The M/G/1 processor-sharing model: transient behavior

This paper deals with the M/G/1 model with processor-sharing service discipline. LetL^*(t, x) denote the number of jobs present at timet whose attained service time is not greater thanx,x0, andV₀(t,z) the sojourn time of a tagged job placed in the system at timet and requiringz units of service. Explicit analytical expressions are obtained for the joint distribution ofL^*(t, ·) andV⁰(t, ·) under various initial conditions in terms of the Laplace transform with respect tot. It is shown that for initial conditions of special kind (there is one job or none) the results can be expressed in a closed form.