1 / 20

Routing and Staffing to Incentivize Servers i n Many Server Systems

Routing and Staffing to Incentivize Servers i n Many Server Systems. Amy Ward (USC) Raga Gopalakrishnan (Caltech/CU-Boulder/USC) Adam Wierman (Caltech) Sherwin Doroudi (CMU). S ervice systems are staffed by humans. m. strategic servers. system performance.

sahara
Download Presentation

Routing and Staffing to Incentivize Servers i n Many Server Systems

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Routing and Staffing to Incentivize Servers in Many Server Systems Amy Ward (USC) Raga Gopalakrishnan (Caltech/CU-Boulder/USC) Adam Wierman (Caltech) Sherwin Doroudi (CMU)

  2. Service systems are staffed by humans. m strategic servers system performance

  3. Service systems are staffed by humans. m Routing and Staffing to IncentivizeServers strategic servers system performance Queueing games: • Strategic arrivals • Service/price competition Classic Queueing: Assumes fixed (arrival and) service rates. [Hassin and Haviv 2003] This talk: Impact of strategic server on system design • Blue for strategic service rates • Yellow for routing/staffing policy parameters • Pink is to highlight.

  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 Routing Staffing which idle server gets the next job? how many servers to hire?

  5. M/M/1/FCFS ? λ m=1/μ m strategic server What is the service rate? Values idleness Cost of effort utility function

  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 Scheduling Staffing

  7. M/M/N/FCFS m1 m2 mN scheduling strategic servers Nash equilibrium symmetric Why symmetric? This is fair. (Server payment is fixed.) existence? performance?

  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 Scheduling Staffing

  9. M/M/N/FCFS m1 m2 scheduling mN When servers are not strategic… • Fastest-Server-First (FSF) is asymptotically optimal for . • Longest-Idle-Server-First (LISF) is asymptotically optimal subject to fairness (idleness distribution). [Lin and Kumar1984] [Armony 2005] [Atar 2008] [Armonyand Ward 2010]

  10. M/M/N/FCFS m1 m2 mN 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. Also, (Haji and Ross, 2013). Q: Can we do better than Random? Answer:Yes, but …

  11. M/M/N/FCFS m1 m2 mN Random Theorem: For every λand N, under mild conditions on c, there exists a unique symmetric equilibrium service rate μ* under Random. Furthermore, U(μ*)>0. What is the symmetric equilibrium service rate? First order condition:

  12. Proposition: Under Random routing, Gumbel (1960) for the fully heterogeneous case. Problem: This is a mess!!! There is no hope to use this to decide on a staffing level.

  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 Scheduling Staffing

  14. M/M/N/FCFS m m staffing Random m When servers are not strategic… Q: How many servers to staff? Objective: Minimize total system cost Answer: Square root staffing is asymptotically optimal. Halfin and Whitt (1981) and Borst, Mandelbaum and Reiman (2004)

  15. M/M/N/FCFS staffing m m m Random When servers are strategic… Q: How many servers to staff? Objective: Minimize total system cost Problem: Explicit expression is unknown. Fortunately, there is hope if we let λbecome large.

  16. M/M/N/FCFS staffing m m m Random When servers are strategic… 1. Rate-independent staffing 2. Rate-dependent staffing

  17. M/M/N/FCFS staffing m m m Random Such a solution is not desirable. In order that there exists μ*,λ with The cost function blows up at rate λ. Eliminates square-root staffing. Must staff order λmore. we must staff

  18. M/M/N/FCFS staffing m m m Random What is a? Fluid scale cost. Set Since servers are strategic. Theorem: The staffingNλ is asymptotically optimal in the sense that

  19. M/M/N/FCFS staffing m m m Random Example: Suppose Then Convexity helps. Efficiency is decreased.

  20. Concluding remarks • We need to rethink optimal system design to account for how servers respond to incentives (i.e., when servers are strategic)! $$$$ M/M/N/FCFS m FSF,SSF LISF m ? = Random m We solved for an asymptotically optimal staffing There is a loss of efficiency.

More Related