A Diffusion Approximation Framework for Ride-hailing with Travel Delays

A Dynamic Model for Managing Volunteer Engagement

“…Note that the presence of infinite-server queues leads to the scaling below (25), which differs from the usual scaling for closed networks of singe-server queues in heavy traffic. In that setting, queue lengths are of the same order of magnitude as the total number of jobs in the system; see for example, Harrison et al (1990), Harrison and Wein (1990a), Chevalier andWein (1993), andAta et al (2020). Here, we define the scaled queue-length process as follows:…”

“…More specifically, our paper relates to the asymptotic analysis of closed queueing networks with infinite-server queues, see for example Krichagina and Puhalskii (1997), Kogan and Lipster (1993), Krichagina and Puhalskii (1986), Smorodinskii (1986), and Alwan and Ata (2020). Krichagina and Puhalskii (1997) studies a closed queueing model containing a single-server queue and an infiniteserver queue that has general service time distributions.…”

“…Krichagina and Puhalskii (1986) and Smorodinskii (1986) prove limit theorems for related systems. Alwan and Ata (2020) considers a closed queueing network with multiple infinite-server queues and multiple single-server queues to study a ride-hailing system. The authors prove a heavy traffic limit theorem, but do not consider the control of that system.…”