TY - GEN
T1 - Routing and staffing when servers are strategic
AU - Gopalakrishnan, Ragavendran
AU - Doroudi, Sherwin
AU - Ward, Amy R.
AU - Wierman, Adam
PY - 2014
Y1 - 2014
N2 - 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.
AB - 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.
KW - routing
KW - scheduling
KW - service systems
KW - staffing
KW - strategic servers
UR - http://www.scopus.com/inward/record.url?scp=84903150359&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903150359&partnerID=8YFLogxK
U2 - 10.1145/2600057.2602831
DO - 10.1145/2600057.2602831
M3 - Conference contribution
AN - SCOPUS:84903150359
SN - 9781450325653
T3 - EC 2014 - Proceedings of the 15th ACM Conference on Economics and Computation
SP - 713
EP - 714
BT - EC 2014 - Proceedings of the 15th ACM Conference on Economics and Computation
PB - Association for Computing Machinery
T2 - 15th ACM Conference on Economics and Computation, EC 2014
Y2 - 8 June 2014 through 12 June 2014
ER -