1. Raga Gopalakrishnan University of Colorado at Boulder Adam Wierman (Caltech) Amy R. Ward (USC) Sherwin Doroudi (CMU) Routing and Staffing when Servers are Strategic

2. server Routing and Staffing strategic server is fixed Routing and Staffing

3. strategic server Journal reviews Call centers Crowd/Out-sourcing Cloud computing Enterprise data centers … service systems system performance

4. strategic server system performance Classic Queueing: Assumes fixed (arrival and) service rates, fixed control/policies. [Hassin & Haviv 2003] [Kalai, Kamien, & Rubinovitch 1992] [Gilbert & Weng 1998] [Cachon & Harker 1999] [Chen & Wan 2002] [Cachon & Zhang 2007] This talk: Impact of strategic servers on optimal system design Routing and Staffing CS-Econ Literature: Servers strategically misreport their service rates. [Nisan & Ronen 1999] [Archer & Tardos 2001] [Christodoulou & Koutsoupias 2009] [Halfin & Whitt 1981] [Borst, Mandelbaum, & Reiman 2004] [Armony 2005] [Atar 2008] [Armony & Ward 2010] [Armony & Mandelbaum 2011] Queueing Games: Strategic arrivals and service/pricing amidst competition between different firms. (within the same firm) [Zhan & Ward 2014] Compensation and Staffing for Strategic Employees: How to Incentivize a Speed-Quality Trade-off in a Large Service System. Working Paper.

5. Outline The M/M/1 queue – a simple example Model for a strategic server The strategic M/M/N queue Classic policies in non-strategic setting Impact of strategic servers Asymptotically optimal policy Routing Staffing which idle server gets the next job? how many servers to hire?

6. M/M/1/FCFS   strategic server idleness cost utility function    LHS RHS

7. Outline The M/M/1 queue – a simple example Model for a strategic server The strategic M/M/N queue Classic policies in non-strategic setting Impact of strategic servers Asymptotically optimal policy Routing Staffing which idle server gets the next job? how many servers to hire?

8. M/M/N/FCFS strategic servers routing symmetric Nash equilibrium Nash equilibrium existence? performance? Blue for strategic service rates Yellow for control/policy parameters   

9. Outline The M/M/1 queue – a simple example Model for a strategic server The strategic M/M/N queue Classic policies in non-strategic setting Impact of strategic servers Asymptotically optimal policy Routing Staffing which idle server gets the next job? how many servers to hire?

10.    Classical Results: (nonstrategic setting) [Lin and Kumar 1984] [de Véricourt & Zhou 2005] [Armony 2005] [Atar 2008] (1) Fastest Server First (FSF) is “asymptotically optimal” for minimizing the mean response time (2) Longest Idle Server First (LISF) is “asymptotically fair” in distributing idle time proportionately among the servers routing M/M/N/FCFS

11. Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random Goal: minimize the mean response time at symmetric Nash equilibrium Our Results: routing M/M/N/FCFS

12. Rate-based policies FSF SSF Random & Idle-time-based policies First order condition: same unique symmetric equilibrium Goal: minimize the mean response time at symmetric Nash equilibrium Our Results: routing M/M/N/FCFS [Haji & Ross 2013]

13. same unique symmetric equilibrium Rate-based policies FSF SSF Random & Idle-time-based policies Can we do better than Random? Yes, but… Goal: minimize the mean response time at symmetric Nash equilibrium Our Results: routing M/M/N/FCFS

14. Outline The M/M/1 queue – a simple example Model for a strategic server The strategic M/M/N queue Classic policies in non-strategic setting Impact of strategic servers Asymptotically optimal policy Routing Staffing which idle server gets the next job? how many servers to hire?

15.    Random per-unit staffing cost per-unit waiting cost mean waiting time “asymptotically optimal” [Borst, Mandelbaum, & Reiman 2004] Classical Result: (nonstrategic setting) M/M/N/FCFS

16. Random Our Result: M/M/N/FCFS

17. STEP 1: Discard infeasible policies Random Proof Outline: M/M/N/FCFS

18. STEP 2: Analyze the limiting cost and the limiting FOC Random Proof Outline: Limiting FOC: Limiting Cost: Observation: M/M/N/FCFS

19. Concluding remarks We need to rethink optimal system design when servers are strategic! Joint routing-staffing optimization? Empirical studies / Experimental evaluation? Asymmetric models / equilibria? Interaction between strategic arrivals and strategic servers? Random loss of efficiency? $ $$$$ $$ ? ? M/M/N/FCFS

20. Ragavendran Gopalakrishnan University of Colorado at Boulder Adam Wierman (Caltech) Amy R. Ward (USC) Sherwin Doroudi (CMU) Routing and Staffing when Servers are Strategic [Zhan & Ward 2014] Compensation and Staffing for Strategic Employees: How to Incentivize a Speed-Quality Trade-off in a Large Service System. Working Paper. Companion Talk MSOM: Saturday@11:15am