We consider an M/G/1 queue with regular and optional phase vacation and withstate dependent arrival rate. The vacation policy is after completion of service if there are no customers in the system, the server takes vacation consisting of K -phases, each phase is generally distributed. Here the first phase is compulsory where as the other phases are optional. For this model the supplementary var...

Some servers are to be located at nodes of a network. Demand for services of these servers is located at each node and a subset of the nodes is to be chosen to locate one server in each. Each customer selects a server with a probability dependent on distance and a certain amount of benefit is achieved after giving service to the customer. Customers may waive receiving service with a known prob...