A single server queue in a hard-real-time environment

Abstract

We consider a single server first in first out queue in which each arriving task has to be completed within a certain period of time (its deadline). More precisely, each arriving task has its own deadline - a non-negative real number - and as soon as the response time of one task exceeds its deadline, the whole system in considered to have failed. (In that sense the deadline is hard.) The main practical motivation for analyzing such queues comes from the need to evaluate mathematically the reliability of computer systems working with real time constraints (space or aircraft systems for instance). We shall therefore be mainly concerned with the analytical characterization of the transient behavior of such a queue in order to determine the probability of meeting all hard deadlines during a finite period of time (the ‘mission time’). The probabilistic methods for analyzing such systems are suggested by earlier work on impatience in telecommunication systems [1,2].