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Equilibrium threshold strategies in observable queueing systems with setup/closedown times

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Abstract

This paper considers two types of setup/closedown policies: interruptible and insusceptible setup/closedown policies. When all customers are served exhaustively in a system under the interruptible setup/closedown policy, the server shuts down (deactivates) by a closedown time. When the server reactivates since shutdown, he needs a setup time before providing service again. If a customer arrives during a closedown time, the service is immediately started without a setup time. However, in a system under the insusceptible setup/closedown policy, customers arriving in a closedown time can not be served until the following setup time finishes. For the systems with interruptible setup/closedown times, we assume both the fully and almost observable cases, then derive equilibrium threshold strategies for the customers and analyze the stationary behavior of the systems. On the other hand, for the systems with insusceptible setup/closedown times, we only consider the fully observable case. We also illustrate the equilibrium thresholds and the social benefits for systems via numerical experiments. As far as we know, there is no work concerning equilibrium behavior of customers in queueing systems with setup/closedown times.

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References

  • Arumuganathan R, Jeyakumar S (2004) Analysis of a bulk queue with multiple vacations and closedown times. Int J Inform Manag Sci 15(1): 45–60

    Google Scholar 

  • Arumuganathan R, Jeyakumar S (2005) Steady state analysis of a bulk queue with multiple vacations, setup times with N-policy and closedown times. Appl Math Model 29: 972–986

    Article  Google Scholar 

  • Artalejo JR, Economou A, Lopez-Herrero MJ (2005) Analysis of a multiserver queue with setup times. Queueing Syst 52: 53–76

    Article  Google Scholar 

  • Bischof W (2001) Analysis of M/G/1 queues with setup times and vacations under six different service disciplines. Queueing Syst 39: 265–301

    Article  Google Scholar 

  • Burnetas A, Economou A (2007) Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst 56: 213–228

    Article  Google Scholar 

  • Choudhury G (1998) On a batch arrival poisson queue with a random setup and vacation period. Comput Oper Res 25: 1013–1026

    Article  Google Scholar 

  • Choudhury G (2000) An M X/G/1 queueing system with a setup period and a vacation period. Queueing Syst 36: 23–38

    Article  Google Scholar 

  • Doshi BT (1986) Queueing systems with vacations—a survey. Queueing Syst 1: 29–66

    Article  Google Scholar 

  • Hassin R, Haviv M (2003) Equilibrium behavior in queueing systems: to Queue or not to queue. Kluwer, Dordrecht

    Google Scholar 

  • Hassin R, Henig M (1986) Control of arrivals and departures in a state-dependent input–output system. Oper Res Lett 5: 33–36

    Article  Google Scholar 

  • Johansen SG, Stidham S Jr (1980) Control of arrivals to a stochastic input–output system. Adv Appl Probab 12: 972–999

    Article  Google Scholar 

  • Ke JC (2003) The optimal control of an M/G/1 queueing system with server startup and two vacation types. Appl Math Model 27: 437–450

    Article  Google Scholar 

  • Ke JC (2006) On M/G/1 system under NT policies with breakdowns, startup and closedown. Appl Math Model 30: 49–66

    Article  Google Scholar 

  • Ke JC (2007) Batch arrival queues under vacation policies with server breakdowns and startup/close-down times. Appl Math Model 31: 1282–1292

    Article  Google Scholar 

  • Krishna Reddy GV, Nadarajan R, Arumuganathan R (1998) Analysis of a bulk queue withN-policy multiple vacations and setup times. Comput Oper Res 25(11): 957–967

    Article  Google Scholar 

  • Mendelson H, Whang S (1990) Optimal incentive-compatible priority pricing for the M/M/1 queue. Oper Res 38: 870–883

    Article  Google Scholar 

  • Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37: 15–24

    Article  Google Scholar 

  • Niu Z, Takahashi Y (1999) A finite-capacity queue with exhaustive vacation/close-down/setup times and Markovian arrival processes. Queueing Syst 31: 1–23

    Article  Google Scholar 

  • Niu Z, Shu T, Takahashi Y (2003) A vacation queue with setup and close-down times and batch Markovian arrival processes. Perform Eval 54(3): 225–248

    Article  Google Scholar 

  • Rosenblum DM (1992) Allocation of waiting time by trading in position on a GI/M/s queue. Oper Res 40: S338–S342

    Article  Google Scholar 

  • Stidham S Jr (1985) Optimal control of admissions to a queueing system. IEEE Trans Autom Contr AC-30(8): 705–713

    Article  Google Scholar 

  • Takagi H (1991) Queueing analysis: a foundation of performance evaluation, vacation and priority systems, part I, vol I. North-Holland, Amsterdam

    Google Scholar 

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Correspondence to Wei Sun.

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Sun, W., Guo, P. & Tian, N. Equilibrium threshold strategies in observable queueing systems with setup/closedown times. Cent Eur J Oper Res 18, 241–268 (2010). https://doi.org/10.1007/s10100-009-0104-4

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  • DOI: https://doi.org/10.1007/s10100-009-0104-4

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