5 PHASE-TYPE QUEUES
- Numerical Methods for Structured Markov Chains
D. A. Bini
- Oxford University Press
In this chapter a series of processes with a variety of transition structures are considered and their analysis is presented in a unifying manner. These processes are grouped under the generic name of Phase-type queues, they include G/M/1-type Markov chains, QBD processes, Markov chains with Toeplitz-like transitions and limited displacements (non-skip-free), and tree-like processes. A duality property between M/G/1 and G/M/1 Markov chains is described and a reduction of M/G/1 and G/M/1 Markov chains to QBD is analysed.
G/M/1-type Markov chains, QBD processes, tree-like processes, limited displacement, non-skip-free processes, duality property
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