Customer-dependent group instantaneous replacement models for unreliable service systems - Liu, G.-S.; Burnetas, A (Proceedings - Annual Meeting of the Decision Sciences Institute, 2002)
In this paper we are going to develop group replacement policies for a service system by considering the number of customers dynamically in the queue. We consider a service system with multiple independent servers operating in parallel and a single queue. Customers arrive in accordance with a Poisson process, and the service time for each customer follows an exponential distribution. The servers are unreliable with identically exponentially distributed failure times and the repair time is assumed negligible. We formulate this model as a continuous time Markov decision process, and prove the optimal group replacement policy has a threshold structure.
Keywords: Customer satisfaction; Decision theory; Exponential distributions; Exponential transitions; Markov processes; Mathematical models; Public policy; Servers