• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.511-525
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• 2004

we model communication and computer systems that process interactive and several and several types of background jobs. The scheduling policy in use is to share the processor among all interactive jobs and, at most, one background job of each type at a time according to the process sharing discipline. Background jobs of each type are served on a first-come-first-served basis. Such scheduling policy is called Processor Sharing with Background jobs (PSBJ). In fact, the PSBJ policy is commonly used on many communication and computer systems that allow interactive usage of the systems and process certain jobs in a background mode. In this paper, the stability conditions for the PSBJ policy are given and proved. Since an exact analysis of the policy seems to be very difficult, an approximate analytic model is proposed to obtain the average job sojourn times. The model requires the solution of a set of nonlinear equations, for which an iterative algorithm is given and its convergence is proved. Our results reveal that the model provides excellent estimates of average sojourn times for both interactive and background jobs with a few percent of errors in most of the cases considered.

• The Transactions of the Korea Information Processing Society
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• v.1 no.3
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• pp.367-379
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• 1994

This paper describes scheduling algorithms of the UNIX operating system and shows an analytical approach to approximate the average conditional response time for a process in the UNIX operating system. The average conditional response time is the average time between the submittal of a process requiring a certain amount of the CPU time and the completion of the process. The process scheduling algorithms in thr UNIX system are based on the priority service disciplines. That is, the behavior of a process is governed by the UNIX process schuduling algorithms that (ⅰ) the time-shared computer usage is obtained by allotting each request a quantum until it completes its required CPU time, (ⅱ) the nonpreemptive switching in system mode and the preemptive switching in user mode are applied to determine the quantum, (ⅲ) the first-come-first-serve discipline is applied within the same priority level, and (ⅳ) after completing an allotted quantum the process is placed at the end of either the runnable queue corresponding to its priority or the disk queue where it sleeps. These process scheduling algorithms create the round-robin effect in user mode. Using the round-robin effect and the preemptive switching, we approximate a process delay in user mode. Using the nonpreemptive switching, we approximate a process delay in system mode. We also consider a process delay due to the disk input and output operations. The average conditional response time is then obtained by approximating the total process delay. The results show an excellent response time for the processes requiring system time at the expense of the processes requiring user time.