Vacation model for Markov machine repair problem with two heterogeneous unreliable servers and threshold recovery

Abstract

Markov model of multi-component machining system comprising two unreliable heterogeneous servers and mixed type of standby support has been studied. The repair job of broken down machines is done on the basis of bi-level threshold policy for the activation of the servers. The server returns back to render repair job when the prespecified workload of failed machines is build up. The first (second) repairman turns on only when the work load of N 1 (N 2 ) failed machines is accumulated in the system. The both servers may go for vacation in case when all the machines are in good condition and there are no pending repair jobs for the repairmen. Runge-Kutta method is implemented to solve the set of governing equations used to formulate the Markov model. Various system metrics including the mean queue length, machine availability, throughput, etc., are derived to determine the performance of the machining system. To provide the computational tractability of the present investigation, a numerical illustration is provided. A cost function is also constructed to determine the optimal repair rate of the server by minimizing the expected cost incurred on the system. The hybrid soft computing method is considered to develop the adaptive neuro-fuzzy inference system (ANFIS). The validation of the numerical results obtained by Runge-Kutta approach is also facilitated by computational results generated by ANFIS.

Algorithmic Analysis of Finite-Source Multi-Server Heterogeneous Queueing Systems

“…As for finite-source systems operating under a threshold policy, we know only research papers dedicated to single server systems with a unit threshold N-policy, see e.g., [11]. Here the threshold policy states that the server in a repair facility must be switched on only when the number of failed machines reaches to predefined threshold level N. In [12], the authors generalized the model to the case of two heterogeneous unreliable servers operating under policies N 1 and N 2 . Although there is a considerable amount of results on finite-source queues, the controlled systems with heterogeneous servers operating without preemption have not been investigated before.…”

ANFIS and Cost Optimization for Markovian Queue with Operational Vacation

“…Bhargava and Jain (2014) presented a comparative study of analytical formulae based numerical results and ANFIS results for the unreliable multi server queueing system. Jain and Meena (2018) also considered the hybrid soft computing ANFIS approach to study the performance of machining system. By considering the admission control based on F policy, Sanga and Jain (2019) investigated M/M/1/K queueing system with general retrial times and gave cost optimization and ANFIS results.…”

Performance Analysis of Machine Repair System with Balking, Reneging, Multiple Working Vacations and Two Removable Servers Operating under the Triadic (0,Q,N,M) Policy

“…Chen et al (2016) dealt with the reliability and sensitivity analysis of a machine repair system with warm standbys and an unreliable server having multiple-vacation wherein Laplace transform technique is used to derive the reliability function and the mean time to system failure. Jain and Meena (2018) applied a vacation model for a Markovian machine repair model. He et al (2019) discussed a machine repair problem with a single working vacation.…”