Equilibrium Customer Strategies and Social-Profit Maximization in the Single Server Constant Retriak Queue Articles uri icon



publication date

  • March 2011

start page

  • 107

end page

  • 122


  • 2


  • 58

International Standard Serial Number (ISSN)

  • 0894-069X

Electronic International Standard Serial Number (EISSN)

  • 1520-6750


  • We consider the single-server constant retrial queue with a Poisson arrival process and exponential service and retrial times. This system has not waiting space, so the customers that find the server busy are
    forced to abandon the system, but they can leave their contact details.
    Hence, after a service completion, the server seeks for a customer among
    those that have unsuccessfully applied for service but left their
    contact details, at a constant retrial rate. We assume that the arriving
    customers that find the server busy decide whether to leave their
    contact details or to balk based on a natural reward-cost structure,
    which incorporates their desire for service as well as their
    unwillingness to wait. We examine the customers' behavior, and we
    identify the Nash equilibrium joining strategies. We also study the
    corresponding social and profit maximization problems. We consider
    separately the observable case where the customers get informed about
    the number of customers waiting for service and the unobservable case
    where they do not receive this information. Several extensions of the
    model are also discussed.