1. Scheduling and staffing strategic servers

2. strategic servers system performance Journal reviews Call centers Crowdsourcing Cloud computing Enterprise data centers … service systems 

3. strategic servers system performance Journal reviews Call centers Crowdsourcing Cloud computing Enterprise data centers … service systems This talk: Impact of strategic servers on optimal system design  Classic Queueing: Assumes fixed (arrival and) service rates, fixed control/policies. Queueing games: Strategic arrivals Service/price competition [Hassin and Haviv 2003] Scheduling and staffing strategic servers

4. Outline The M/M/1 Queue – a simple example Model for a strategic server The M/M/N Queue Classic policies in non-strategic setting Impact of strategic servers SchedulingStaffing which idle server gets the next job? how many servers to hire?

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

6. 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 SchedulingStaffing

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

8. 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 SchedulingStaffing

9. M/M/N/FCFS scheduling    When servers are not strategic… [Lin et al. 1984] [Véricourt et al. 2005] [Armony 2005] [Atar 2008] [Armony et al. 2010]

10. M/M/N/FCFS  scheduling   Q: Which policy does better – FSF or its counterpart, SSF? Theorem: No symmetric equilibrium exists under either FSF or SSF. Q: How about Longest-Idle-Server-First (LISF)? Theorem: All idle-time-order-based policies result in the same symmetric equilibrium as Random. Q: Can we do better than Random? Answer: Yes! (ask me later!)

11. M/M/N/FCFS  Random   First order condition:

12. Problem: This is a mess!!!

13. 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 SchedulingStaffing

14. M/M/N/FCFS    When servers are not strategic… Random staffing asymptotically optimal [Borst et al. 2004]

15. M/M/N/FCFS  Random  staffing When servers are strategic… Problem: Explicit expression unknown!

16. M/M/N/FCFS  Random  staffing When servers are strategic… (ask me later!)

19. Concluding remarks We need to rethink optimal system design when servers are strategic! M/M/N/FCFS  Random   loss of efficiency? $ $$$$ $$ ? ?

20. Scheduling and staffing strategic servers