`a`
Journal of Industrial and Management Optimization (JIMO)
 

On the multi-server machine interference with modified Bernoulli vacation

Pages: 1191 - 1208, Volume 10, Issue 4, October 2014      doi:10.3934/jimo.2014.10.1191

 
       Abstract        References        Full Text (761.5K)       Related Articles       

Tzu-Hsin Liu - Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, 404, Taiwan (email)
Jau-Chuan Ke - Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, 404, Taiwan (email)

Abstract: We study the multi-server machine interference problem with repair pressure coefficient and a modified Bernoulli vacation. The repair rate depends on the number of failed machines waiting in the system. In congestion, the server may increase the repair rate with pressure coefficient $\theta$ to reduce the queue length. At each repair completion of a server, the server may go for a vacation of random length with probability $p$ or may continue to repair the next failed machine, if any, with probability $1-p$. The entire system is modeled as a finite-state Markov chain and its steady state distribution is obtained by a recursive matrix approach. The major performance measures are evaluated based on this distribution. Under a cost structure, we propose to use the Quasi-Newton method and probabilistic global search Lausanne method to search for the global optimal system parameters. Numerical examples are presented to demonstrate the application of our approach.

Keywords:  Bernoulli vacation schedule, machine interference problem, Quasi-Newton method, repair pressure, probabilistic global search Lausanne.
Mathematics Subject Classification:  Primary: 90B22; Secondary: 60K25.

Received: April 2013;      Revised: November 2013;      Available Online: February 2014.

 References