Abstract
We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Further-more, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 299-323 |
| Number of pages | 25 |
| Journal | Journal of Industrial and Management Optimization |
| Volume | 8 |
| Issue number | 2 |
| DOIs | |
| State | Published - May 1 2012 |
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Keywords
- Demand allocation
- Principal-agent problem
- Queueing system
- Strategic server
- Threshold allocation
Cite this
Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment. / Choi, Sin Man; Huang, Ximin; Ching, Wai Ki.
In: Journal of Industrial and Management Optimization, Vol. 8, No. 2, 01.05.2012, p. 299-323.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment
AU - Choi, Sin Man
AU - Huang, Ximin
AU - Ching, Wai Ki
PY - 2012/5/1
Y1 - 2012/5/1
N2 - We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Further-more, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.
AB - We study the optimal demand allocation policies to induce high service capacity and achieve minimum expected sojourn times in equilibrium in a queueing system with multiple strategic servers. We propose the mixed threshold allocation policy as an optimal state-dependent policy that induces optimal service capacity from strategic servers. Compensation to the server can be paid at customer allocation or upon job completion. Our study focuses on the use of a multiple-server mixed threshold allocation policy to replicate the demand of a given state-independent policy to achieve a symmetric equilibrium with lower expected sojourn time. The results indicate that, under both payment schemes, for any given multiple-server state-independent policy, there exists a multiple-server threshold policy that produces identical demand allocation and Nash equilibrium (if any). Moreover, the policy can be designed to minimize the expected sojourn time at a symmetric equilibrium. Further-more, under the payment-at-allocation scheme, our results, combining with existing results on the optimality of the multiple-server linear allocation policy, show that the mixed threshold policy can achieve the maximum feasible service capacity and thus the minimum feasible equilibrium expected sojourn time. Hence, our results agree with previous two-server results and affirm that a trade-off between incentives and efficiency need not exist in the case of multiple servers.
KW - Demand allocation
KW - Principal-agent problem
KW - Queueing system
KW - Strategic server
KW - Threshold allocation
UR - http://www.scopus.com/inward/record.url?scp=84861766682&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84861766682&partnerID=8YFLogxK
U2 - 10.3934/jimo.2012.8.299
DO - 10.3934/jimo.2012.8.299
M3 - Article
AN - SCOPUS:84861766682
VL - 8
SP - 299
EP - 323
JO - Journal of Industrial and Management Optimization
JF - Journal of Industrial and Management Optimization
SN - 1547-5816
IS - 2
ER -