Goods allocation by queuing and the occurrence of violence: A probabilistic analysis

Goods for which demand greatly exceeds supply are frequently allocated to citizens using queuing mechanisms. However, violence can occur either when queues are very long or when large numbers of citizens are not provided goods being allocated with queuing mechanisms. Hence, we use the theory of discrete-time Markov chains (DTMCs) to construct and analyze models in which we explicitly account for queue length and the number of citizens who are not provided a good that is allocated with a queuing mechanism. Specifically, we first delineate a version of our DTMC model in which there is no capacity constraint. Second, we state two key properties of this model and then we derive our first metric of the likelihood of violence. Finally, we describe an alternate version of our DTMC model with a capacity constraint and then we derive our second metric of the likelihood of violence.