An MMAP/M/$$\infty $$ Queueing System with an Offer Zone Working in a Random Environment

We consider a tandem queueing network with two service stations without buffers. An infinite capacity station named as the main station provides usual paid service. Another station is a finite capacity station named as the offer zone. The offer zone is an intermediate station strategically designed to attract the maximum number of customers to the main station. The offer zone works under various random environments. Sojourn times of each random environment follows Phase Type distribution. Two types of customers arrive to the system according to an MMAP. Service times of customers at both the stations are exponentially distributed. The stationary probability distribution of the states of the Markov chain representing the proposed model is computed. Some operational and probabilistic characteristics of the system are determined. A control problem is discussed. A cost function is proposed. The effect of the maximum capacity of the offer zone on various performance measures are considered. Numerical as well as graphical illustrations are given.