State probabilities for an M/M/1 queuing system with two capacity levels

Flexible capacity of production system gets in times of short-time working and economic crisis an increasingly important status. Therefore, models to handle flexible capacity of production systems are necessary. In production planning queuing theory is a widely applied modeling approach. Since classical M/M/1 queuing models neglect flexible capacity this work implements two production rates in an M/M/1 queuing model. Whenever the queue length is more than k, the system runs at high speed otherwise low speed is used. The aim of this paper is the calculation of the state probabilities of the Markov chain. The state probabilities are the basis for developing an approximation for the production lead time which is dedicated to further research. Finally, a simulation study for the evaluation of state probabilities for flexible capacity with one and two switching points is conducted.