G/1 queues in which the arrival rate, service speed, and/or jump size distribution may be adapted depending on whether the workload  ...  Feedback information about the level of the Lévy process ('workload level') may lead to adaptation of the Lévy exponent.  ...  Acknowledgements This research was done within the framework of the BRICKS project and the European Network of Excellence Euro-NGI.  ... 
doi:10.1239/aap/1240319581 fatcat:bqxdmssazvcple4dii3ry4sbma
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