Approximate steady state probability distribution of the stock level for the single product production-inventory system when the demand is a Markov-modulated Poisson process (MMPP) with finite number of states under the on/off production rate control is obtained. The control causes the stock level to fluctuate around a given value by reducing the production rate when the stock exceeds this value. The asymptotic distributions of the stock-out and overproduction periods are also obtained. Exact steady state distribution of the stock level for MMPP demand arrivals with two states and exponential batch size distribution is compared with the approximate one.
Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 17th International Conference, ITMM 2018, named after A. F. Terpugov and 12th Workshop on Retrial Queues and Related Topics, WRQ 2018, Tomsk, Russia, September 10-15, 2018 : selected papers. Cham, 2018. P. 248-262