Advertisement

TOP

pp 1–3 | Cite as

Comments on: recent developments in the queueing problem

  • Leticia LorenzoEmail author
Discussion

The problem of queues and waiting times is part of our daily life and so it is a situation that deserves a thorough study. Queueing theory mathematically studies the waiting lines and is part of the operations research field. This problem involves more complexity since it considers: the arrival process of the agents (customers) according to some probability distribution; the service time distribution and the number of available servers (in line or in parallel); and, finally, the queue discipline that determines the method used to serve the agents: first come, first served; last come, first served; etc.

Chun presents a nice survey about the recent results on queueing problems where: there is only one server; the service time is the same for all agents (normalized to one); agents arrive according to some stochastic process; congestion may occur, and so the agents incur in waiting costs. The objective in this model, introduced by Dolan (1978), is to find an allocation rule that fixes the...

Notes

References

  1. Chun Y (2006) A pessimistic approach to the queueing problem. Math Soc Sci 51:171–181CrossRefGoogle Scholar
  2. Clarke EH (1971) Multi-part pricing of public goods. Public Choice 11:17–33CrossRefGoogle Scholar
  3. Dolan RJ (1978) Incentive mechanisms for priority queuing problems. Bell J Econ 9:421–436CrossRefGoogle Scholar
  4. Groves T (1973) Incentives in teams. Econometrica 41:617–631CrossRefGoogle Scholar
  5. Ju Y, Chun Y, van den Brink R (2014) Auctioning and selling positions: a non-cooperative approach to queueing conflicts. J Econ Theory 153:33–45CrossRefGoogle Scholar
  6. Maniquet F (2003) A characterization of the Shapley value in queueing problems. J Econ Theory 109:90–103CrossRefGoogle Scholar
  7. Mitra M (2005) Incomplete information and multiple machine queueing problems. Eur J Oper Res 165:251–266CrossRefGoogle Scholar
  8. Vickrey W (1961) Counterspeculation, auctions and competitive sealed tenders. J Finance 16:8–37CrossRefGoogle Scholar

Copyright information

© Sociedad de Estadística e Investigación Operativa 2019

Authors and Affiliations

  1. 1.Universidade de VigoVigoSpain

Personalised recommendations