UNRELIABLE QUEUING WITH REPEATED ORDERS

The study of queuing models with repeated orders is motivated by new developments in telecommunication technology as the use of ''repeat-last-number'', ''auto-repeat'', ''ring-back-when- free'' and other facilities [31,38.40]. In this paper we focalise our attention in an important aspect: the influence of the reliability of the communication line on the distribution of the number A(t) of customers in the system. First we give a short review of studies in this area. Next, we consider a version of the unreliable N/G/1/1 queue with repeated orders. The distribution of the non-markovian jump-process {A(t), t greater-than-or-equal-to 0} is studed by an adequate ''markovization''. We obtain a generalization of the Pollaczek-Khintchin-Alexandrov formula