A finite capacity G_(1,2) / M _(1,2)/1 queue with markov dependent shift in service

Abstract

A queueing system with one server giving services to two types of customers is considered. The interarrival times are i.i.d random variables with a general distribution. An arrival is of Type 1 with probability p and that of Type 2 with probability 1–p. The server picks the type o f unit to be served according to a Markov Chain Rule (MCR) between the two type of customers. Only one unit is served at a time. We obtain the time dependent and limiting system state probability distributions. Some optimization problem are examined

Keywords:

• Markov chain rule
• Semi-Markov process
• Markov renewal process
• Stationary distribution