The basic MVA algorithm is quite powerful and elegant. It is applicable across a wide set of performance models. It has been the focus of much research and several extensions have been developed. These include: Several approximation techniques have also be adapted to MVA to model systems having non-product form features, including first-come-first-serve and priority multi-class networks. The extension of MVA to product form, load-independent, multi-class networks is the topic of the following chapter. Chapter 14 extends MVA and the treatment of multiclass open QNs to the load-dependent case. Several approximations to deal with non-product form QNs are presented in Chapter 15. However, even with its widespread applicability, there are limitations and shortcomings surrounding MVA. For example: MVA does not provide the steady state probabilities of individual system states. Thus, if it were important to know the probability that there were, say, less than five customers at a device in order to meet some QoS criteria, MVA would not be helpful. It would be necessary to revert to solving the global balance equations. As its name implies, MVA only provides the mean values of various performance metrics, not the associated distributions. MVA does not provide transient analysis information. For instance, if it were necessary to know how long it would take the system to recover from a temporary overload in one sector of the system and return to "steady state" behavior, MVA would be inadequate. MVA does not model state dependent behavior. For example, consider the modeling of a simple routing protocol, with two paths between a particular source and destination, where the customers (i.e., message packets) select the path least busy (i.e., dependent on the particular system state). Although a Markovian model can be easily constructed and solved for this situation, MVA is of little use. MVA solves product form networks. As a result, MVA is not directly applicable to non-product form situations. These restrictions exclude certain device service distributions (e.g., Gaussian, uniform, constant), certain device queuing disciplines (e.g., priority, multi-class FCFS), and certain device loading strategies (e.g., shortest queue routing, deterministic routing). In some of these cases, approximate MVA techniques have been developed as discussed in Chapter 15. |