×

Equilibrium customer strategies in a single server Markovian queue with setup times. (English) Zbl 1124.60069

Summary: We consider a single server Markovian queue with setup times. Whenever this system becomes empty, the server is turned off. Whenever a customer arrives to an empty system, the server begins an exponential setup time to start service again. We assume that arriving customers decide whether to enter the system or balk based on a natural reward-cost structure, which incorporates their desire for service as well as their unwillingness to wait.
We examine customer behavior under various levels of information regarding the system state. Specifically, before making the decision, a customer may or may not know the state of the server and/or the number of present customers. We derive equilibrium strategies for the customers under the various levels of information and analyze the stationary behavior of the system under these strategies. We also illustrate further effects of the information level on the equilibrium behavior via numerical experiments.

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Adan, I., van der Wal, J.: Difference and differential equations in stochastic operations research, Online Notes, URL: http://www.win.tue.nl/\(\sim\)iadan/ (1998) · Zbl 0903.90047
[2] Artalejo, J.R., Lopez-Herrero, M.J.: On the M/M/m queue with removable servers. In: Srinivasan, S.K., Vijayakumar, A. (eds.) Stochastic Point Processes, pp. 124–143. Narosa Publishing House (2003)
[3] Artalejo, J.R., Economou, A., Lopez-Herrero, M.J.: Analysis of a multiserver queue with setup times. Queueing Syst. 52, 53–76 (2005) · Zbl 1098.90020 · doi:10.1007/s11134-005-1740-6
[4] Bischof, W.: Analysis of M/G/1-queues with setup times and vacations under six different service disciplines. Queueing Syst. 39, 265–301 (2001) · Zbl 0994.60088 · doi:10.1023/A:1013992708103
[5] Borthakur, A., Choudhury, G.: A multiserver Poisson queue with a general startup time under N-Policy. Calcutta Stat. Assoc. Bull. 49, 199–213 (1999) · Zbl 0966.60099
[6] Chen, H., Frank, M.: State dependent pricing with a queue. IIE Trans. 33, 847–860 (2001)
[7] Chen, H., Frank, M.: Monopoly pricing when customers queue. IIE Trans. 36, 569–581 (2004) · doi:10.1080/07408170490438690
[8] Choudhury, G.: On a batch arrival Poisson queue with a random setup and vacation period. Comput. Oper. Res. 25, 1013–1026 (1998) · Zbl 1040.90511 · doi:10.1016/S0305-0548(98)00038-0
[9] Choudhury, G.: An MX/G/1 queueing system with a setup period and a vacation period. Queueing Syst. 36, 23–38 (2000) · Zbl 0966.60100 · doi:10.1023/A:1019170817355
[10] Edelson, N.M., Hildebrand, K.: Congestion tolls for Poisson queueing processes. Econometrica 43, 81–92 (1975) · Zbl 0292.60153 · doi:10.2307/1913415
[11] Elaydi, S.N.: An Introduction to Difference Equations. Mathematics. Springer, New York (1999) · Zbl 0930.39001
[12] Hassin, R.: Consumer information in markets with random products quality: the case of queues and balking. Econometrica 54, 1185–1195 (1986) · doi:10.2307/1912327
[13] Hassin, R., Haviv, M.: Equilibrium threshold strategies: the case of queues with priorities. Oper. Res. 45, 966–973 (1997) · Zbl 0895.90093 · doi:10.1287/opre.45.6.966
[14] Hassin, R., Haviv, M.: Nash equilibrium and subgame perfection in observable queues. Ann. Oper. Res. 113, 15–26 (2002) · Zbl 1013.90035 · doi:10.1023/A:1020945525108
[15] Hassin, R., Haviv, M.: To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic, Boston (2003) · Zbl 1064.60002
[16] He, Q.M., Jewkes, E.: Flow time in the MAP/G/1 queue with customer batching and setup times. Stoch. Models 11, 691–711 (1995) · Zbl 0844.60078 · doi:10.1080/15326349508807367
[17] Naor, P.: The regulation of queue size by levying tolls. Econometrica 37, 15–24 (1969) · Zbl 0172.21801 · doi:10.2307/1909200
[18] Neuts, M.F.: Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. Johns Hopkins University Press, Baltimore (1981). Reprinted by Dover Publications Inc., New York (1994). · Zbl 0469.60002
[19] Takagi, H.: Vacation and Priority Systems. Queueing Analysis–A Foundation of Performance Evaluation, vol. 1. North-Holland, New York (1991) · Zbl 0744.60114
[20] Tian, N., Zhang, Z.G.: Vacation Queueing Models: Theory and Applications. Springer, New York (2006) · Zbl 1104.60004
[21] Yechiali, U.: On optimal balking rules and toll charges in the GI/M/1 queue. Oper. Res. 19, 349–370 (1971) · Zbl 0227.60054 · doi:10.1287/opre.19.2.349
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.