A Service System with Randomly Behaving On-demand Agents

Lam M. Nguyen, Alexander L. Stolyar

Research output: Contribution to journalArticlepeer-review


We consider a service system where agents (or, servers) are invited on-demand. Customers arrive as a Poisson process and join a customer queue. Customer service times are i.i.d. exponential. Agents' behavior is random in two respects. First, they can be invited into the system exogenously, and join the agent queue after a random time. Second, with some probability they rejoin the agent queue after a service completion, and otherwise leave the system. The objective is to design a real-time adaptive agent invitation scheme that keeps both customer and agent queues/waiting-times small. We study an adaptive scheme, which controls the number of pending agent invitations, based on queue-state feedback. We study the system process fluid limits, in the asymptotic regime where the customer arrival rate goes to infinity. We use the machinery of switched linear systems and common quadratic Lyapunov functions to derive sufficient conditions for the local stability of fluid limits at the desired equilibrium point (with zero queues). We conjecture that, for our model, local stability is in fact sufficient for global stability of fluid limits; the validity of this conjecture is supported by numerical and simulation experiments. When the local stability conditions do hold, simulations show good overall performance of the scheme.

Original languageEnglish (US)
Pages (from-to)365-366
Number of pages2
JournalPerformance Evaluation Review
Issue number1
StatePublished - Jun 2016
Externally publishedYes


  • call centers
  • common quadratic lyapunov function
  • exponential stability
  • fluid limit
  • on-demand agent invitation
  • service systems
  • switched linear systems

ASJC Scopus subject areas

  • Software
  • Hardware and Architecture
  • Computer Networks and Communications


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