The L-phenomenon
4.4 Related Bibliography
4.4.2 Reversibility
Dattatreya (1978) Defined C- and D-reversibility, as follows. A tandem queueing system is said to be C-reversible if the original system has the same throughput as its reversed system. A blocking system, on the other hand, is defined as D-reversible if the distributions of times of the departure epochs from both systems are all identical.
Makino (1964) proved C-reversibility for simple systems.
Yamazaki and Sakasegawa (1975) proved D-reversibility, whereas Dattatreya (1978) and Muth (1979) proved independently the reversibility property.
Yamazaki, Kawashima and Sakasegawa (1985) proved C-reversibility in two- station blocking systems with parallel machines at each station and stochastic service times. The same authors proved that this property cannot be extended to larger similar systems (with parallel machines at each station, stochastic service times and finite intermediate buffers).
Melamed (1986) provided some results on the reversibility and duality of some tandem blocking queueing systems.
Dallery, Liu and Towsley (1991) considered reversibility in fork/join queueing networks with blocking after servcie (manufacturing blocking).
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