A service system with on-demand agent invitations
Guodong Pang, Alexander L. Stolyar

TL;DR
This paper analyzes a service system with on-demand agent invitations, establishing fluid and diffusion limits, proving stability, and demonstrating that waiting times vanish asymptotically, with simulations confirming the effectiveness of the adaptive scheme.
Contribution
It introduces a novel feedback-based adaptive agent invitation scheme and proves its stability and asymptotic optimality using advanced Lyapunov drift methods.
Findings
System stability is established under the proposed scheme.
Waiting times for customers and agents vanish asymptotically.
Simulation results confirm the accuracy of fluid limit approximations.
Abstract
We consider a service system where agents are invited on-demand. Customers arrive exogenously as a Poisson process and join a customer queue upon arrival if no agent is available. Agents decide to accept or decline invitations after some exponentially distributed random time, and join an agent queue upon invitation acceptance if no customer is waiting. A customer and an agent are matched in the order of customer arrival and agent invitation acceptance under the non-idling condition, and will leave the system simultaneously once matched (service times are irrelevant here). We consider a feedback-based adaptive agent invitation scheme, which controls the number of pending agent invitations, depending on the customer and/or agent queue lengths and their changes. The system process has two components -- `the difference between agent and customer queues' and `the number of pending…
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Taxonomy
TopicsAdvanced Queuing Theory Analysis · Advanced Wireless Network Optimization · Network Traffic and Congestion Control
