Varun Gupta

We consider a queueing theoretical model of resource sharing systems. Users arrive according to a Poisson process to a queue that is served by a Processor Sharing server. A user may choose not to join the system on arrival (balk), or join but quit at any later point (renege). Since a user who reneges wastes resources, the central question we study in the paper is what is the welfare loss of allowing users to renege, compared to when they can only balk? We show that reneging does lead to weakly smaller welfare than balking, but this result is brittle to the reneging model. We compare two different models of reneging, a random lottery-based model, and an age-based model, and show that for the latter, the equilibrium is identical to the balking equilibrium. We also prove that any non-zero penalty fees on reneging removes this feature from equilibrium behavior. Finally, we provide asymptotic and numerical comparisons of welfare under the socially optimal policy and under balking and reneging equilibria.

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