Analysis of a Strategy of Adaptive Group Admission of Customers to Single Server Retrial System

Recent advances in wireless communication networks led to possibility of multi-rate transmission of information. In terms of queueing theory this means that a group of requests from users can be processed simultaneously in parallel and processing of the whole group is considered finished if processing of all individual requests belonging to this group is over. In this paper we consider a novel retrial queueing model where the requests (customers) are served in groups of finite size which are formed during a period of random length that is called admission period. The problem of choosing the optimal length of admission period and optimal size of the groups is faced here under assumptions that the input flow of customers is described by a MAP (Markovian Arrival Process), length of admission period and individual service time have phase type distribution. Advantages of the proposed customers service discipline are numerically illustrated.