Time Sharing with Priorities

Two priority rules are analyzed which give preferential treatment to short jobs over long jobs. Both rules treat the central processor as a single channel queue and allocate a positive block of time to each job as it enters the processor. The job is either completed during the block of time or it is interrupted. For the feedback rule, an interrupted job joins a queue of lower priority. For the round robin rule, there is only one queue; interrupted jobs join the end of the queue. The stochastic model (without priorities) is that of an $M/G/ 1$ queue. For the feedback rule, explicit expressions for expected delay are obtained. For the round robin rule, the corresponding expected delays are determined implicitly as a solution of a set of linear equations. Conditions under which the solution is unique are determined.