### Abstract

Using operator analytic techniques, the author develops a nonstationary Markovian queueing theory starting with the M(t)/M(t)/1 queue. The author employs an asymptotic approach quite different from the usual large time analysis. Instead, the author uniformly accelerates the queue length process. That is, he divides the arrival and service rate by a common parameter epsilon . Then, for a fixed time interval, the author considers the asymptotics for the distribution, mean, and variance of the queue length process as epsilon goes to zero. The effects of epsilon can be quite different for the given time interval. This gives a dynamic asymptotic behavior for the queue length process. It is possible to formulate a time dependent traffic intensity parameter that determines when the process is asymptotically stable and when it is asymptotically unstable.

Original language | English (US) |
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Pages (from-to) | 305-327 |

Number of pages | 23 |

Journal | Mathematics of Operations Research |

Volume | 10 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 1985 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Computer Science Applications
- Management Science and Operations Research