Download presentation

Presentation is loading. Please wait.

Published byRuth Hutcheon Modified over 2 years ago

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
strategic servers system performance Service systems are staffed by humans.

3
strategic servers system performance This talk: Impact of strategic server on system design Classic Queueing: Assumes fixed (arrival and) service rates. Queueing games: Strategic arrivals Service/price competition [Hassin and Haviv 2003] Routing and Staffing to Incentivize Servers Service systems are staffed by humans. 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 RoutingStaffing which idle server gets the next job? how many servers to hire?

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

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 existence?performance? Why symmetric? This is fair. (Server payment is fixed.)

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… Fastest-Server-First (FSF) is asymptotically optimal for. Longest-Idle-Server-First (LISF) is asymptotically optimal subject to fairness (idleness distribution). [Lin and Kumar 1984] [Armony 2005] [Atar 2008] [Armony and Ward 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, but … Also, (Haji and Ross, 2013).

11
M/M/N/FCFS Random First order condition: What is the symmetric equilibrium service rate? 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.

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

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 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) staffing

15
M/M/N/FCFS When servers are strategic… Random staffing 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 Random When servers are strategic… 1. Rate-independent staffing 2. Rate-dependent staffing staffing

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

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

19
M/M/N/FCFS Random staffing 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 FSF,SSF LISF There is a loss of efficiency. $$$$ ? We solved for an asymptotically optimal staffing = Random

Similar presentations

OK

Scheduling and staffing strategic servers. strategic servers system performance Journal reviews Call centers Crowdsourcing Cloud computing Enterprise.

Scheduling and staffing strategic servers. strategic servers system performance Journal reviews Call centers Crowdsourcing Cloud computing Enterprise.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on earth movements and major landforms of the united Ppt on food supplements Ppt on solid dielectrics effect Ppt on tokyo stock exchange Ppt on service oriented architecture Ppt on single phase and three phase dual converter operation Ppt on intelligent manufacturing software Ppt on leverages parker Ppt on ergonomics computer workstations Ppt on sea level rise toolbox