Optimal Task Switching Policy for a Multilevel Storage System

Capacity demands for computer memory are increasing. A multilevel storage system provides an economically feasible solution without seriously affecting the total response time. An M-level storage system is considered in this paper. The capability of a digital computer with a multilexel storage system is best enhanced in a multiprogramming environment. In a high level storage system, determination of a best task switching policy becomes an important consideration. In this paper a queuing network is introduced to describe distribution and flow of tasks in the system. An optimal switching policy is determined in relation to the system’s overhead time. It is shown that in heavily CPU-limited cases the determination becomes a very simple one; namely, the best policy is given as the threshold level at which the accumulation of the average access time exceeds the overhead time. introduction The trend in the design of computer storage systems is toward multilevel storage hierarchies. The first level or cache has a small capacity but a very low access time, which can be realized with expensive technology. Storage devices at the lower levels are realized with slower and less expensive technology and have larger capacities. Our basic assumption, in this paper, is that with the development of new technologies we may reach a situation for which the CPU might become the bottleneck of the system. In such a case, an optimal task switching policy is needed to obtain maximum throughput. We assume that only one switching policy exists in a two-level storage system and that there are two policies in a three-level storage system: The execution will be switched to another task only when 1 ) there is a page fault in the first level or 2) the referenced page is not found in either the first or the second level. We call the former the first policy and the latter the second policy. In the past, attention has been limited to the first policy only. Let us consider an M-level storage system as shown in Fig. 1. There are M 1 task switching policies in general. The mth policy in an M-level’storage system is defined as follows: The present task is executed without interruption as long as the CPU references pages that are found within the first m levels, and the execution is switched to the next task only if the CPU requests a page that is found in one of the remaining M m levels. The purpose of this paper is to analyze an M-level storage system in a multiprogramming environment and to search for an optimal task switching policy related to the system’s overhead time. We will consider a multilevel linear storage system in which data transfers take place only between adjacent levels as indicated by the arrows in Fig. 1, although other types of data transfer are conceivable [ 1 3. Each level is usually divided into a set of smaller units called “pages” or “page frames” [2, 31; a page is also a unit of data transferred from one level to the next level. Careful consideration is needed in order to determine the suitable page size at each level [2]. Here we assume that the page size at each level is already determined and that its effect is included in the access times {ti}. The hit ratio or the probability that a referenced page is found in level i is assumed to be given as {pi}, where i = 1, 2; . ., M [3, 41. In the past, performance evaluation for a multiprogramming environment has been carried out mostly for a two-level storage system [5, 61. Quite recently there have appeared several works on the design of multilevel storage systems [ 3, 4, 7 91 that investigate technologies and capacities at each level of the storage hierarchy. To the best of the author’s knowledge, however, there is no work which pays specific attention to a task switching policy for a multilevel storage system. System overhead time In the determination of an optimal task switching policy, the system overhead time plays a major role. Lewis and Shedler [ I O ] studied the effect of the overhead in a twolevel storage system. They pointed out four services as system overhead functions: 1 ) service for picking up the IBM J. RES. DEVELOP. next program for processing and restoring the machine state; 2 ) service for saving the machine state of the (present) program relinquishing the CPU, executing the replacement algorithm, constructing the channel control program for the required page, and placing an entry into the paging queue; 3) service for picking up the next page request and executing the channel control program; and 4) service for placing a new entry in the CPU queue. The first and second are concerned with service between the CPU and the first level of storage, and the last two are concerned with service between the first and the second levels. The major overhead activity is represented by the second service. In a multilevel storage system with more than two levels, additional services are needed, e.g., the administration of page directories (if a page replacement algorithm such as the "least recently used" is invoked) and of the queues that transfer the data from one level to another. Comparing the mth and (m + 1 )th policies in an "level storage system, the number of page directories is M for both but the number of transferring queues is decreased by one for the latter. When the CPU is used to govern all the services, a very complex problem arises in establishing the CPU's priority rules [IO]. Since we analyze a relatively high level storage system (say more than four levels), we assume here that dedicated special hardware is employed to carry out most of the services, so that the services assigned to the CPU are minimal. Let us denote by B,, the average overhead time in an "level storage system when the mth task switching policy is used. Our problem is to determine the optimal policy under given overhead times {B i ,M} and a fixed number of programs in an "level storage system characterized with access times {ti} and hit ratios {pi}. The criterion for optimality considered here is to increase the throughput or the number of useful instructions executed per unit of time. Queuing model In order to derive the expression for throughput we employ a queuing network model [3, 101 2 1 . To apply a queuing network model to an "level storage system, the following assumptions are made; 1 . The priority rule for service to the queue is First2. The probability distribution for the service time at Come-First-Served (FCFS). each server is negative exponential, i.e. P(Y < Yo) = 1 exp ( -Yo/t) , ( 1 ) where t is the average service time. 3. The pages at each level are referenced independently; p i is the probability that a referenced page will be JULY 1974 PI 1 tl First level