109. M/G/1/K machine repair system with general vacation under N-policy
Invited abstract in session WB-54: Stochastic Models and Optimization I, stream Stochastic modelling.
Wednesday, 10:30-12:00Room: Liberty 1.08
Authors (first author is the speaker)
| 1. | Sudeep Singh Sanga
|
| Mathematics, SV National Institute of Technology Surat |
Abstract
This study focuses on the modeling and performance of an M/G/1/K machine repair system that incorporates a general vacation feature under the N-policy, along with handling failure recovery and reboot processes. In the system design, the repairman can take a vacation only when no failed machines are in the system. He returns from vacation when the number of failed machines reaches the threshold value of N. In cases where faults in the system are not successfully detected, the system reconfigures itself by initiating a reboot process. To develop the mathematical model for the M/G/1/K machine repair system, supplementary variables corresponding to remaining repair and vacation times are employed to formulate the steady-state equations. These equations are the foundation for deriving explicit formulae for the probability distributions using the Laplace-Stieltjes transform and the recursive method. Various performance measures have also been developed, including the expected system size, machine availability, etc. Furthermore, we construct the cost function and formulate an optimization problem to determine the minimum cost. The objective is to find optimal values for the decision variables, such as the number of operating machines, the threshold parameter, the repair rate, and the vacation rate. Particle swarm optimization (PSO) is employed to solve the optimization problem.
Keywords
- Optimization Modeling
- Queuing Systems
- Stochastic Models
Status: accepted
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