Large finite population queueing systems. The single server model

Stochastic variables associated to a single-server queueing system with finite population are shown to weakly converge, on some time regions, to Gaussian processes, Brownian motions or stochastic integrals on such when the population size increases. Queue length, unfinished work, storage occupied (in a computer system model) and idle time show different limiting behaviour, depending on the arrival and service distribution.