Abstract
This paper derives a conservation law for mean waiting times in a single-server multi-class service queueing system (M X/G/1 type queue) with setup times which may be dependent on multiple customer classes and its arrival batch size by using the work decomposition property in the queueing system with vacations.
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References
O.J. Boxma and W.P. Groenendijk, Pseudo-conservation laws in cyclic-service systems, J. Appl. Prob.24(1985)949–964.
O.J. Boxma, Workloads and waiting times in single-server systems with multiple customer classes, Queueing Systems 5(1989)185–214.
M.L. Chaudhry and J.G.C. Templeton,A First Course in Bulk Queues (Wiley, New York, 1983).
B.T. Doshi, A note on stochastic decomposition in aGI/G/1 queue with vacations or set-up times, J. Appl. Prob. 22(1985)419–428.
B.T. Doshi, Queueing systems with vacations -a survey, Queueing Systems 1(1986)29–96.
I.M. Dukhovnyi, Single-server system with alternating priorities and “warm up”, Izv. Akad. Nauk SSSR, Tekh. Kibernet. 4(1969)66–74.
S.W. Fuhrmann and A. Moon, Queues served in cyclic order with an arbitrary start-up distribution, Naval Res. Logist. 37(1990)123–133.
N.K. Jaiswal,Priority Queues (Academic Press, New York, 1968).
M. Hofri and K.W. Ross, On the optimal ccontrol of two queues with server setup times and its analysis, SIAM J. Comput. 16(1987)399–420.
T. Katayama and Y. Takahashi, Analysis of a priority queue with Bernoulli schedules,Proc. Int. Conf. on the Performance of Distributed Systems and Integrated Communication Networks, ed. T. Hasegawa et al. (Kyoto University, Kyoto, 1991), pp. 87–105.
O. Kella and U. Yechiali, Priorities inM/G/1 queues with server vacation, Naval Res. Logist. 35(1988)23–34.
L. Kleinrock and M.O. Scholl, Packet switching in radio channels: New conflict-free multiple access schemes, IEEE Trans. Commun. COM-28(1980)1015–1029.
H. Levy and L. Kleinrock, A queue with starter and a queue with vacation: Delay analysis by decomposition, Oper. Res. 34(1986)426–436.
G. Nakamura and O. Hashida, Analysis of a non-preemptive priority queueing system with set-up times,Proc. 6th Int. Teletraffic Congress, Stuttgart, Germany (1979), pp. 313/1–7.
H. Takagi, Priority queues with setup times, Oper. Res. 38(1990)667–677.
H. Takagi,Queueing Analysis: A Foundation of Performance Evaluation, Vol. 1: Vacation and Priority Systems, Part 1 (Elsevier Science, Amsterdam, 1991).
Y. Takahashi, On the relationship between work load and waiting time in single-server queues with batch inputs, Oper. Res. Lett. 7(1988)51–56.
P.D. Welch, On a generalizedM/G/1 queueing process in which the first customer of each busy period receives exceptional service, Oper. Res. 12(1964)736–752.
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Katayama, T. A note on conservation laws for a multiclass service queueing system with setup times. Queueing Syst 11, 299–306 (1992). https://doi.org/10.1007/BF01164007
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DOI: https://doi.org/10.1007/BF01164007