Abstract
A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.
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References
G. Bitran and D. Tirupati, Multiproduct queueing networks with deterministic routing: decomposition approach and the notion of interference, Man. Sci. 34 (1988) 75–100.
P.J. Burke, The output of a queueing system, Operations Research 4 (1956) 699–704.
R.W. Conway, W. Maxwell and L. Miller,Theory of Scheduling (Addison-Wesley, Reading, Mass. 1967).
D.J. Daley, Queueing output processes, Adv. Appl. Prob. 8 (1976) 395–415.
D. Gross, C.M. Harris,Fundamentals of Queueing Theory (Wiley, New York, 1974).
L. Kleinrock,Queueing Systems, Vol. I: Theory (Wiley, New York, 1975).
P.J. Kuehn, Approximate analysis of general queueing networks by decomposition, IEEE Transactions on Communications, COM-27 (1979) 113–126.
K.T. Marshall, Some inequalities in queuing, Operations Research, 16 (1968) 651–665.
P. Nain, Interdeparture times from a queueing system with preemptive resume priority, Performance Evaluation 4 (1984) 93–98.
M. Segal and W. Whitt, A Queueing network analyzer for manufacturing, Proc. 12th Int'l. Teletraffic Congress, Turin, Italy, June 1988.
D.A. Stanford, Modelling priority queueing characteristics in approximate analytical tools for open queueing networks, in:Modelling Techniques and Tools for Performance Analysis (Elsevier-North-Holland, 1986) pp. 131–143.
L. Takács,Introduction to the Theory of Queues (Oxford University Press, 1962).
W. Whitt, The queueing network analyzer, Bell System Technical Journal 62, No. 9 (1983) 1779–2815.
W. Whitt, Approximations for departure processes and queues in series, Nav. Res. Log. Qtrly. 31 (1984) 499–521.
W. Whitt, A light traffic approximation for single-class departure processes from multi-class queues, Man. Sci. 34 (1988) 1333–1346.
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Stanford, D., Fischer, W. The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue. Queueing Syst 4, 179–191 (1989). https://doi.org/10.1007/BF02100265
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DOI: https://doi.org/10.1007/BF02100265