Time-Shared Computer Operations With Both Interarrival and Service Times Exponential

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 interarrival and 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 instants 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 and 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 parameters upon user congestion, system response time and computer efficiency.