# The BMAP/PH/1 retrial queueing system operating in random environment

@article{Kim2007TheBR, title={The BMAP/PH/1 retrial queueing system operating in random environment}, author={Che Soong Kim and Valentina I. Klimenok and Sang Cheon Lee and Alexander N. Dudin}, journal={Journal of Statistical Planning and Inference}, year={2007}, volume={137}, pages={3904-3916} }

## 15 Citations

The BMAP/PH/N retrial queueing system operating in Markovian random environment

- MathematicsComput. Oper. Res.
- 2010

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

- Mathematics
- 2016

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 number of available servers, the…

Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment

- Mathematics
- 2011

The MAP/PH/N retrial queue in a random environment

- Mathematics
- 2013

We consider the MAP/PH/N retrial queue with a finite number of sources operating in a finite state Markovian random environment. Two different types of multi-dimensional Markov chains are…

Analysis of an MMAP/PH1, PH2/N/∞ queueing system operating in a random environment

- Business, MathematicsInt. J. Appl. Math. Comput. Sci.
- 2014

A multi-server queueing system with two types of customers and an infinite buffer operating in a random environment as a model of a contact center is investigated and the criterion of ergodicity for a multi-dimensional Markov chain describing the behavior of the system and the algorithm for computation of its steady-state distribution are outlined.

The Unreliable M/M/1 Retrial Queue in a Random Environment

- Mathematics
- 2012

We examine an M/M/1 retrial queue with an unreliable server whose arrival, service, failure, repair, and retrial rates are all modulated by an exogenous random environment. Provided are conditions…

Performance Analysis of a Block-Structured Discrete-Time Retrial Queue with State-Dependent Arrivals

- MathematicsDiscret. Event Dyn. Syst.
- 2010

A new discrete block state-dependent arrival (D-BSDA) distribution is introduced which provides fresh insights leading to a successful generalization of the discrete-time Markovian arrival process ( D-MAP).

Cellular mobile networks with repeated calls operating in random environment

- Computer Science, BusinessComput. Oper. Res.
- 2010

Dynamic balancing in finite processor sharing queues with guard bandwidth policy, multiclass retrial users and signals

- Computer SciencePerform. Evaluation
- 2017

## References

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A Retrial BMAP/PH/N System

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A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed and the existence conditions for the stationary distribution are obtained and the algorithms for calculating the stationary state probabilities are elaborate.

A BMAP/SM/1 Queueing System with Hybrid Operation Mechanism

- Mathematics
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A single-server queueing system BMAP/SM/1 is studied. It operates as a retrial queueing system under decentralized and centralized retrial strategies with and without loss of primary customers, as…

A BMAPPH1 queue with feedback operating in a random environment

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A Multi-Server Retrial Queue with BMAP Arrivals and Group Services

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This paper considers a c-server queuing model in which customers arrive according to a batch Markovian arrival process (BMAP) and the steady state analysis of the model is performed by exploiting the structure of the coefficient matrices.

Single-Server Queues with Markov-Modulated Arrivals and Service Speed

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This paper considers single-server queues with several customer classes and derives the Laplace–Stieltjes transform of the actual waiting time distribution in the original queue from the joint distribution of the length of a busy period and the number of customers served during the busy period.

The map/ph/1 retrial queue

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We consider the MAP/PH/1 retrial queue. We obtain a sufficient condition for ergodicity and derive a numerical method for obtaining the stationary distribution of states and the distribution and…

New results for the single server queue with a batch Markovian arrival process

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This work generalizes results to the single server queue with the batch arrival process and emphasizes the resulting simplifications of the computational complexity of the algorithmic solution of single server queues with a general Markovian arrival process.