Analysis of the M/G/1 processor-sharing queue with bulk arrivals

We analyze the single server processor-sharing queue for the case of bulk arrivals. We obtain an expression for the expected response time of a job as a function of its size, when the service times of jobs have a generalized hyperexponential distribution and more generally for distributions with rational Laplace transforms. Our analysis significantly extends the class of distributions for which processor-sharing queues with bulk arrivals were previously analyzed.