Technical Appendix for: Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers
نویسندگان
چکیده
Proof of Proposition 3.1: We prove the Proposition using sample-path coupling arguments. Consider two coupled systems both with the same initial conditions, and the same sequence of arrivals. System 1 operates under an arbitrary policy π ∈ Πp while System 2 operates under FSFp. For all t ≥ 0 and i = 1, 2, let Q(t), Y (t), and Ab(t) be the queue length at time t, the head-count at this time, and the total number of abandonment up to this time in System i, respectively. We claim that the two systems can be coupled such that the following three properties hold for all t ≥ 0.
منابع مشابه
Routing and Staffing in Large-Scale Service Systems: The Case of Homogeneous Impatient Customers and Heterogeneous Servers
Motivated by call centers, we study large-scale service systems with homogeneous impatient customers and heterogeneous servers. The servers differ with respect to their speed of service. For this model, we propose staffing and routing rules that are jointly asymptotically optimal as the system approaches the heavy-traffic many-server QED regime. Our routing rule is FSF, which assigns customers ...
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