Queueing games with an endogenous number of machines

Ata Atay and Christian Trudeau

No 2202, Working Papers from University of Windsor, Department 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: 24 pages
Date: 2022-07
New Economics Papers: this item is included in nep-gth
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http://web2.uwindsor.ca/economics/RePEc/wis/pdf/2202.pdf First version, 2022 (application/pdf)

Related works:
Journal Article: Queueing games with an endogenous number of machines (2024)
Working Paper: Queueing games with an endogenous number of machines (2022)
Working Paper: Queueing games with an endogenous number of machines (2022)
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