On the allocation of commodities by queuing and the prevention of violence

In times of acute scarcity, demand for a commodity greatly exceeds its supply. In such situations, queuing mechanisms are frequently used to allocate scarce goods to citizens. However, inordinately long queues lead to excessive wait times and this can lead to violence. As such, the general purpose of this paper is to theoretically analyze the problem of preventing violence in a queuing context. To this end, we first formulate a queuing model with a finite capacity. Next, we determine the smallest capacity that will keep the likelihood of violence below an exogenously specified value. Finally, we illustrate the working of our model with a simple numerical example.