Determination of the conditional response for quantum allocation algorithms
Theodore J. Brown · Journal of the ACM · 1982
~STRACr.An analytic-numeric procedure for fmdmg the response time for a givenjob size ("condiUonal response") Is demonstrated for a wide class of quanta-of-service allocation disciplines The procedure is demonstrated for a discipline that is like standard round robin except that the queue of waiting jobs is ordered by the number of services previously received.Laplace-Stieltjes transforms (LST) are found for this "ordered round robin" for an M/G/I queue allowing allocation of nonidentical quanta of service for a job.The denvauon of the mean is shown explicitly, and higher moments can be derived by differentiation of the LST The mean conditional response is found for the steady state, and tt is shown that the method is capable as well of determining the mean conditional response under specified initial condmons.The methodology can be broadly applied.It applies to a class of disciplines that includes the ordered round robin and feedback to lower priority queues, as well as variants and combinaUons of these.