Computation of availability of a real-time system using queueing theory methodology
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Computation of availability of a real-time system using queueing theory methodology J Kreimer and A Mehrez Ben-Gurion University of the Negev, Beer Sheva, Israel In this paper we consider a real-time multiserver (such as machine controllers) and multichannel (such as regions and assembly lines) systems involving maintenance. Our objective is to ®t these systems into the framework of queueing models and thus to justify the use of the powerful queueing theory analytical methods in the analysis of real-time systems. The main dif®culty is that real-time systems by their very nature do not permit queues. To resolve this contradiction we use a dual approach in which we consider jobs as servers and servers as jobs. We adjust the traditional de®nition of availability for the real-time systems under consideration and show how to compute the system's availability, when both service and maintenance times are exponentially distributed (birth-and-death process). At this stage we restrict ourselves to a worst case (maximum load regime), which is most typical in high-performance data acquisition and control (production and military) systems. Keywords: availability; maintenance; production control; real-time data processing; unmanned systems
Introduction Real-time (RT) systems have received considerable scienti®c attention in the last two decades, mainly because of their great popularity and rapid development in such areas as production control and manufacturing in industry, and intelligence, radar systems, self-guided missiles and unmanned (robotic) systems in military applications. In RT systems, jobs arriving are served immediately (conditional on system availability) in real time without delays. That part of the job which is not served immediately is lost forever and cannot be processed later. Therefore, by their very nature, queues do not exist in these systems and the direct use of queueing theory is impossible. The ®rst interest of the operations research (OR) community in RT systems appears in the early seventies. Several authors: Labetaulle,1 Liu and Layland,2 and Serlin,3 proposed priority algorithms for scheduling `time-critical' (that is, real-time) tasks on a single processor. Dhall and Liu4 considered the problem of specifying an order in which the requests made by a set of `periodic-time-critical' (that is, real time) tasks are to be executed by a multiprocessor (multiserver) system, which the goal of meeting all the deadlines with a minimum number of processors. More recent RT scheduling problems are considered by Akkan5 (overtime scheduling) and by Litoin and Tadei6 (fuzzy due dates).
Correspondence: Dr J Kreimer, Department of Industrial Engineering and Management, Ben-Gurion University of the Negev, PO Box 653, BeerSheva 84105, Israel. E-mail: [email protected]
The most recent and extensive survey on real-time decision problems (RTDP) can be found in Seguin et al.7 Good surveys on applic
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