A service system with randomly behaving on-demand agents

Lam M. Nguyen, Alexander L. Stolyar

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 uid limits, in the asymp- Totic regime where the customer arrival rate goes to infinity. We use the machinery of switched linear systems and com- mon quadratic Lyapunov functions to derive suffcient condi- Tions for the local stability of uid limits at the desired equi-librium point (with zero queues). We conjecture that, for our model, local stability is in fact suffcient for global stability of uid 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)
Title of host publicationSIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science
PublisherAssociation for Computing Machinery, Inc
Pages365-366
Number of pages2
ISBN (Electronic)9781450342667
DOIs
StatePublished - Jun 14 2016
Externally publishedYes
Event13th Joint International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS / IFIP Performance 2016 - Antibes Juan-les-Pins, France
Duration: Jun 14 2016Jun 18 2016

Publication series

NameSIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science

Other

Other13th Joint International Conference on Measurement and Modeling of Computer Systems, ACM SIGMETRICS / IFIP Performance 2016
CountryFrance
CityAntibes Juan-les-Pins
Period6/14/166/18/16

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Hardware and Architecture

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  • Cite this

    Nguyen, L. M., & Stolyar, A. L. (2016). A service system with randomly behaving on-demand agents. In SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science (pp. 365-366). (SIGMETRICS/ Performance 2016 - Proceedings of the SIGMETRICS/Performance Joint International Conference on Measurement and Modeling of Computer Science). Association for Computing Machinery, Inc. https://doi.org/10.1145/2896377.2901484