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

Strategic Servers misreport their service rates    jobs servers Goal: schedule jobs to servers in order to minimize the “makespan” pp pp pKpK manager [Nisan & Ronen 1999] [Archer & Tardos 2001] [Christodoulou & Koutsoupias 2009]

   jobs pp pp pKpK [Nisan & Ronen 1999] [Archer & Tardos 2001] [Christodoulou & Koutsoupias 2009] strategic servers Servers are “lazy” and want to minimize total work-time manager Strategic Servers misreport their service rates

   jobs pp pp pKpK Servers are “lazy” and want to minimize total work-time manager [Nisan & Ronen 1999] [Archer & Tardos 2001] [Christodoulou & Koutsoupias 2009] strategic Goal: design a truthful mechanism in order to minimize the “makespan” servers Strategic Servers misreport their service rates

 Journal reviews Call centers Crowdsourcing Cloud computing Enterprise data centers … service systems Strategic Servers choose their service rates system performance THIS TALK:

Our Model for a Strategic Server Servers are “lazy” and want to minimize total work-time a)value “idle time” b)incur “cost of effort” [Labor Economics Literature] [G., Doroudi, Ward, Wierman 2014]  Strategic Servers choose their service rates [ model- dependent ]

Classic job scheduling model Our Model for a Service System jobs pp pp pKpK    servers

Our Model for a Service System Classic job scheduling model jobs 1 2 K Stochasticity    servers

Our Model for a Service System Classic job scheduling model Queueing model Motivation: call centers 12 Stochasticity Dynamic/Online    servers FIFO/FCFS jobs arrive over time

FCFS    manager scheduling policy staffing policy 1 2 Rest of this talk: classic results (nonstrategic) our results (strategic)

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

   idleness costutility function scheduling policy Blue for strategic service rates Yellow for control/policy parameters symmetric Nash equilibrium Nash equilibrium scheduling FCFS

Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random Goal: minimize the mean “response time” at symmetric Nash equilibrium scheduling FCFS Our Results: [G., Doroudi, Ward, Wierman 2014]

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 scheduling FCFS Our Results: [G., Doroudi, Ward, Wierman 2014]

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 scheduling FCFS Our Results: [G., Doroudi, Ward, Wierman 2014]

   Random per-unit staffing cost per-unit waiting cost mean waiting time “asymptotically optimal” [Borst et al. 2004] FCFS staffing Classical Result: (nonstrategic setting)

staffing Random FCFS Our Result: [G., Doroudi, Ward, Wierman 2014]

STEP 1: Discard infeasible policies staffing Random FCFS Proof Outline:

STEP 2: Analyze the limiting cost and the limiting FOC staffing Random FCFS Proof Outline: Limiting FOC: Limiting Cost: Observation:

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

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