This paper is concerned with the basic theory and algorithms of multi-layer Markov modulated fluid flow (MMFF) processes and an MAP/PH/K queue with customer abandonment. For multi-layer MMFF processes, we review and refine the existing theory to make it easy to understand, and to make related algorithms meticulously organized. For the queueing system, we combine the MMFF approach and the count-server-for-phase (CSFP) method to make it possible to analyze it, and to develop an algorithm for computing queueing quantities related to customer abandonment, waiting times, and queue lengths. Some of the quantities are difficult to compute through other means. For both the multi-layer MMFF processes and the queueing system, we try to make the analysis easy to follow and the algorithm easy to implement.