Queueing games with an endogenous number of machines

Abstract

We study queueing problems with an endogenous number of machines, the novelty being that coalitions not only choose how to queue, but on how many machines. After minimizing the processing costs and machine costs, we share the proceeds of this cooperation, and study the existence of stable allocations. First, we study queueing problems, 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. Next, we study requeueing problems, 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 stable allocations may not exist, we guarantee their existence when all machines are considered public goods, and we start with an initial queue in which agents with larger waiting costs are processed first