In this section we will introduce evaluation: lies in the fact that it can be applied almost unconditionally to all queueing models and at many levels of abstraction. Its strength furthermore lies in the fact that its form is both intuitively appealing and simple. Little’s law and explain it intuitively. A more thorough In Section we introduce proof is given in | Performance of Computer Communication Systems A Model-Based Approach. Boudewijn R. Haverkort Copyright 1998 John Wiley Sons Ltd ISBNs 0-471-97228-2 Hardback 0-470-84192-3 Electronic Chapter 2 Little s law and the M M 1 queue IN Section we present Little s law a very general law that can be applied in many queueing models. Using Little s law we are able to study the simplest queueing model the M M 1 queueing model in Section . Little s law In this section we will introduce the probably most general law in model-based performance evaluation Little s law named after the author who first proved it 186 . Its generality lies in the fact that it can be applied almost unconditionally to all queueing models and at many levels of abstraction. Its strength furthermore lies in the fact that its form is both intuitively appealing and simple. In Section we introduce Little s law and explain it intuitively. A more thorough proof is given in Section . Understanding Little s law Little s law relates the average number of jobs in a queueing station to the average number of arrivals per time unit and the average time a job spends in a queueing station. Consider a queueing station as a black box at which on average A jobs per time unit arrive see Figure A is called the arrival rate or the arrival intensity. When we assume that jobs are served on a first come-first served basis FCFS whenever a job arrives at the queueing station two things might happen. Either the job is immediately served which implies that there are no other jobs in the queueing station or it has to wait until the jobs already in the queueing station are served before it gets its turn. Notice that we do not 22 2 Little s law and the M M 1 queue arrivals service providing entity departures Figure Black box view of a job servicing system assume anything about the distributions of the interarrival and service times only their means are used Denote the average time a job spends in the
