### Abstract

This paper is concerned with reliable multistation series queueing networks. Items arrive at the first station according to a Poisson distribution and an operation is performed on each item by a server at each station. Every station is allowed to have more than one server with the same characteristics. The processing times at each station are exponentially distributed. Buffers of nonidentical finite capacities are allowed between successive stations. The structure of the transition matrices of these specific type of queueing networks is examined and a recursive algorithm is developed for generating them. The transition matrices are blockstructured and very sparse. By applying the proposed algorithm the transition matrix of a K-station network can be created for any K. This process allows one to obtain the exact solution of the large sparse linear system by the use of the Gauss-Seidel method. From the solution of the linear system the throughput and other performance measures can be culculated.

Original language | English |
---|---|

Pages (from-to) | 853-883 |

Number of pages | 31 |

Journal | Computers and Operations Research |

Volume | 28 |

Issue number | 9 |

DOIs | |

Publication status | Published - Aug 2001 |

Externally published | Yes |

### Fingerprint

### Keywords

- Blocking phenomenon
- Finite queues
- Large sparse matrices
- Markov chains
- Multistation multiserver queueing networks
- Numerical solution
- Quasi-birth-death processes

### ASJC Scopus subject areas

- Information Systems and Management
- Management Science and Operations Research
- Applied Mathematics
- Modelling and Simulation
- Transportation

### Cite this

*Computers and Operations Research*,

*28*(9), 853-883. https://doi.org/10.1016/S0305-0548(00)00012-5

**A recursive algorithm for generating the transition matrices of multistation multiserver exponential reliable queueing networks.** / Vidalis, M. I.; Papadopoulos, H. T.

Research output: Contribution to journal › Article

*Computers and Operations Research*, vol. 28, no. 9, pp. 853-883. https://doi.org/10.1016/S0305-0548(00)00012-5

}

TY - JOUR

T1 - A recursive algorithm for generating the transition matrices of multistation multiserver exponential reliable queueing networks

AU - Vidalis, M. I.

AU - Papadopoulos, H. T.

PY - 2001/8

Y1 - 2001/8

N2 - This paper is concerned with reliable multistation series queueing networks. Items arrive at the first station according to a Poisson distribution and an operation is performed on each item by a server at each station. Every station is allowed to have more than one server with the same characteristics. The processing times at each station are exponentially distributed. Buffers of nonidentical finite capacities are allowed between successive stations. The structure of the transition matrices of these specific type of queueing networks is examined and a recursive algorithm is developed for generating them. The transition matrices are blockstructured and very sparse. By applying the proposed algorithm the transition matrix of a K-station network can be created for any K. This process allows one to obtain the exact solution of the large sparse linear system by the use of the Gauss-Seidel method. From the solution of the linear system the throughput and other performance measures can be culculated.

AB - This paper is concerned with reliable multistation series queueing networks. Items arrive at the first station according to a Poisson distribution and an operation is performed on each item by a server at each station. Every station is allowed to have more than one server with the same characteristics. The processing times at each station are exponentially distributed. Buffers of nonidentical finite capacities are allowed between successive stations. The structure of the transition matrices of these specific type of queueing networks is examined and a recursive algorithm is developed for generating them. The transition matrices are blockstructured and very sparse. By applying the proposed algorithm the transition matrix of a K-station network can be created for any K. This process allows one to obtain the exact solution of the large sparse linear system by the use of the Gauss-Seidel method. From the solution of the linear system the throughput and other performance measures can be culculated.

KW - Blocking phenomenon

KW - Finite queues

KW - Large sparse matrices

KW - Markov chains

KW - Multistation multiserver queueing networks

KW - Numerical solution

KW - Quasi-birth-death processes

UR - http://www.scopus.com/inward/record.url?scp=0035427488&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035427488&partnerID=8YFLogxK

U2 - 10.1016/S0305-0548(00)00012-5

DO - 10.1016/S0305-0548(00)00012-5

M3 - Article

AN - SCOPUS:0035427488

VL - 28

SP - 853

EP - 883

JO - Surveys in Operations Research and Management Science

JF - Surveys in Operations Research and Management Science

SN - 0305-0548

IS - 9

ER -