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ON APPROXIMATIONS FOR GI/G/c RETRIAL QUEUES

Yang Woo Shin, Dug Hee Moon
2013 Journal of Applied Mathematics and Informatics  
The results reveal the performance measures are more sensitive with respect to the interarrival time than the service time.  ...  The effects of the moments of the interarrival time and service time on the system performance measures such as blocking probability, mean and standard deviation of the number of customers in service facility  ...  and related references for approximations of ordinary GI/G/c queue see [18] .  ... 
doi:10.14317/jami.2013.311 fatcat:ryqnpvofgvg4nnn5h2jctqz5ne

A Generalized Loss Network Model with Overflow for Capacity Planning of a Perinatal Network [article]

Md Asaduzzaman, Thierry J Chaussalet
2011 arXiv   pre-print
A two-moment approximation is performed to obtain the steady state solution of the GI/G/c/0 loss systems, and expressions for rejection probability and overflow probability have been derived.  ...  Decomposing the network by hospitals, each unit is analyzed with a GI/G/c/0 overflow loss network model.  ...  Atkinson (2009) developed a heuristic approach for the numerical analysis of GI/G/c/0 queueing systems with examples of the two-phase Coxian distribution.  ... 
arXiv:1110.6544v2 fatcat:s43uxvj2cfc2bkjedwvauhhsva

Capacity planning of a perinatal network with generalised loss network model with overflow

Md Asaduzzaman, Thierry J. Chaussalet
2014 European Journal of Operational Research  
A two-moment approximation is performed to obtain the steady state solution of the GI/G/c/0 loss systems, and expressions for rejection probability and overflow probability have been derived.  ...  Decomposing the network by hospitals, each unit is analysed with a GI/G/c/0 overflow loss network model.  ...  developed a heuristic approach for the numerical analysis of GI/G/c/0 queueing systems with examples of the two-phase Coxian distribution.  ... 
doi:10.1016/j.ejor.2013.06.037 fatcat:e4otwxrjdrc2toxmdvdoyoo5cq

Page 1111 of Mathematical Reviews Vol. , Issue 85c [page]

1985 Mathematical Reviews  
With this approach, upper bounds of mean actual/virtual waiting times and mean queue length at random epochs can be derived for the bulk arrival queues GI* /G/1 and GI* /G/c (lower bounds can be derived  ...  The author derives easily computable upper bounds for the vari- ance 7, of the stationary waiting time in GI/G/1 queues, us- ing a formula for of, which contains moments of the idle time.  ... 

A review of open queueing network models of manufacturing systems

Gabriel R. Bitran, Sriram Dasu
1992 Queueing systems  
As a result researchers have been able to approximate some of the optimal design problems by convex programs. In the second part of this paper we describe these developments.  ...  In this paper we review open queueing network models of manufacturing systems. The paper consists of two parts. In the first part we discuss design and planning problems arising in manufacturing.  ...  Wein for their comments and suggestions.  ... 
doi:10.1007/bf01158637 fatcat:bruggsutqfdj3ctfngclc5raoa

Bayesian control of the number of servers in a queueing system

M. Concepción Ausín, Rosa E. Lillo, Michael P. Wiper
2007 Journal of Statistical Planning and Inference  
In this paper we consider the problem of designing a GI/M/c queueing system.  ...  We provide a numerical example based on real data obtained from a bank in Madrid. Abstract In this paper we consider the problem of designing a GI/M/c queueing system.  ...  Acknowledgements We acknowledge the financial support partially provided by project DGICYT BEC2000-0167.  ... 
doi:10.1016/j.jspi.2006.05.016 fatcat:ihvbhpvy4radhoegckeb5pokm4

Finite Queueing Modeling and Optimization: A Selected Review

F. R. B. Cruz, T. van Woensel
2014 Journal of Applied Mathematics  
This review provides an overview of the queueing modeling issues and the related performance evaluation and optimization approaches framed in a joined manufacturing and product engineering.  ...  Such networks are represented as queueing networks. The performance of the queueing networks is evaluated using an advanced queueing network analyzer: the generalized expansion method.  ...  Acknowledgments The research of professor Frederico Cruz has been partially funded by the Brazilian agencies, CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) of the Ministry for Science  ... 
doi:10.1155/2014/374962 fatcat:euv3sfjo4rawtbinhvjf3r54vm

Properties and performance modelling of finite buffer M/G/1/K networks

J. MacGregor Smith
2011 Computers & Operations Research  
A two-moment approximation schema is developed for the probability distribution of M/G/1/K systems and extended to the analysis of M/G/1/K queueing networks.  ...  Finite buffer, single-server queueing systems and networks are difficult to analyze since the length of time a customer spends in the system does not follow the Markovian property.  ...  Acknowledgement I am indebted to the reviewer for insights and help in clarifying the logistics curve properties for the M/G/1/K system as well as numerous suggestions for improving the manuscript.  ... 
doi:10.1016/j.cor.2010.08.014 fatcat:vv5ptmmpmzglhd2bv2yne5zrli

Optimal Routing in General Finite Multi-Server Queueing Networks

Tom van Woensel, Frederico R. B. Cruz, Gerardo Adesso
2014 PLoS ONE  
The performance of the finite queueing network is evaluated with a known approximate performance evaluation method and the optimization is done by means of a heuristics based on the Powell algorithm.  ...  We show numerical results for some networks to quantify the quality of the routing vector approximations obtained.  ...  the extension to GI=G=c=K queueing networks.  ... 
doi:10.1371/journal.pone.0102075 pmid:25010660 pmcid:PMC4092093 fatcat:ejxwmyhsizegvfve3wnnqskhh4

Maximum entropy analysis to the N policy M/G/1 queueing system with a removable server

Kuo-Hsiung Wang, Shu-Lung Chuang, Wen-Lea Pearn
2002 Applied Mathematical Modelling  
Applying the method of maximum entropy to the ordinary GI/ G/C queueing system, Wu and Chan [6] derived the approximate formulae for the steady-state probability distributions of the number of customers  ...  with parameter k and service times are independent and identically distributed (i.i.d.) random variables obeying a general distribution SðuÞðu P 0Þ with a mean service time 1=l and a finite variance r  ...  The exact and the approximate expected waiting time in the queue Here we derive the exact and the approximate formulae for the expected waiting time in the queue for the N policy M/G/1 queueing system.  ... 
doi:10.1016/s0307-904x(02)00056-2 fatcat:kixlfgodv5a7rb2pnyrs6jdvju

Modeling the performance of FDL buffers with wavelength conversion

W. Rogiest, D. Fiems, K. Laevens, H. Bruneel
2009 IEEE Transactions on Communications  
Relying on generating functions, we developed a Fiber Delay Line (FDL) buffer model with wavelength conversion, which assumes the buffer located at the output of an optical switch, having access to multiple  ...  Several numerical examples assess the applicability of our approximation, and show that our approach yields accurate results.  ...  The same methodology can also be applied to the more general setting of GI/G/c optical buffers whereby the probability generating function of the inter-arrival times is a rational function.  ... 
doi:10.1109/tcomm.2009.12.080040 fatcat:dg4vlrmpyjfvhht7ktooxjlnuy

Error Bounds for Perturbing Nonexponential Queues

Nico M. van Dijk, Masakiyo Miyazawa
2004 Mathematics of Operations Research  
Finally, for the GI/M/c/N queue, a similar result is obtained with a perturbation of the inter-arrival time distribution.  ...  The general framework is worked out in detail for the three types of finite or infinite buffer queues: GI/G/1/N , M/G/c/N , and GI/M/c/N .  ...  Acknowledgment We are grateful to the anonymous referee for his careful reading and valuable comments. We appreciate the international exchange program of the Japan Society for the Promotion  ... 
doi:10.1287/moor.1040.0111 fatcat:znnk67kuavbfznxuryaqke6u5a

Analysis of a discrete-time single-server queue with an occasional extra server

Herwig Bruneel, Sabine Wittevrongel
2017 Performance evaluation (Print)  
We consider a discrete-time queueing system having two distinct servers: one server, the "regular" server, is permanently available, while the second server, referred to as the "extra" server, is only  ...  appearing in the formulas can be expressed in terms of a finite number of independent unknowns.  ...  Acknowledgement This research has been partly funded by the Interuniversity Attraction Poles Programme initiated by the Belgian Science Policy Office (BelSPO), Belgium.  ... 
doi:10.1016/j.peva.2017.08.009 fatcat:okbjkvujgzggta4o45fc7vusye

Variance Reduction Techniques for the Simulation of Markov Processes, I: Multiple Estimates

Philip Heidelberger
1980 IBM Journal of Research and Development  
For this example we are interested in estimating the expected stationary waiting time in a GI/G/c queue . The number of servers itt the queue , c , is assumed to be greater than 1 .  ...  further research in this direc- ... , N where N is a finite positive integer and 0 < A , ~ < cc~ The process CX (t) , t >0 ) is then the queue length process for an 11/14/1 queue with finite queue capacity  ...  D E C LA S S I F IC A T I O N / O O W N G R A O I NG SCHEDULE C : 5 r R t a u rIo N S T A T E M EN T (el thia R.po rt) A pproved for public release : distribution unlimited .  ... 
doi:10.1147/rd.245.0570 fatcat:jqadqmamazfkhf2c4jqwephlru

Perfect and nearly perfect sampling of work-conserving queues

Yaofei Xiong, Duncan J. Murdoch, David A. Stanford
2015 Queueing systems  
It is a variant of dominated CFTP that we call the CFTP Block Absorption (CFTP-BA) method. Time-varying queues with periodic Poisson arrivals are being considered in this thesis.  ...  Besides the First Come First Served (FCFS) queues, many efforts are putted on the accumulating priority queue (APQ), where a customer accumulates priority linearly while waiting.  ...  Miscellaneous algorithms 2.5.1 Ordinary simulation of GI/G/c FCFS queue with random assignment This algorithm is introduced because the Random Assignment (RA) model serves as a stochastic upper bound (  ... 
doi:10.1007/s11134-015-9437-y fatcat:74fpzjqufrfcrbbrrzpe7gvuqq
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