Abstract
In this paper, we study an M/G/1 multi-queueing system consisting ofM finite capacity queues, at which customers arrive according to independent Poisson processes. The customers require service times according to a queue-dependent general distribution. Each queue has a different priority. The queues are attended by a single server according to their priority and are served in a non-preemptive way. If there are no customers present, the server takes repeated vacations. The length of each vacation is a random variable with a general distribution function. We derive steady state formulas for the queue length distribution and the Laplace transform of the queueing time distribution for each queue.
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References
C. Blondia, An M/G/1 finite capacity queue with vacations and priorities, In:Proc. Performance '87, Brussels, eds. P.-J. Courtois and G. Latouche (North-Holland, 1987) 305–325.
R.W. Conway, W.L. Maxwell and L.W. Miller,Theory of scheduling (Addison-Wesley, Reading, Mass., 1967).
R.B. Cooper, Queues served in cyclic order: waiting times, Bell System Tech. J. 49 (1970) 399–413.
P.J. Courtois, The M/G/1 finite capacity queue with delays, IEEE Trans. Comm. 28 (1980) 165–172.
B.T. Doshi, Queueing systems with vacations-a survey, Queueing Systems 1 (1986) 29–66.
D.P. Gaver, A waiting line with interrupted service, including priorities, J. Roy. Stat. Soc. B24 (1962) 73–90.
N.K. Jaiswal,Priority Queues (Mathematics in Science and Engineering, Vol. 50, Academic Press, New York and London, 1968).
J. Keilson and L.D. Servi, Blocking probability for M/G/1 vacation systems with occupation level dependent schedules, Report TN86.413.5, GTE Laboratories (1986).
O. Kella and U. Yechiali, Priorities in M/G/1 queue with server vacations, Naval Research Logistics 35 (1988) 23–34.
M. Kramer, Wartesysteme M/G/1 beschränkter Kapazität mit Sperrphasen un relativen Prioritäten, Informatik-Fachberichte 61, In:Messung, Modellierung und Bewertung von Rechensystemen (Springer-Verlag 61, 1983) 150–164.
M. Kramer, Waiting times in a queueing system with capacity constraints and preemptive priorities, OR Spectrum 9 (1987) 33–39.
T.T. Lee, M/G/1/N queue with vacation time and exhaustive service discipline, Oper. Res. 32 (1984) 774–784.
J. Loris-Teghem, Vacation policies in an M/G/1 type queueing system with finite capacity, Queueing Systems 3 (1988) 41–52.
L.W. Miller, A note on the busy period of an M/G/1 finite queue, Oper. Res. 23 (1975) 1179–1182.
H. Takagi, Queueing analysis of vacation models, Part I: M/G/1 and Part II: M/G/1 with vacations, IBM Tokyo Research Laboratory Report TR87-0032 (1987) 76 p.
H. Takagi, Queueing analysis of vacation models, Part III: M/G/1 with priorities, IBM Tokyo Research Laboratory Report TR87-0038 (1987) 89 p.
T. Takenaka, Analysis of a nonpreemptive ΣM i /G/1/(ΣN i ) system, Trans. Institute of Electronics, Information and Communication Engineers J70-B (1987) 1330–1337.
J. Teghem, Jr., Control of the service process in a queueing system, Europ. J. of Oper. Res. 23 (1986) 141–158.
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Blondia, C. A finite capacity multi-queueing system with priorities and with repeated server vacations. Queueing Syst 5, 313–330 (1989). https://doi.org/10.1007/BF01225322
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DOI: https://doi.org/10.1007/BF01225322