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Retrial BMAP/PH/N Queueing System with a Threshold-Dependent Inter-Retrial Time Distribution

Valentina I. Klimenok, Alexander N. Dudin, Vladimir M. Vishnevsky, Olga V. Semenova
2022 Mathematics  
We made sure numerically that there was a reasonable value of the threshold under which our model can be served as a good approximation of the BMAP/PH/N queueing system with the PH distribution of inter-retrial  ...  Only a few publications dealt with retrial queueing systems with non-exponential inter-retrial times.  ...  Model Description The system with retrials under study is of the BMAP/PH/N type.  ... 
doi:10.3390/math10020269 fatcat:pss7oqnv6fbexnprwj44xannhu

A matrix continued fraction approach to multiserver retrial queues

Tuan Phung-Duc, Hiroyuki Masuyama, Shoji Kasahara, Yutaka Takahashi
2011 Annals of Operations Research  
Artalejo and Pla [6] further evaluate the effect of customer retrials on operations of telecommunication systems, by a retrial queue with  ...  Retrial queues arise in various systems such as telecommunications, computer networks and call centers [1, 6, 7, 21, 22, 27, 31] .  ...  [9] and Klimenok and Dudin [20] consider a BMAP/PH/N retrial queue, which is more general than the model of this paper.  ... 
doi:10.1007/s10479-011-0840-4 fatcat:xawxu2bxrrgqjlmcgqnzqev3ca

The retrial queueing system operating in random environment

Che Soong Kim, Valentina Klimenok, Sang Cheon Lee, Alexander Dudin
2007 Journal of Statistical Planning and Inference  
The system has R operation modes which are switched by a Markovian random environment.  ...  A single-server retrial queueing model with the batch Markovian arrival process and phase-type service time distribution is analyzed.  ...  In the paper Breuer et al. (2002) , the retrial BMAP/PH/N system with a constant and infinitely increasing retrial rate is analyzed.  ... 
doi:10.1016/j.jspi.2007.04.009 fatcat:b2bomr2ykzf3na2hqmemz3ucmy

Modeling the access to a wireless network at hot spots

L. Breuer, V. Klimenok, A. Birukov, A. Dudin, Udo R. Krieger
2005 Transactions on Emerging Telecommunications Technologies  
This paper presents a model of such networks in terms of a BMAP/ PH/N retrial queue.  ...  First, the loss model BMAP/PH/N with retrials is described.  ...  CONCLUSIONS The access to a wireless network at hot spots has been modeled at the connection level by a BMAP/PH/N retrial queue.  ... 
doi:10.1002/ett.1000 fatcat:tftmnoblzzghfcoq4lu5sgizp4

On the BMAP_1, BMAP_2/PH/g, c retrial queueing system [article]

Jinbiao Wu, Yi Peng, Zaiming Liu
2015 arXiv   pre-print
In this paper, we analyze a retrial queueing system with Batch Markovian Arrival Processes and two types of customers.  ...  We find that the performance measures are mainly affected by the two types of customers' arrivals and service patterns, but the retrial rate plays a less crucial role.  ...  Conclusions In this paper, we have investigated the BMAP/PH/N type retrial queue with two types of customers.  ... 
arXiv:1504.01191v1 fatcat:72m6sks6qfddxjda4bqgud4zee

On the \begin{document}$ BMAP_1, BMAP_2/PH/g, c $\end{document} retrial queueing system

Yi Peng, ,School of Mathematical Science, Changsha Normal University, Changsha 410100, Hunan, China, Jinbiao Wu, ,School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
2017 Journal of Industrial and Management Optimization  
We find that the performance measures are mainly affected by the two types of customers' arrivals and service patterns, but the retrial rate plays a less crucial role.  ...  In this paper, we consider the BMAP/PH/c retrial queue with two types of customers where the rate of individual repeated attempts from the orbit is modulated according to a Markov Modulated Poisson Process  ...  In this paper, we have investigated the BMAP/PH/N type retrial queue with two types of customers which is a generalization of the MAP/M/N retrial queue with two types of customers studied in [13] .  ... 
doi:10.3934/jimo.2020124 fatcat:znu5snsgfjem3bf3bt5ynisbne

Page 1235 of Mathematical Reviews Vol. , Issue 2003B [page]

2003 Mathematical Reviews  
BMAP/PH/N system.  ...  The system has a partial acceptance policy for batch arrivals. If an arriving batch would cause the system state to become larger than k, then the state becomes A and the excess arrivals are lost.  ... 

Analysis of BMAP(r)/M(r)/N(r) Type Queueing System Operating in Random Environment
BMAP(r)/M(r)/N(r) 대기행렬시스템 분석

Chesoong Kim, Sergey Dudin
2016 Journal of Korean Institute of Industrial Engineers  
A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment.  ...  The main performance measures of the system are calculated. Numerical results are presented.  ...  In Kim et al. (2009) , the BMAP/PH/N/N queue operating in the RE is investigated. The arrival flow is described by the batch Markov arrival process (BMAP). The system does not have a buffer.  ... 
doi:10.7232/jkiie.2016.42.1.030 fatcat:j4ovhyedgvd6ljiwjmvvb4ums4

Mathematical Analysis of Queue with Phase Service: An Overview

Richa Sharma
2014 Advances in Operations Research  
A large number of models have been developed in the area of queueing theory incorporating the concept of phase service.  ...  The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein  ...  /PH/N Batch Arrival, server breakdown, -policy, and phase type service Kim et al. [139] Probability generating function 1 p 1 2 p 2 p 1 1 2 Table 3 : 3 Literature on vacation queue  ... 
doi:10.1155/2014/240926 fatcat:w4cx7rksdvgfrgqom3iu4vloj4

Generalized survivability analysis of systems with propagated failures

Khalid Al-Begain, Alexander Dudin, Valentina Klimenok, Sergey Dudin
2012 Computers and Mathematics with Applications  
The paper presents a generalized model for quantifying and evaluating the survivability of systems and the services provided by the systems.  ...  For this purpose, we consider a multi-server system with infinite buffer, Markovian Arrival Process (MAP) and phase type (PH) service time distribution.  ...  Besides already mentioned papers [6, 4] , we can refer only to the paper [7] where very general multi-server unreliable BMAP/PH/N retrial queue was considered and the paper [8] where unreliable MAP  ... 
doi:10.1016/j.camwa.2012.02.053 fatcat:qxjfe6vfffbxlhx43yn4mfg5ge

From Exhaustive Vacation Queues to Preemptive Priority Queues with General Interarrival Times

Dieter Fiems, Stijn De Vuyst
2018 International Journal of Applied Mathematics and Computer Science  
By a transform approach, we obtain an expression for the probability generating function of the waiting time of customers in such a system.  ...  system.  ...  Analysis of unreliable BMAP/PH/N type queue with Markovian flow of breakdowns, Applied Mathematics and Computation 314: 154-172. Klimenok, V. (2001).  ... 
doi:10.2478/amcs-2018-0053 fatcat:l5yqze5x3nhtzlooz2otdi6nou

Page 2647 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
J. see Borovkoy, A. A. et al., 2003m:60255 Brémaud, Pierre see Baccelli, Francois, 2003m:60001 Breuer, Lothar (with Dudin, Aleksandr; Klimenok, Valentina) A retrial BMAP/PH/N system.  ...  On the critical sample size of the statistical estimator for some queueing systems. (English summary) 2003j:60129 Lebedev, E. A. On the first passage time of removing level for retrial queues.  ...