Optimal Control of Service Rate in a Service Facility System Maintenance and Retrial Demands

This paper, deals with a problem of optimally controlling service rates for a retrial service facility system. We consider a finite capacity service facility system with Poisson arrivals and exponentially distributed service times. Here, the customer who sees the server busy, joins the orbit and reattempts the facility with exponential distributed time interval. The system is formulated as Markov Decision Process and we find the optimum service rates to be employed at each instant of time. Linear Programming method is implemented in the context of minimizing the long-run expected cost rate.