Summary
This paper reviews some interesting but scattered results that are known about correlation in bivariate Poisson distributions and processes and presents some new results. A particular concern in both contexts is with results and examples relating to negative correlation.
Abstracl. The concept of time-shared computer operations is briefly described and a model of a time-sharing system is proposed, based on the assumption that both interarriw~l ~1(t service times possess an exponential distribution. Although the process described by this model is non-Markovian, an imbedded Markov chain is analyzed by exploiting the fact that the instunts of completion of a "quantum" of service are regeneration points. It is shown that user congestion possesses a limiting distribution, and the method of generating functions is used to derive this distribution. The concept of cycle time is discussed ,,rod two measures of cycle time developed for a scheduling discipline employing a single queue, Finally, a number of numerical examples are presented to illustrate the effect of the system part, meters upon user congestio~i, system response time and computer efficiency.]. tnS'oduclion ....In recent months considerable attention has been paid to the use of computers on a time-shared basis (see [1] to [6]). In palOficular, Coffman and Krishnamoorthi [11 have presented both an empirical investigation of an existing time-sharing system a~id an ~malysis of a mathematical model of this type of operation [6]. In ~his paper a model is considered based on a somewhat different set of assumptions them those of the cited pape:r--assumptions that are more amenable to an analysis of the effect~ of certain design parameters.The presentation of the material is as follows. In the remainder of Section 1, what is meant by time-shared operation of a computer is briefly described; in Section 2 a mathematical model of the operation and present analytic expressions for user co~lgestion and :measur~ of system response is developed and analyzed; in Section 3 t, hese concepts are illustrated with some numerical examples, and based on these, the effect of system parameters upon user congestion, system response time and computer efficiency are discussed.WHAT IS TIME-SHARING? In a time-shared computer operation a request for computation is not necessarily serviced to completion upon the first entry of that request into the computer, but is truncated and the remaining computation postponed according to a given scheduling discipline. The vehicle that provides for this type of operation will be called a time-sharing system (TSS) and tan be generally described as having the following properties:*simultaneity--a number of people use the computer at essentially the same time;
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