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

Royi Jacobovic | PhD candidate, The Hebrew University of Jerusalem

25 Oct 2022, 14:00 PM, Room 206& via zoom

Abstract:

Externalities are the costs that a user of a common resource imposes on others. For example, consider a FCFS M/G/1 queue and a customer with service demand of x ≥ 0 minutes who arrived into the system when the workload level was v ≥ 0 minutes. Let Ev(x) be the total waiting time which could be saved if this customer gave up on his service demand. In this work, we analyze the externalities process {Ev(x); x ≥ 0}. The analysis includes a decomposition which yields several results: Convexity of Ev(・), an exact expression for the auto-covariance and a Gaussian approximation of Ev(・). Finally, we also consider the extended framework when v 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)

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 NET-WORKS program in April 2022 as a postdoctoral researcher, working with Prof. Michel Mandjes. His research includes various topics in applied prob-ability, stochastic operations research and mathematical statistics.