### Abstract

We consider a load-sharing problem for a multiprocessor system in which jobs have real-time constraints: if the waiting time of a job exceeds a given random amount (called the laxity of the job), then the job is considered lost. To minimize the steady-state probability of loss with respect to the load-sharing parameters, we propose to use the likelihood ratio derivative estimate approach, which has recently been studied for sensitivity analysis of stochastic systems. We formulate a recursive stochastic optimization algorithm using likelihood ratio estimates to solve the optimization problem and provide a proof for almost sure convergence of the algorithm. The algorithm can be used for on-line optimization of the real-time system and does not require a priori knowledge of the arrival rate of customers to the system or the service time and laxity distributions. To illustrate our results, we provide simulation examples.

Original language | English (US) |
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Pages (from-to) | 23-48 |

Number of pages | 26 |

Journal | Journal of Optimization Theory and Applications |

Volume | 82 |

Issue number | 1 |

DOIs | |

State | Published - Jul 1 1994 |

### All Science Journal Classification (ASJC) codes

- Control and Optimization
- Management Science and Operations Research
- Applied Mathematics

### Keywords

- Load sharing
- likelihood ratios
- real-time systems
- score function
- stochastic approximation