Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T21:16:09.924Z Has data issue: false hasContentIssue false
  • English
  • Français

STRATEGIC CUSTOMERS IN MARKOVIAN QUEUES WITH VACATIONS AND SYNCHRONIZED ABANDONMENT

Part of: Computer system organization Special processes Operations research and management science

Published online by Cambridge University Press:  03 July 2020

GOPINATH PANDA Open the ORCID record for GOPINATH PANDA [Opens in a new window]  and
VEENA GOSWAMI Open the ORCID record for VEENA GOSWAMI [Opens in a new window]
GOPINATH PANDA
Affiliation:
Engineering Systems and Design, Singapore University of Technology and Design, Singapore email gopinath.panda@gmail.com
VEENA GOSWAMI*
Affiliation:
School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar, India email veena_goswami@yahoo.com
*
✉veena_goswami@yahoo.com
Get access Rights & Permissions [Opens in a new window]

Abstract

We study impatient customers’ joining strategies in a single-server Markovian queue with synchronized abandonment and multiple vacations. Customers receive the system information upon arrival, and decide whether to join or balk, based on a linear reward-cost structure under the acquired information. Waiting customers are served in a first-come-first-serve discipline, and no service is rendered during vacation. Server’s vacation becomes the cause of impatience for the waiting customers, which leads to synchronous abandonment at the end of vacation. That is, customers consider simultaneously but independent of others, whether to renege the system or to remain. We are interested to study the effect of both information and reneging choice on the balking strategies of impatient customers. We examine the customers’ equilibrium and socially optimal balking strategies under four cases of information: fully/almost observable and fully/almost unobservable cases, assuming the linear reward-cost structure. We compare the social benefits under all the information policies.

Keywords

equilibrium balking strategyinformation policiesmultiple vacationssocial benefitstrategic customerssynchronized abandonment

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 1 , January 2020 , pp. 89 - 120
Copyright
© 2020 Australian Mathematical Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adan, I., Economou, A. and Kapodistria, S., “Synchronized reneging in queueing systems with vacations”, Queueing Syst. 62 (2009) 1–33; doi:10.1007/s11134-009-9112-2.CrossRefGoogle Scholar
Altman, E. and Yechiali, U., “Analysis of customers’ impatience in queues with server vacations”, Queueing Syst. 52 (2006) 261–279; doi:10.1007/s11134-006-6134-x.CrossRefGoogle Scholar
Assaf, D. and Haviv, M., “Reneging from processor sharing systems and random queues”, Math. Oper. Res. 15 (1990) 129–138; doi:10.1287/moor.15.1.129.CrossRefGoogle Scholar
Burnetas, A. and Economou, A., “Equilibrium customer strategies in a single server Markovian queue with setup times”, Queueing Syst. 56(3–4) (2007) 213–228; doi:10.1007/s11134-007-9036-7.CrossRefGoogle Scholar
Dimou, S. and Economou, A., “The single server queue with catastrophes and geometric reneging”, Methodol. Comput. Appl. Probab. 15 (2013) 595–621; doi:10.1007/s11009-011-9271-6.CrossRefGoogle Scholar
Dimou, S., Economou, A. and Fakinos, D., “The single server vacation queueing model with geometric abandonments”, J. Statist. Plann. Inference 141 (2011) 2863–2877; doi:10.1016/j.jspi.2011.03.010.CrossRefGoogle Scholar
Economou, A. and Kapodistria, S., “Synchronized abandonments in a single server unreliable queue”, European J. Oper. Res. 203 (2010) 143–155; doi:10.1016/j.ejor.2009.07.014.CrossRefGoogle Scholar
Guo, P. and Hassin, R., “Strategic behavior and social optimization in Markovian vacation queues”, Oper. Res. 59 (2011) 986–997; doi:10.1287/opre.1100.0907.CrossRefGoogle Scholar
Hassin, R., Rational queueing (CRC Press, New York, NY, 2016).CrossRefGoogle Scholar
Hassin, R. and Haviv, M., “Equilibrium strategies for queues with impatient customers”, Oper. Res. Lett. 17 (1995) 41–45; doi:10.1016/0167-6377(94)00049-c.CrossRefGoogle Scholar
Hassin, R. and Haviv, M., To queue or not to queue: equilibrium behavior in queueing systems (Springer Science & Business Media, Boston, MA, 2003).CrossRefGoogle Scholar
Haviv, M. and Ritov, Y., “Homogeneous customers renege from invisible queues at random times under deteriorating waiting conditions”, Queueing Syst. 38 (2001) 495–508; doi:10.1023/A:1010908330518.CrossRefGoogle Scholar
Kapodistria, S., “The M/M/1 queue with synchronized abandonments”, Queueing Syst. 68 (2011) 79–109; doi:10.1007/s11134-011-9219-0.CrossRefGoogle Scholar
Lee, D. H., “Equilibrium balking strategies in Markovian queues with a single working vacation and vacation interruption”, Qual. Technol. Quant. Manag. (2018) 1–22; doi:10.1080/16843703.2018.1429805.Google Scholar
Liu, J. and Wang, J., “Strategic joining rules in a single server Markovian queue with Bernoulli vacation”, Oper. Res. Int. J. 17 (2017) 413–434; doi:10.1007/s12351-016-0231-3.CrossRefGoogle Scholar
Mandelbaum, A. and Shimkin, N., “A model for rational abandonments from invisible queues”, Queueing Syst. 36 (2000) 141–173; doi:10.1023/A:1019131203242.CrossRefGoogle Scholar
Panda, G., Goswami, V. and Banik, A. D., “Equilibrium and socially optimal balking strategies in Markovian queues with vacations and sequential abandonment”, Asia-Pac. J. Oper. Res. 33 (2016) 1650036; doi:10.1142/s0217595916500366.CrossRefGoogle Scholar
Shimkin, N. and Mandelbaum, A., “Rational abandonment from tele-queues: nonlinear waiting costs with heterogeneous preferences”, Queueing Syst. 47 (2004) 117–146; doi:10.1023/b:ques.0000032804.57988.f3.CrossRefGoogle Scholar
Tian, R., Hu, L. and Wu, X., “Equilibrium and optimal strategies in M/M/1 queues with working vacations and vacation interruptions”, Math. Probl. Eng. 2016 (2016) 1–10; doi:10.1155/2016/9746962.Google Scholar
Yechiali, U., “Queues with system disasters and impatient customers when system is down”, Queueing Syst. 56 (2007) 195–202; doi:10.1007/s11134-007-9031-z.CrossRefGoogle Scholar
Zhang, F., Wang, J. and Liu, B., “Equilibrium balking strategies in Markovian queues with working vacations”, Appl. Math. Model. 37 (2013) 8264–8282; doi:10.1016/j.apm.2013.03.049.CrossRefGoogle Scholar
Zohar, E., Mandelbaum, A. and Shimkin, N., “Adaptive behavior of impatient customers in tele-queues: theory and empirical support”, Manag. Sci. 48 (2002) 566–583; doi:10.1287/mnsc.48.4.566.211.CrossRefGoogle Scholar