Work

Stochastic Volterra integral equations with ranks as scaling limits of parallel infinite-server queues under weighted shortest queue policy

Year: 2025

Type: article

Abstract: We study a queueing system with a fixed number of parallel service stations of infinite servers, each having a dedicated arrival process, and one flexible arrival stream that is routed to one of the service stations according to a ‘weighted’ shortest queue policy. We consider the model with general arrival processes and general service time distributions. Assuming that the dedicated arrival rates are of order n and the flexible arrival rate is of order StartRoot n EndRoot n $\sqrt{n}$ , we show that the diffusion-scaled queueing processes converge to a stochastic Volterra integral equation with ‘ranks’ driven by a continuous Gaussian process. It reduces to the limiting diffusion with a discontinuous drift in the Markovian setting.

Source: Journal of Applied Probability

DOI: 10.1017/jpr.2025.10046

Authors: Tomoyuki Ichiba, Guodong Pang

Institutions: University of California, Santa Barbara, Rice University

Language: English

Topic: Advanced Queuing Theory Analysis

Subfield: Management Information Systems

Field: Business, Management and Accounting

Domain: Social Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funder: National Science Foundation