Stochastic Modeling of Processor Scheduling with Application to Data Base Management Systems

This paper is concerned with the stochastic modeling of processor scheduling and of queuing due to contention for resources in data base management systems. The processing services rendered in searching the data base and retrieving and processing information are modeled explicitly, as is the algorithm used to schedule these services on the processor. The scheduling of the processor is based on a total priority ordering of a set of queues for processing service. A queuing model incorporating the processor scheduling algorithm for IMS (Information Management System) is formulated in order to illustrate the modeling ideas. The model is analyzed under rather general distributional assumptions, based on the observation that certain stochastic processes in the model are cumulative processes defined over the same embedded semiMarkov process. The model is not used in a performance study of IMS, nor is it proposed that the model developed here is one upon which a performance study of IMS should be undertaken. The model should be viewed as illustrative of stochastic models which can be constructed to incorporate algorithms for processor scheduling. Introduction The algorithms used to schedule a computer system’s resources can affect system performance. This paper is concerned with the formulation of stochastic models of the contention for resources in computer systems, which incorporate explicit representations of algorithms for processor scheduling. The modeling is illustrated in the context of data base management systems. A data base management system is a processing program that operates under the operating system of a computer and facilitates the accessing of large quantities of data shared in common by several applications. When a data base management system runs on a computer there can be contention by the data base management program and the application programs for the processing and inputoutput resources of the Svstem. The processor provides several types of service in searching the data base and retrieving and processing information, and the scheduling of these services on the processor can affect system performance significantly. The several types of service rendered by the processor are modeled explicitly. The scheduling of these services on the processor is represented as follows. There can be more than one queue for each type of processor service and the queue entered by a particular customer requiring processor service depends on the type of service required and on the service just completed for that customer. The scheduling of the processor is based on a total static priority ordering of the queues for processor service. This formulation allows rather complex processor scheduling algorithms to be represented. To illustrate these modeling ideas, a model is formulated which represents the processor scheduling algorithm for a particular data base management system, IMS (Information Management System) [ 11. Most of the previous literature analyzing priority scheduling in queuing models has been concerned with single resource models, i.e., the single server queue (see Kleinrock [ 2 ] for an account of such models). Here priority scheduling is incorporated in a multiple resource model; i.e., both processor and input-output resources are represented. An explicit representation of different types of processor service and processor scheduling in a multiple resource queuing model can be found in Lewis and Shedler [3]. Lavenberg [4] formulated a class of multiple resource models incorporating priority scheduling based on a total ordering of queues. However, unlike the model developed here, there can be only one queue for each type of service. An alternative representation of multiple types of service is possible via the notion of customer classes as used by Baskett, et al. [SI. (The models considered in [5] do not incorporate priority scheduling, however.) The model developed here is analyzed based on the existence of an embedded finite state semi-Markov process, using techniques similar to those in [3]. In order that an embedded semi-Markov process exist, it is assumed that certain service times are mutually independent and exponentially distributed random variables. However, all services that cannot be performed simultaneously (e.g., all processor services) and that are not 437 MODELING OF PROCESSOR SCHEDULING SEPTEMBER I S 176