Optimal information policy in discrete-time queues with strategic customers

Veena Goswami; Gopinath Panda

doi:10.3934/jimo.2018065

Article Contents

2019, Volume 15, Issue 2: 689-703. Doi: 10.3934/jimo.2018065

This issue Previous Article A joint dynamic pricing and production model with asymmetric reference price effect Next Article Three concepts of robust efficiency for uncertain multiobjective optimization problems via set order relations

Optimal information policy in discrete-time queues with strategic customers

Veena Goswami^1, and
Gopinath Panda^2,

1.
School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar-751024, India
2.
School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar-752050, India

Received: April 30, 2016

Revised: February 28, 2018

Early access: June 2018

Published: January 2019

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Abstract

This paper studies optimal information revelation policies in discrete-time $Geo/Geo/1$ queue. Revealing the queue length information to arriving customers plays an important role in their decision making, that is, whether to join the system or balk. We consider policies where a service provider discloses information to some customers and conceals it from others, depending upon the number of waiting customers. This partial information disclosure policy helps the service provider minimize the idle period of the system and maximize the revenue.

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Mathematics Subject Classification: Primary: 60K25, 68M20; Secondary: 90B22.

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Figure 1. Various time epochs in late-arrival system with delayed access (LAS-DA)

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Figure 2. State transition diagram of the $Geo/Geo/1$ model with selective threshold policy $\xi_D$.

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Figure 3. Various time epochs in early arrival system (EAS)

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Figure 4. Uniformed policy ($\xi_-$) is optimal for the $Geo/Geo/1/30$ queue with $\lambda = 0.5, \mu = 0.6, R = 50.$

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Figure 5. Informed policy ($\xi_+$) is optimal for the $Geo/Geo/1/30$ queue with $\lambda = 0.65, \mu = 0.6, R = 50.$

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Figure 6. Expected waiting time for different joining probabilities for $\lambda = 0.65, \mu = 0.6, D = 5.$

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Figure 7. Expected waiting time for different joining probabilities for $\lambda = 0.5, \mu = 0.6, D = 5.$

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