Retrials and balks (queueing)

An overloaded service system may reject customers if it has no queue to store them. In practice, rejected customers return later to make retrials and may not leave permanently (balk) until several retrials fail. A single-server system with Poisson arrivals is examined in which rejected customers balk or make retrials according to a simple probabilistic model. Customer service times are independent random variables, all with the same given distribution function b(t). The stationary probability distribution for the number of customers waiting to make retrials satisfies a complicated functional equation. The solution is elusive in general but can be obtained for special b(t) (exponential distribution) or special values of model parameters. When the solution cannot be found, bounds on the fraction of customers served can be obtained