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

Externalities are the costs that a user of a common resource imposes on others. For example, consider a FCFS queue and a customer with service demand of minutes who arrived into the system when the workload level was minutes. Let be the total waiting time which could be saved if this customer gave up on his service demand. In this work, we analyse the externalities process . The analysis includes a decomposition which yields several results: Convexity of , an exact expression for the auto-covariance and a Gaussian approximation of . Finally, we also consider the extended framework when is a general nonnegative random variable which is independent from the arrival process and the service demands. This leads to a generalization of an existing result from a previous work of Haviv and Ritov (1998). (A joint work with Michel Mandjes)

Short-bio:

 Royi Jacobovic received his Ph.D. in operations research from The Hebrew University of Jerusalem in October 2020 under the supervision of Prof. Offer Kella. Since that time, he has been a postdoctoral researcher at University of Haifa and The Hebrew University of Jerusalem. Royi joined the NETWORKS program in April 2022 as a postdoctoral researcher, working with Prof. Michel Mandjes. His research includes various topics in applied probability, stochastic operations research and mathematical statistics.