Abstract
In this paper, we consider multiple‐class queueing systems with N‐policy in which the idle server starts service as soon as the number of customers in the “start‐up class” reaches threshold N. We consider the cases of FCFS and nonpreemptive priority. We obtain the Laplace–Stieltjes transform of the waiting times of each class of customers. We also show some results for the general behavior of such systems.
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References
K.R. Balachandran and H. Tijms, On the D-policy for the M/G/1 queue, Managm. Sci. 21(9) (1975) 1073–1076.
A. Brandwajn, A finite difference equations approach to a priority queue, Oper. Res. 30(1) (1982) 74–81.
L. Green, A limit theorem on subintervals of interrenewal times, Oper. Res. 30(1) (1982) 210–216.
D.P. Heyman, The T-policy for the M/G/1 queue, Managm. Sci. 23(7) (1977) 775–778.
N.K. Jaiswal, Priority Queues (Academic Press, New York/London, 1968).
O. Kella, The threshold policy in the M/G/1 queue with server vacations, Naval Res. Logist. 36 (1989) 111–123.
O. Kella and U. Yechiali, Priority in M/G/1 queue with server vacations, Naval Res. Logist. 35(1) (1988) 23–34.
H.S. Lee, Steady state probabilities for the server vacation model with group arrivals and under control-operating policy, J. Korean OR/MS Soc. 16(2) (1991) 36–48 (in Korean).
H.W. Lee and S.S. Lee, Operating characteristics of M X /G/1 queue with N-policy, Queueing Systems 15 (1994) 387–399.
H.W. Lee, S.S. Lee, J.O. Park and K.C. Chae, Analysis of the M X /G/1 queue with N-policy and multiple vacations, J. Appl. Probab. 31 (1994) 476–496.
S.S. Lee, H.W. Lee, S.H. Yoon and K.C. Chae, Batch arrival queue with N-policy and single vacation, Comput. Oper. Res. 22(2) (1995) 173–189.
H.W. Lee and J.O. Park, Optimal strategy in N-policy system with early set-up, J. Oper. Res. Soc. 47 (1996) 1–8.
H.S. Lee and M.M. Srinivasan, Control policies for the M X /G/1 queueing system. Managm. Sci. 35(6) (1989) 708–721.
D.R. Miller, Computation of steady-state probabilities for M/M/1 priority queues, Oper. Res. 29(5) (1981) 945–958.
M.F. Neuts, Matrix-Geometric Solutions in Stochastic Models (Johns Hopkins Univ. Press, Baltimore, MD, 1981).
J.G. Shanthikumar, M/G/1 queues with scheduling within generations and removable server, Oper. Res. 29(5) (1981) 1010–1018.
J.G. Shanthikumar, Optimal control of an M/G/1 priority queue via N-control, Amer. J. Math. Managm. Sci. 1(3) (1981) 192–212.
M.J. Sobel, Optimal average-cost policy for a queue with start-up and shut-down costs, Oper. Res. 17 (1969) 145–162.
H. Takagi, Time dependent analysis of M/G/1 vacation models with exhaustive service, Queueing Systems 6 (1990) 369–390.
H. Takagi, Priority queues with set-up times, Oper. Res. 38(4) (1990) 667–677.
H. Takagi, Queueing Analysis, Vol. 1 (North-Holland, Amsterdam, 1991).
H. Takagi, Time dependent process of M/G/1 vacation models with exhaustive service, J. Appl. Probab. 29 (1992) 418–429.
H. Takagi, T. Takine and O.J. Boxma, Distribution of the workload in multiclass queueing systems with server vacations, Naval Res. Logist. 39 (1992) 41–52.
R.W. Wolff, Poisson arrivals see time averages, Oper. Res. 30(2) (1982) 223–231.
M. Yadin and P. Naor, Queueing systems with a removable service station, O.R. Qrtly 14 (1963) 393–405.
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Lee, H., Yoon, S. & Seo, W. Start‐up class models in multiple‐class queues with N‐policy. Queueing Systems 31, 101–124 (1999). https://doi.org/10.1023/A:1019150028799
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DOI: https://doi.org/10.1023/A:1019150028799