EconPapers    
Economics at your fingertips  
 

Queueing games with an endogenous number of machines

Ata Atay () and Christian Trudeau ()

No 2022/429, UB Economics Working Papers from Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics

Abstract: This paper studies queueing problems with an endogenous number of machines with and without an initial queue, the novelty being that coalitions not only choose how to queue, but also on how many machines. For a given problem, agents can (de)activate as many machines as they want, at a cost. After minimizing the total cost (processing costs and machine costs), we use a game theoretical approach to share to proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems with an endogenous number of machines, and examine how to share the total cost. We provide an upper bound and a lower bound on the cost of a machine to guarantee the non-emptiness of the core (the set of stable allocations). Next, we study requeueing problems with an endogenous number of machines, where there is an existing queue. We examine how to share the cost savings compared to the initial situation, when optimally requeueing/changing the number of machines. Although, in general, stable allocation may not exist, we guarantee the existence of stable allocations when all machines are considered public goods, and we start with an initial schedule that might not have the optimal number of machines, but in which agents with large waiting costs are processed first.

Keywords: Queueing problems; convexity; cost sharing; allocation problems. (search for similar items in EconPapers)
JEL-codes: C44 C71 D61 D63 (search for similar items in EconPapers)
Pages: 26 pages
Date: 2022
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: Track citations by RSS feed

Downloads: (external link)
http://hdl.handle.net/2445/188596 (application/pdf)

Related works:
Working Paper: Queueing games with an endogenous number of machines (2022) Downloads
Working Paper: Queueing games with an endogenous number of machines (2022) Downloads
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:ewp:wpaper:429web

Access Statistics for this paper

More papers in UB Economics Working Papers from Universitat de Barcelona, Facultat d'Economia i Empresa, UB School of Economics Av. Diagonal 690, 08034 Barcelona. Contact information at EDIRC.
Bibliographic data for series maintained by UB School of Economics ().

 
Page updated 2023-01-26
Handle: RePEc:ewp:wpaper:429web