Routing and Staffing when Servers are Strategic

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 the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective 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 order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. 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.Comment: First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 201

Routing and staffing when servers are strategic

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

Many-Server Queueing Systems with Heterogeneous Strategic Servers in Heavy Traffic

In most service systems, the servers are humans who desire to experience a certain level of idleness. In call centers, this manifests itself as the call avoidance behavior, where servers strategically adjust their service rate to strike a balance between the idleness they receive and effort to work harder. Moreover, being humans, each server values this trade-off differently and has different capabilities. Drawing ideas on mean-field games we develop a novel framework relying on measure-valued processes to simultaneously address strategic server behavior and inherent server heterogeneity in service systems. This framework enables us to extend the recent literature on strategic servers in four new directions by: (i) incorporating individual choices of servers, (ii) incorporating individual abilities of servers, (iii) modeling the discomfort experienced by servers due to low levels of idleness, and (iv) considering more general routing policies. Using our framework, we are able to asymptotically characterize asymmetric Nash equilibria for many-server systems with strategic servers. In simpler cases, it has been shown that the purely quality-driven regime is asymptotically optimal. However, we show that if the discomfort increases fast enough as the idleness approaches zero, the quality-and-efficiency-driven regime and other quality driven regimes can be optimal. This is the first time this conclusion appears in the literature.Comment: 42 pages, 3 figure

Staffing, Routing, and Payment to Trade off Speed and Quality in Large Service Systems

Most common queueing models used for service-system design assume that the servers work at fixed (possibly heterogeneous) rates. However, real-life service systems are staffed by people, and people may change their service speed in response to incentives. The delicacy is that the resulting service speed is jointly affected by staffing, routing, and payment decisions. Our objective in this paper is to find a joint staffing, routing, and payment policy that induces optimal service-system performance. We do this under the assumption that there is a trade-off between service speed and quality and that employees are paid based on both. The employees selfishly choose their own service speed to maximize their own expected utility (which depends on the staffing through their busy time). The endogenous service-rate assumption leads to a centralized control problem in which the system manager jointly optimizes over the staffing, routing, and service rate. By solving the centralized control problem under fluid scaling, we find four different economically optimal operating regimes: critically loaded, efficiency driven, quality driven, and intentional idling (in which there is simultaneous customer abandonment and server idling). Then we show that a simple piece-rate payment scheme can be used to solve the associated decentralized control problem under fluid scaling

EUROPEAN CONFERENCE ON QUEUEING THEORY 2016

International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"