References
Avi-Itzhak, B. and Yadin, M. (1965). A sequence of two servers with no intermediate queue,Management Sci.,11, 553–564.
Bessler, S. and Veinott, A. F. (1966). Optimal policy a dynamic multiechelon inventory model,Naval Res. Logist. Quart.,13, 355–389.
Borovkov, A. A. (1970). Factorization identities and properties of the distribution of the supremum of sequential sums,Theory Prob. Appl.,15, 359–402.
Brumelle, S. L. (1971). Some inequalities for parallel-server queues,Operat. Res.,19, 402–413.
Kawashima, T. (1975). Reverse ordering of services in tandem queues,Memoirs of the Defense Academy,15, 151–159.
Miyazawa, M. (1976). Stochastic order relations amongGI/G/1 queues with a common traffic intensity,J. Operat. Res. Soc. Japan,19, 193–208.
Sakasegawa, H. and Yamazaki, G. (1977). Inequalities and approximation formula for the mean delay time in tandem queueing systems,Ann. Inst. Statist. Math.,29, A, 445–466.
Stidham, S., Jr. (1970). On the optimality of single-server queuing systems,Operat. Res.,18, 708–732.
Stoyan, H. and Stoyan, D. (1969). Monotonieeigenschaften der Kundewartezeiten im ModelGI/G/1,Zeit. angew. Math. Mech.,49, 729–734.
Suzuki, T. (1964). On a tandem queue with blocking,J. Operat. Res. Soc. Japan,6, 137–157.
Tumura, Y. and Ishikawa, A. (1978). Numerical calculation of the tandem queueing systems.TRU Math.,14, 57–70.
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Yamazaki, G. An ordering relation of the blocking two-stage tandem queueing system to the reduced single server queueing system. Ann Inst Stat Math 33, 115–123 (1981). https://doi.org/10.1007/BF02480924
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DOI: https://doi.org/10.1007/BF02480924