There are many CPU scheduling algorithms in the literature like FIFO, Round Robin, Shortest Job First and so on. The Multilevel Queue Scheduling is superior to these due to its better management of a variety of processes. In this paper, a general class of multi-level queue scheduling schemes is designed and studied under a Markov Chain model. The scheduler is assumed to perform random movement on queues over predefined quantum of time. Three different scheduling schemes, as members of the class, are examined and compared under this model with the special consideration of a rest (waiting) state. It is found that the scheme III of the class is more appropriate than scheme I and scheme II in reference to the minimum rest state probability criteria. All the conclusions are well supported through a simulation study based on three different data sets. The Markov Chain model advocates for noble properties in scheduling scheme III of the class4f7