Geodesic
Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations
Panda, Gopinath1  ; Goswami, Veena2  ; Banik, Abhijit Datta1
1 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Odisha, India.
2 School of Computer Application, KIIT University, Bhubaneswar, Odisha, India.
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 685-707

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We study customers’ equilibrium behaviour and social optimization in a single-server Markovian queue with impatient customers and variant of multiple working vacations, where the impatience is due to slow service rate. Under the variant of multiple working vacations, the server takes a working vacation as soon as the system gets empty. When an arriving customer joins the vacation system, it activates an impatience timer. If its patience timer expires before it gets service, the customer abandons the system, and never returns. The server is allowed to take at most J successive working vacations, if at the end of a working vacation the system remains empty. An arriving customer takes a decision on the basis of available information whether to join or to balk, which unifies wish for the service as well as reluctance to wait. We discuss equilibrium threshold strategies on the basis of linear reward-cost structure in the fully observable and fully unobservable cases. We present numerical results that establish the impact of the information level as well as various parameters on the equilibrium balking strategies and social benefits. The research outputs may be useful for decision makers to convey information to customers in net benefit maximization and for examining the corresponding social optimization problems.

DOI : 10.1051/ro/2016056
Classification : 60K25, 68M20, 90B22
Keywords: Equilibrium balking strategies, customer impatience, multiple working vacations, social optimization

Panda, Gopinath 1 ; Goswami, Veena 2 ; Banik, Abhijit Datta 1

1 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Odisha, India.
2 School of Computer Application, KIIT University, Bhubaneswar, Odisha, India. 
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     title = {Equilibrium behaviour and social optimization in {Markovian} queues with impatient customers and variant of working vacations},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
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Panda, Gopinath; Goswami, Veena; Banik, Abhijit Datta. Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 685-707. doi: 10.1051/ro/2016056

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