ABSTRACT

In the previous chapter, we studied the M/M/1/∞ system with constant arrival and service rates. In many applications, the arrival and service rates can change over time. If the changes are at arbitrary time instants, we cannot conduct a general analysis. However, if arrival and service rates are functions of the number of customers only, we can analyze the system. Additionally, we can also deal with several other logical combinations of situations affecting the arrival and service rates. We find many practical applications that fall within this category. The principles of continuous parameter Markov chains are essential to the analysis of such state dependent queues. In addition to state dependent queues, Markov chains have many other applications within the realm of computer networks. A Markov chain is a special case of the more general stochastic process.