A Service System with Randomly Behaving On-demand Agents

Abstract

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.

References

1. Z. Aksin, M. Armony, and V. Mehrotra. The modern call center: a multi-disciplinary perspective on operations management research. Production and Operations Management, 16(6):665--688, 2007.
2. American Telemedicine Association. Core Operational Guidelines for Telehealth Services Involving Provider-Patient Interactions, 2014.
3. P. Formisano. Flexibility for changing business needs: Improve customer service and drive more revenue with a virtual crowdsourcing solution. White paper, 2014.
4. I. Gurvich and A. Ward. On the dynamic control of matching queues. Stochastic Systems, 4(2):479--523, 2014.
5. B. R. K. Kashyap. The double-ended queue with bulk service and limited waiting space. Operations Research, 14(5):822--834, 1966.
6. L. Nguyen and A. Stolyar. A service system with randomly behaving on-demand agents, 2016. http://arxiv.org/pdf/1603.03413v1.pdf.
7. G. Pang and A. Stolyar. A service system with on-demand agent invitations. Queueing Systems, 2015. http://arxiv.org/pdf/1409.7380v2.pdf.
8. R. Shorten, F. Wirth, O. Mason, K. Wulff, and C. King. Stability criteria for switched and hybrid systems. SIAM Review, 49(4):545--592, 2007.
9. A. Stolyar, M. Reiman, N. Korolev, V. Mezhibovsky, and H. Ristock. Pacing in knowledge worker engagement, 2010. United States Patent Application 20100266116-A1.

Index Terms

• Mathematics of computing

  • Probability and statistics

    • Statistical paradigms

      • Queueing theory

    • Stochastic processes

      • Markov processes

• Networks

  • Network services

• Theory of computation

  • Design and analysis of algorithms

    • Online algorithms

      • Online learning algorithms

        • Scheduling algorithms