Abstract: There is much literature which analyses a queueing
system in which customers can call in to request service. Here we consider a
case that, if the arrival finds the server free, he will enter the service
immediately. Otherwise, if the service system is occupied, the arrival either
leaves the system completely with probability p, or joins a source of unsatisfied customers,
called the orbit, with probability We consider two models
characterized by the discipline governing the order of re-requests for service
from the orbit. First, all the customers from the orbit apply at a fixed rate.
Secondly, customers from the orbit are discouraged and reduce their rate of
demand as more customers join the orbit. The arrival at and the demands from the
orbit are both assumed to be according to the Poisson Process. The service times
for both customers from the orbit and primary customers are assumed to have a
general distribution with given density function. We calculate several
characteristic quantities of these queueing systems.
Keywords and phrases: queueing system, single line queues, repeated demands, Poisson distribution, communication networks.
