Title: M/G/1/K machine repair system with general vacation under N-policy
Speaker: Dr. Sudeep Singh Sanga
Venue: Seminar hall, second floor, IEOR Building.
Day, Date, Time: Wednesday, 24th July 2024, 10:30AM-11:30AM.
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(1≤N≤K-1). 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
Brief Bio: Dr. Sudeep Singh Sanga is an Assistant Professor in the Department of Mathematics at S.V. National Institute of Technology, Surat, Gujarat. He holds a Ph.D. and M.Sc. in Mathematics from the Indian Institute of Technology Roorkee, Uttarakhand. His research interests include queueing models and optimal control policies. He joined NIT Surat in April 2021. Before his current position, he served as an Assistant Professor of Mathematics at NIT Delhi, India, from December 2019 to March 2021.