# 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
##### References:

show all references

##### 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 $b = 10, \mu = 0.15, R = 30, C = 1$
 [1] Veena Goswami, Gopinath Panda. Optimal information policy in discrete-time queues with strategic customers. Journal of Industrial & Management Optimization, 2019, 15 (2) : 689-703. doi: 10.3934/jimo.2018065 [2] Michiel De Muynck, Herwig Bruneel, Sabine Wittevrongel. Analysis of a discrete-time queue with general service demands and phase-type service capacities. Journal of Industrial & Management Optimization, 2017, 13 (4) : 1901-1926. doi: 10.3934/jimo.2017024 [3] Bart Feyaerts, Stijn De Vuyst, Herwig Bruneel, Sabine Wittevrongel. The impact of the $NT$-policy on the behaviour of a discrete-time queue with general service times. Journal of Industrial & Management Optimization, 2014, 10 (1) : 131-149. doi: 10.3934/jimo.2014.10.131 [4] Biao Xu, Xiuli Xu, Zhong Yao. Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1599-1615. doi: 10.3934/jimo.2018113 [5] Bara Kim, Jeongsim Kim. Explicit solution for the stationary distribution of a discrete-time finite buffer queue. Journal of Industrial & Management Optimization, 2016, 12 (3) : 1121-1133. doi: 10.3934/jimo.2016.12.1121 [6] Yung Chung Wang, Jenn Shing Wang, Fu Hsiang Tsai. Analysis of discrete-time space priority queue with fuzzy threshold. Journal of Industrial & Management Optimization, 2009, 5 (3) : 467-479. doi: 10.3934/jimo.2009.5.467 [7] Shaojun Lan, Yinghui Tang, Miaomiao Yu. System capacity optimization design and optimal threshold $N^{*}$ for a $GEO/G/1$ discrete-time queue with single server vacation and under the control of Min($N, V$)-policy. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1435-1464. doi: 10.3934/jimo.2016.12.1435 [8] Sheng Zhu, Jinting Wang. Strategic behavior and optimal strategies in an M/G/1 queue with Bernoulli vacations. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1297-1322. doi: 10.3934/jimo.2018008 [9] Shan Gao, Jinting Wang. On a discrete-time GI$^X$/Geo/1/N-G queue with randomized working vacations and at most $J$ vacations. Journal of Industrial & Management Optimization, 2015, 11 (3) : 779-806. doi: 10.3934/jimo.2015.11.779 [10] Pradeep Dubey, Rahul Garg, Bernard De Meyer. Competing for customers in a social network. Journal of Dynamics & Games, 2014, 1 (3) : 377-409. doi: 10.3934/jdg.2014.1.377 [11] Zsolt Saffer, Wuyi Yue. A dual tandem queueing system with GI service time at the first queue. Journal of Industrial & Management Optimization, 2014, 10 (1) : 167-192. doi: 10.3934/jimo.2014.10.167 [12] Hideaki Takagi. Times until service completion and abandonment in an M/M/$m$ preemptive-resume LCFS queue with impatient customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1701-1726. doi: 10.3934/jimo.2018028 [13] Shaojun Lan, Yinghui Tang. Performance analysis of a discrete-time $Geo/G/1$ retrial queue with non-preemptive priority, working vacations and vacation interruption. Journal of Industrial & Management Optimization, 2019, 15 (3) : 1421-1446. doi: 10.3934/jimo.2018102 [14] Pikkala Vijaya Laxmi, Singuluri Indira, Kanithi Jyothsna. Ant colony optimization for optimum service times in a Bernoulli schedule vacation interruption queue with balking and reneging. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1199-1214. doi: 10.3934/jimo.2016.12.1199 [15] Gopinath Panda, Veena Goswami, Abhijit Datta Banik, Dibyajyoti Guha. Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption. Journal of Industrial & Management Optimization, 2016, 12 (3) : 851-878. doi: 10.3934/jimo.2016.12.851 [16] Xuemei Zhang, Malin Song, Guangdong Liu. Service product pricing strategies based on time-sensitive customer choice behavior. Journal of Industrial & Management Optimization, 2017, 13 (1) : 297-312. doi: 10.3934/jimo.2016018 [17] Lih-Ing W. Roeger, Razvan Gelca. Dynamically consistent discrete-time Lotka-Volterra competition models. Conference Publications, 2009, 2009 (Special) : 650-658. doi: 10.3934/proc.2009.2009.650 [18] Ciprian Preda. Discrete-time theorems for the dichotomy of one-parameter semigroups. Communications on Pure & Applied Analysis, 2008, 7 (2) : 457-463. doi: 10.3934/cpaa.2008.7.457 [19] Lih-Ing W. Roeger. Dynamically consistent discrete-time SI and SIS epidemic models. Conference Publications, 2013, 2013 (special) : 653-662. doi: 10.3934/proc.2013.2013.653 [20] H. L. Smith, X. Q. Zhao. Competitive exclusion in a discrete-time, size-structured chemostat model. Discrete & Continuous Dynamical Systems - B, 2001, 1 (2) : 183-191. doi: 10.3934/dcdsb.2001.1.183

2018 Impact Factor: 1.025