A Generalized Analysis Technique for Queueing Networks with Mixed Priority Strategy and Class Switching

A very well known and popular technique for the performance evaluation of current computer and operating systems is analytical modeling based on queueing networks because it is easy to understand and use compared to other modeling techniques. For so called product form queueing networks e cient exact and approximate analysis algorithms exist but most queueing networks of realistic systems do not ful ll the requirements of product form queueing networks. To solve this kind of networks Markovian analysis or discrete event simulation is used. The disadvantage of these techniques is that they are very time consuming to prepare, implement and run, especially when we want to analyze the system on a wide range of parameter values. Because of these disadvantages our goal is to transform queueing networks that can not be solved with standard analysis techniques into networks that can be solved with standard analysis techniques (like MVA, SCAT or Convolution). Problems that appear very often in realistic systems are priorities with and without preemption, mixed priorities and class switching. These problems appear especially in the eld of operating system modeling [BoGr94, GBT94, Jung91]. The paper is organized as follows. In Section 1 we introduce the notation used in this paper and present already existing techniques to solve networks with priorities. Then we show how to combine the presented techniques to solve networks with a certain type of mixed priority classes. In Section 2 we introduce the concept of chains to handle open, closed and mixed networks with class switching. The goal is to derive a solution technique for any type of mixed priority strategy. Therefore the well known shadow technique is introduced and extended for open, closed and mixed networks with class switching and priorities. In Section 3 we apply these techniques to a simple non product form network with the problems mentioned above. It is shown how this network can be transformed into a product form network and solved using a standard analysis technique. In Section 4 the presented techniques are demonstrated on the example of a UNIX based multiprocessor operating system kernel.