Loss probabilities of hand-in traffic under various protocols, I: Models and algebraic results

Mobile telephone traffic business demands that a given base station be able to handle both newly originating traffic and 'hand-in' traffic from neighbouring base stations, with priority to be given to the latter, existing traffic. Starting from a baseline standard model in which all channels are available to all traffic, this note examines three other models, each with its own access control protocol that allocates a reserve capacity R amongst the N_tot channels to give priority to the hand-in traffic. These different protocols give different loss probabilities for the two types of traffic. All the results are proved on the basis of assuming a Poisson arrival process and independent exponential service times. This paper concentrates on presenting explicit expressions for many of the loss probabilities, some of them given by the Erlang B loss formula or variants, as well as simple approximations and bounds. A companion paper presents results comparing the various models.