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Optimal information policy in discrete-time queues with strategic customers

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  • 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.

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

    Citation:

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

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

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

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

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

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

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

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