Full Text:   <2974>

CLC number: O22

On-line Access: 

Received: 2008-02-02

Revision Accepted: 2008-05-14

Crosschecked: 0000-00-00

Cited: 8

Clicked: 4984

Citations:  Bibtex RefMan EndNote GB/T7714

-   Go to

Article info.
Open peer comments

Journal of Zhejiang University SCIENCE A 2008 Vol.9 No.10 P.1437-1445


Optimization on bicriterion policies for M/G/1 system with second optional service

Author(s):  Jau-chuan KE, Yunn-kuang CHU

Affiliation(s):  Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, China

Corresponding email(s):   jauchuan@ntit.edu.tw

Key Words:  Average operating cost, Bicriterion policy, Optimization comparisons, Optional service, Optimal threshold values

Jau-chuan KE, Yunn-kuang CHU. Optimization on bicriterion policies for M/G/1 system with second optional service[J]. Journal of Zhejiang University Science A, 2008, 9(10): 1437-1445.

@article{title="Optimization on bicriterion policies for M/G/1 system with second optional service",
author="Jau-chuan KE, Yunn-kuang CHU",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

%0 Journal Article
%T Optimization on bicriterion policies for M/G/1 system with second optional service
%A Jau-chuan KE
%A Yunn-kuang CHU
%J Journal of Zhejiang University SCIENCE A
%V 9
%N 10
%P 1437-1445
%@ 1673-565X
%D 2008
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A0820103

T1 - Optimization on bicriterion policies for M/G/1 system with second optional service
A1 - Jau-chuan KE
A1 - Yunn-kuang CHU
J0 - Journal of Zhejiang University Science A
VL - 9
IS - 10
SP - 1437
EP - 1445
%@ 1673-565X
Y1 - 2008
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A0820103

We compare the optimal operating cost of the two bicriterion policies, <p,T> and <p,N>, for an M/G/1 queueing system with second optional service, in which the length of the vacation period is randomly controlled either by the number of arrivals during the idle period or by a timer. After all the customers are served in the queue exhaustively, the server immediately takes a vacation and may operate <p,T> policy or <p,N> policy. For the two bicriterion policies, the total average cost function per unit time is developed to search the optimal stationary operating policies at a minimum cost. Based upon the optimal cost the explicit forms for joint optimum threshold values of (p,T) and (p,N) are obtained.

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


[1] Doshi, B.T., 1986. Queueing system with vacations—a survey. Queueing Systems, 1(1):29-66.

[2] Feinberg, E.A., Kim, D.J., 1996. Bicriterion optimization of an M/G/1 queue with a removable server. Prob. Eng. Inf. Sci., 10:57-73.

[3] Gakis, K.G., Rhee, H.K., Sivazlian, B.D., 1995. Distributions and first moments of the busy and idle periods in controllable M/G/1 queueing models with simple and dyadic policies. Stoch. Anal. Appl., 13(1):47-81.

[4] Heyman, D.P., 1968. Optimal operating policies for M/G/1 queueing system. Oper. Res., 16:362-382.

[5] Heyman, D.P., 1977. The T policy for the M/G/1 queue. Manag. Sci., 23:775-778.

[6] Hur, S., Paik, S.J., 1999. The effect of different arrival rates on the N-policy of M/G/1 with server setup. Appl. Math. Model., 23(4):289-299.

[7] Hur, S., Kim, J., Kang, C., 2003. An analysis of the M/G/1 system with N and T policy. Appl. Math. Model., 27(8):665-675.

[8] Ke, J.C., 2003. The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns. Comput. Ind. Eng., 44(4):567-579.

[9] Ke, J.C., 2005. Modified T vacation policy for an M/G/1 queueing system with an un-reliable server and startup. Math. Comput. Model., 41(11-12):1267-1277.

[10] Ke, J.C., 2008. Two thresholds of a batch arrival queueing system under modified T vacation policy with startup and closedown. Math. Methods Appl. Sci., 31(2):229-247.

[11] Kella, O., 1989. The threshold policy in the M/G/1 queue with server vacations. Nav. Res. Logist., 36(1):111-123.

[12] Lee, H.S., Srinivasan, M.M., 1989. Control policies for the M[x]/G/1 queueing system. Manag. Sci., 35:708-721.

[13] Lee, H.W., Park, J.O., 1997. Optimal strategy in N-policy production system with early set-up. J. Oper. Res. Soc., 48:306-313.

[14] Lee, H.W., Lee, S.S., Chae, K.C., 1994a. Operating characteristics of M[x]/G/1 queue with N policy. Queueing Systems, 15(1-4):387-399.

[15] Lee, H.W., Lee, S.S., Park, J.O., Chae, K.C., 1994b. Analysis of M[x]/G/1 queue with N policy and multiple vacations. J. Appl. Prob., 31(2):467-496.

[16] Lee, S.S., Lee, H.W., Yoon, S.H., Chae, K.C., 1995. Batch arrival queue with N policy and single vacation. Comput. Oper. Res., 22(2):173-189.

[17] Levy, Y., Yechiali, U., 1975. Utilization of idle time in an M/G/1 queueing system. Manag. Sci., 22:202-211.

[18] Madan, K.C., 2000. An M/G/1 queue with second optional service. Queueing Systems, 34(1/4):37-46.

[19] Medhi, J., 2002. A single server Poisson input queue with a second optional channel. Queueing Systems, 42(3):239-242.

[20] Medhi, J., Templeton, J.G.C., 1992. A Poisson input queue under N-policy and with a general start up time. Comput. Oper. Res., 19(1):35-41.

[21] Stewart, J., 1995. Calculus (3rd Ed.). Brooks/Cole Publishing Company, Pacific Grove.

[22] Tadj, L., 2003. A quorum queueing system under T-policy. J. Oper. Res. Soc., 54(5):466-471.

[23] Tadj, L., Choudhury, G., 2005. Optimal design and control of queues. Top, 13(2):359-414.

[24] Tadj, L., Ke, J.C., 2005. Control policy of a hysteretic bulk queueing system. Math. Comput. Model., 41(4-5):571-579.

[25] Takagi, H., 1991. Queueing Analysis: A Foundation of Performance Evaluation. North-Holland, Amsterdam.

[26] Teghem, J.Jr., 1987. Optimal control of a removable server in an M/G/1 queue with finite capacity. Eur. J. Oper. Res., 31(3):358-367.

[27] Tijms, H.C., 1986. Stochastic Modelling and Analysis. Wiley, New York.

[28] Wang, K.H., 1995. Optimal control of a Markovian queueing system with a removable and non-reliable server. Microelectron. Rel., 35(8):1131-1136.

[29] Wang, K.H., 1997. Optimal control of an M/Ek/1 queueing system with removable service station subject to breakdowns. J. Oper. Res. Soc., 48(9):936-942.

[30] Wang, K.H., Ke, J.C., 2000. A recursive method to the optimal control of an M/G/1 queueing system with finite capacity and infinite capacity. Appl. Math. Model., 24(12):899-914.

[31] Wang, K.H., Yen, K.L., 2003. Optimal control of an M/Hk/1 queueing system with a removable server. Math. Methods Oper. Res., 57(2):255-262.

[32] Wang, K.H., Chang, K.W., Sivazlian, B.D., 1999. Optimal control of a removable and non-reliable server in an infinite and a finite M/H2/1 queueing system. Appl. Math. Model., 23(8):651-666.

[33] Wang, K.H., Kao, H.T., Chen, G., 2004. Optimal management of a removable and non-reliable server in an infinite and a finite M/Hk/1 queueing system. Qual. Technol. Quant. Manag., 1(2):325-339.

[34] Yadin, M., Naor, P., 1963. Queueing systems with a removable service station. Oper. Res. Quart., 14:393-405.

[35] Zhang, Z.G., Vickson, R.G., van Eenige, M.J.A., 1997. Optimal two-threshold policies in an M/G/1 queue with two vacation types. Perform. Eval., 29(1):63-80.

Open peer comments: Debate/Discuss/Question/Opinion


Please provide your name, email address and a comment

Journal of Zhejiang University-SCIENCE, 38 Zheda Road, Hangzhou 310027, China
Tel: +86-571-87952783; E-mail: cjzhang@zju.edu.cn
Copyright © 2000 - 2024 Journal of Zhejiang University-SCIENCE