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

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Abstract

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.

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References

  • Doshi, B.T., 1986. Queueing system with vacations—a survey. Queueing Systems, 1(1):29–66. [doi:10.1007/BF01149327]

    Article  MathSciNet  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.1080/07362999508809382]

    Article  MathSciNet  MATH  Google Scholar 

  • Heyman, D.P., 1968. Optimal operating policies for M/G/1 queueing system. Oper. Res., 16:362–382.

    Article  MATH  Google Scholar 

  • Heyman, D.P., 1977. The T policy for the M/G/1 queue. Manag. Sci., 23:775–778.

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.1016/S0307-904X(98)10088-4]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1016/S0307-904X(03)00074-X]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1016/S0360-8352(02)00235-8]

    Article  Google Scholar 

  • 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. [doi:10.1016/j.mcm.2004.08.009]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1002/mma.905]

    Article  MathSciNet  MATH  Google Scholar 

  • Kella, O., 1989. The threshold policy in the M/G/1 queue with server vacations. Nav. Res. Logist., 36(1):111–123. [doi:10.1002/1520-6750(198902)36:1<111::AID-NAV3220360109>3.0.CO;2-3]

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.2307/3010429]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1007/BF01189247]

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.2307/3215040]

    MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.1016/0305-0548(94)E0015-Y]

    Article  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Madan, K.C., 2000. An M/G/1 queue with second optional service. Queueing Systems, 34(1/4):37–46. [doi:10.1023/A:1019144716929]

    Article  MathSciNet  MATH  Google Scholar 

  • Medhi, J., 2002. A single server Poisson input queue with a second optional channel. Queueing Systems, 42(3):239–242. [doi:10.1023/A:1020519830116]

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.1016/0305-0548(92)90057-C]

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Tadj, L., 2003. A quorum queueing system under T-policy. J. Oper. Res. Soc., 54(5):466–471. [doi:10.1057/palgrave.jors.2601536]

    Article  MATH  Google Scholar 

  • Tadj, L., Choudhury, G., 2005. Optimal design and control of queues. Top, 13(2):359–414. [doi:10.1007/BF02579061]

    Article  MathSciNet  MATH  Google Scholar 

  • Tadj, L., Ke, J.C., 2005. Control policy of a hysteretic bulk queueing system. Math. Comput. Model., 41(4–5):571–579. [doi:10.1016/j.mcm.2003.07.017]

    Article  MathSciNet  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • 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. [doi:10.1016/0377-2217(87)90045-2]

    Article  MathSciNet  MATH  Google Scholar 

  • Tijms, H.C., 1986. Stochastic Modelling and Analysis. Wiley, New York.

    Google Scholar 

  • Wang, K.H., 1995. Optimal control of a Markovian queueing system with a removable and non-reliable server. Microelectron. Rel., 35(8):1131–1136. [doi:10.1016/0026-2714(94)00164-J]

    Article  Google Scholar 

  • 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. [doi:10.1057/palgrave.jors.2600419]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1016/S0307-904X(00)00024-X]

    Article  MATH  Google Scholar 

  • 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. [doi:10.1007/s001860200263]

    Article  MathSciNet  MATH  Google Scholar 

  • 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. [doi:10.1016/S0307-904X(99)00002-5]

    Article  MATH  Google Scholar 

  • 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.

    Article  MathSciNet  Google Scholar 

  • Yadin, M., Naor, P., 1963. Queueing systems with a removable service station. Oper. Res. Quart., 14:393–405.

    Article  Google Scholar 

  • 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. [doi:10.1016/S0166-5316(96)00005-3]

    Article  MATH  Google Scholar 

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  1. Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan, China

    Jau-chuan Ke & Yunn-kuang Chu

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  1. Jau-chuan Ke
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  2. Yunn-kuang Chu
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Correspondence to Jau-chuan Ke.

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Ke, Jc., Chu, Yk. Optimization on bicriterion policies for M/G/1 system with second optional service. J. Zhejiang Univ. Sci. A 9, 1437–1445 (2008). https://doi.org/10.1631/jzus.A0820103

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  • DOI: https://doi.org/10.1631/jzus.A0820103

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