Routing and staffing when servers are strategic

Ragavendran Gopalakrishnan, Sherwin Doroudi, Amy R. Ward, Adam Wierman

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


Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by these policies. This observation has consequences when modeling service system performance, and our objective in this paper is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate, in which there is a trade-off between an "effort cost" and a "value of idleness": faster service rates require more exertion of effort, but also lead to more idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time (such as the Longest Idle Server First policy). This allows us to (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. We find that an asymptotically optimal staffing policy staffs strictly more than the common square-root staffing policy. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.

Original languageEnglish (US)
Title of host publicationEC 2014 - Proceedings of the 15th ACM Conference on Economics and Computation
PublisherAssociation for Computing Machinery
Number of pages2
ISBN (Print)9781450325653
StatePublished - 2014
Event15th ACM Conference on Economics and Computation, EC 2014 - Palo Alto, CA, United States
Duration: Jun 8 2014Jun 12 2014

Publication series

NameEC 2014 - Proceedings of the 15th ACM Conference on Economics and Computation


Other15th ACM Conference on Economics and Computation, EC 2014
Country/TerritoryUnited States
CityPalo Alto, CA


  • routing
  • scheduling
  • service systems
  • staffing
  • strategic servers


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