## Abstract

We consider a system comprised of two connected M/M/•/• type queues, where customers of one queue act as servers for the other queue. One queue, Q _{1}, operates as a limited-buffer M/M/1/N-1 system. The other queue, Q _{2}, has an unlimited-buffer and receives service from the customers of Q _{1}. Such analytic models may represent applications like SETI@home, where idle computers of users are used to process data collected by space radio telescopes. Let L _{1} denote the number of customers in Q _{1}. Then, two models are studied, distinguished by their service discipline in Q _{2}: In Model 1, Q _{2} operates as an unlimited-buffer, single-server M/M/1/∞ queue with Poisson arrival rate λ _{2} and dynamically changing service rate μ _{2} L _{1}. In Model 2, Q _{2} operates as a multi-server M/M/L _{1}/∞ queue with varying number of servers, L _{1}, each serving at a Poisson rate of μ _{2}. We analyze both models and derive the Probability Generating Functions of the system's steady-state probabilities. We then calculate the mean total number of customers present in each queue. Extreme cases are indicated.

Original language | English |
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Pages (from-to) | 271-288 |

Number of pages | 18 |

Journal | Queueing Systems |

Volume | 60 |

Issue number | 3-4 |

DOIs | |

State | Published - Dec 2008 |

## Keywords

- Connected 2-queue systems
- Customers act as servers
- Markovian queues