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Effect of information on the strategic behavior of customers in a discrete-time bulk service queue

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  • We consider the equilibrium and socially optimal behavior of strategic customers in a discrete-time queue with bulk service. The service batch size varies from a single customer to a maximum of 'b' customers. We study the equilibrium and socially optimal balking strategies under two information policies: observable and unobservable. In the former policy, a service provider discloses the queue length information to arriving customers and conceals it in the latter policy. The effect of service batch size and other queueing parameters on the equilibrium strategies under both information policies are compared and illustrated with numerical experiments.

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

    Citation:

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

    Figure 2.  State transition diagram for the original model with maximum batch size $ b $

    Figure 3.  State transition diagram for an observable batch service queueing model with maximum batch size $ b $

    Figure 4.  State transition diagram for the unobservable batch service queueing model with maximum batch size $ b $

    Figure 6.  Effect of customer arrivals on the benefit function under different information policies with parameters $\mu = 0.15, b = 10, R = 30, C = 1$

    Figure 7.  Effect of service rate on the benefit function under different information policies with parameters $\lambda = 0.75, b = 10, R = 30, C = 1$

    Figure 8.  Equilibrium strategy vs batch size under observable policy for $\lambda = 0.2, \mu = 0.3, R = 10, C = 1$

    Figure 9.  Equilibrium strategy vs batch size under unobservable policy for $\lambda = 0.2, \mu = 0.3, R = 5, C = 1$

    Figure 10.  Effect of batch size on the benefit function under different information policies with parameters $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$

    Figure 11.  Dependence of performance measures on customer arrivals under the observable policy with parameters $ \mu = 0.15, b = 10, R = 30, C = 1$

    Figure 12.  Comparison of average system lengths with respect to $b$ for $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$

    Figure 13.  Comparison of average system lengths with respect to $\lambda$ for $b = 10, \mu = 0.15, R = 30, C = 1$

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