# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019007

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

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

Received  February 2018 Revised  October 2018 Published  March 2019

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.

Citation: Gopinath Panda, Veena Goswami. Effect of information on the strategic behavior of customers in a discrete-time bulk service queue. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019007
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##### References:
Various time epochs in a late-arrival system with delayed access (LAS-DA)
State transition diagram for the original model with maximum batch size $b$
State transition diagram for an observable batch service queueing model with maximum batch size $b$
State transition diagram for the unobservable batch service queueing model with maximum batch size $b$
Effect of customer arrivals on the benefit function under different information policies with parameters $\mu = 0.15, b = 10, R = 30, C = 1$
Effect of service rate on the benefit function under different information policies with parameters $\lambda = 0.75, b = 10, R = 30, C = 1$
Equilibrium strategy vs batch size under observable policy for $\lambda = 0.2, \mu = 0.3, R = 10, C = 1$
Equilibrium strategy vs batch size under unobservable policy for $\lambda = 0.2, \mu = 0.3, R = 5, C = 1$
Effect of batch size on the benefit function under different information policies with parameters $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$
Dependence of performance measures on customer arrivals under the observable policy with parameters $\mu = 0.15, b = 10, R = 30, C = 1$
Comparison of average system lengths with respect to $b$ for $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$
Comparison of average system lengths with respect to $\lambda$ for $b = 10, \mu = 0.15, R = 30, C = 1$
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