In Chap. 6 , the simple Markov queueing models are described in detail. The simple Markov queueing models mean that the underlying stochastic process is a BDP. In this chapter, some assorted additional results for the advanced queueing models are provided. The advanced Markov queueing models imply that the underlying stochastic process is a non-BDP or a general CTMC. Most of this new material follows in a logical way from previous chapters in the sense that it ties up some loose theoretical ends and should also help to provide a more complete picture of the kinds of queueing models that may occur in real life. This chapter continues the development of Markov queueing models that are amenable to analytic methods and is concerned especially with Markov models where the underlying stochastic process is a non-birth-death process. That is, changes of more than one are allowed over infinitesimal time intervals but insists on retaining the memory less or Markov property. The Chapman-Kolmogorov backward and forward equations, with the resultant balance equations, are all valid, and together form the essence of the approach to solution for these non-birth-death Markov models. This chapter provides a detailed analysis of the advanced Markov queueing models. Section 7.1 describes Quasi-Birth-Death processes which are the simplest and most well-studied class of multidimensional Markov chains. A solution methodology known as the matrix geometric method has been provided to handle these queueing models. Section 7.3 studies retrial queueing models. In Sect. 7.4 the balking and reneging scenarios in queues have been discussed. Section 7.5 analyzes bulk arrival and bulk service queueing models. Section 7.2 discusses queueing models in which the server goes on some vacation. In Section 7.2, time-dependent probabilities for the fluid queueing models are derived.