Queueing model of a bi-level Markov service-system and its solution using recursion

The authors present a closed queueing model of a bi-level stochastic service system using a Markov process. The existence of two modes of operation in some real situations such as reliability, inventory, and production problems is outlined. A recursive solution technique is developed for computing steady-state probabilities and the relevant performance measures for such a system. A bi-level system is completely analyzed. The effect of the two modes of operation on the system performance measures is also discussed. The recursive solution technique is consistently superior to other common solution techniques with respect to computation time and memory requirement. A procedure is outlined for extension to a multi-level service system