Performance Modeling

Abstract

There are several probability models that are suitable for performance analysis. Each of the models has its own limitations and advantages:

• 1. Series-Parallel Directed Acyclic Graphs. These can be used to model concurrency and synchronization in programs with unlimited resources. However, they cannot model competition for limited resources.

• 2. Product Form Queuing Networks (PFQN). Queueing network models were designed to represent competition for limited resources. However realistic situations like concurrency within a job, synchronization and simultaneous resource possession violate the assumptions required for an efficient (product-form) solution.

• 3. Markov Chains. These overcome the limitations of the above two model types. They provide a general framework that can be used to model all the above mentioned characteristics of systems. However, Markov chains have their own limitations. Their construction can be very difficult and susceptible to error. Small changes in the system being modeled can result in large changes in the Markov model.

• 4. Generalized Stochastic Petri Nets (GSPNs). Generalized stochastic Petri nets also provide a general framework for modeling system/program characteristics. A GSPN is a higher-level specification than a Markov chain and is more concise. Like Markov chains, GSPNs can be difficult to construct, but once constructed, a small change in the system being modeled can sometimes be accomplished simply by a change in the initial marking. In general, GSPNs offer no advantage over Markov chains as far as solution.

• 5. Semi-Markov Chains. One limitation of (homogeneous, continuous-time) Markov chains is that the distribution of the holding time in a state must be exponentially distributed. Semi-Markov chains remove this restriction and hence provide a useful means of solving problems involving non-exponential distributions.