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Externalities are the costs that a user of a common resource imposes onothers. For example, consider a FCFS M/G/1 queue and a customer with servicedemand of $x\geq0$ minutes who arrived into the system when the workload levelwas $v\geq0$ minutes. Let $E_v(x)$ be the total waiting time which could besaved if this customer gave up on his service demand. In this work, we analysethe \textit{externalities process} $E_v(\cdot)=\left\{E_v(x):x\geq0\right\}$.It is shown that this process can be represented by an integral of a (shiftedin time by $v$ minutes) compound Poisson process with positive discrete jumpdistribution, so that $E_v(\cdot)$ is convex. Furthermore, we compute the LSTof the finite-dimensional distributions of $E_v(\cdot)$ as well as its mean andauto-covariance functions. We also identify conditions under which, a sequenceof normalized externalities processes admits a weak convergence on$\mathcal{D}[0,\infty)$ equipped with the uniform metric to an integral of a(shifted in time by $v$ minutes) standard Wiener process. Finally, we alsoconsider the extended framework when $v$ is a general nonnegative randomvariable which is independent from the arrival process and the service demands.This leads to a generalization of an existing result from a previous work ofHaviv and Ritov (1998).

Externalities in queues as stochastic processes: The case of FCFS M/G/1