Paper Info

Title | ||
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An analytic solution of the waiting time distribution for the discrete-time GI/G/1 queue |

Abstract | ||
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In this paper, a GI/G/1 queue in a discrete-time domain is analyzed. The only restriction we introduce for an analysis is that each of the interarrival time distributions for the batches of arriving customers and the service time distribution for each customer can be represented as a rational function. In the analysis, the distribution of an amount of the unfinished work at a certain instance of a batch arrival (say, at ( n + 1)th arrival of the batch) is related to that of the previous one (at n th arrival). Using the relation, the equilibrium distributions for the amount of unfinished work immediately before the arrival instances of the batch of the customers are obtained. The probability generating function for the waiting time distribution of the customers is then derived. An explicit formula for the probability distribution of the waiting time for a special case where the batch arrivals follow a negative binomial distribution is also derived. Furthermore, the analysis is extended to GI/G/1 queues with vacations where the server begins a vacation with random length every time the system becomes empty. |

Year | DOI | Venue |
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1991 | 10.1016/0166-5316(91)90042-2 | Perform. Eval. |

Keywords | Field | DocType |

gi/g/1 queue,discrete-time gi,analytic solution,unfinished work,discrete-time systems,queueing systems,time distribution,waiting time distribution,discrete time | Generating function,G/G/1 queue,Queue,M/G/1 queue,Real-time computing,Probability distribution,Negative binomial distribution,Discrete time and continuous time,Mathematics,Discrete system | Journal |

Volume | Issue | ISSN |

13 | 2 | Performance Evaluation |

Citations | PageRank | References |

6 | 1.52 | 5 |

Authors | ||

2 |

Authors (2 rows)

Cited by (6 rows)

References (5 rows)

Name | Order | Citations | PageRank |
---|---|---|---|

Masayuki Murata | 1 | 1615 | 239.01 |

Hideo Miyahara | 2 | 277 | 56.97 |