Transient/Steady-State solution of a single channel queue with bulk arrivals and intermittently available server

This paper studies a single server queuing model wherein arrivals are in groups following a time homogeneous POISSON process with the group size being a random variable and the server being available intermittently. Using the LAPLACE transform and the probability generating functions, the transient and the stationary distribution of queue size are discussed and in the steady state case various means are obtained explicitly.