Raga Gopalakrishnan University of Colorado at Boulder Adam Wierman (Caltech) Amy R. Ward (USC) Sherwin Doroudi (CMU) Staffing and Routing to incentivize.

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Presentation transcript:

Raga Gopalakrishnan University of Colorado at Boulder Adam Wierman (Caltech) Amy R. Ward (USC) Sherwin Doroudi (CMU) Staffing and Routing to incentivize servers in many-server systems

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

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] to incentivize strategic servers Routing Staffing

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

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

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

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

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

Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random Common routing policies

M/M/N/FCFS routing    Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random When servers are not strategic…

M/M/N/FCFS routing    Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random When servers are not strategic… well-studied, asymptotically optimal [Lin and Kumar 1984] [de Véricourt et al. 2005] [Armony 2005]

M/M/N/FCFS routing    Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random When servers are not strategic… asymptotically “fair” [Atar 2008]

Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random When servers are strategic… M/M/N/FCFS  routing  

Rate-based policies Idle-time-based policies FSF SSF LISF SISF Random When servers are strategic… Our results… M/M/N/FCFS  routing  

Rate-based policies FSF SSF Random & Idle-time-based policies When servers are strategic… Our results… M/M/N/FCFS  routing   First order condition: same unique symmetric equilibrium

Rate-based policies FSF SSF Random & Idle-time-based policies When servers are strategic… Our results… M/M/N/FCFS  routing   Can we do better than Random? Yes, but…

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

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

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

M/M/N/FCFS  Random  staffing When servers are strategic…

Rate-independent Rate-dependent

Rate-independent Rate-dependent Limiting FOC: Policy:

Rate-independent Rate-dependent Limiting FOC: Policy:

Rate-independent Rate-dependent Limiting FOC: Policy:

Rate-independent Rate-dependent Limiting FOC: Policy:

Rate-independent Rate-dependent Limiting FOC: Policy:

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? M/M/N/FCFS  Random   loss of efficiency? $ $$$$ $$ ? ?

Ragavendran Gopalakrishnan University of Colorado at Boulder Adam Wierman (Caltech) Amy R. Ward (USC) Sherwin Doroudi (CMU) Staffing and Routing to incentivize servers in many-server systems