Efficient performance models for layered server systems with replicated servers and parallel behaviour

Capacity planning for large computer systems may require very large performance models, which are difficult or slow to solve. Layered queueing models solved by mean value analysis can be scaled to dozens of servers and hundreds of service classes, with large class populations, but this may not be enough. A common feature of planning models for large systems is structural repetition expressed through replicated subsystems, which can provide both scalability and reliability, and this replication can be exploited to scale the solution technique. A model has recently been described for symmetrically replicated layered servers, and their integration into the system, with a mean-value solution approximation. However, parallelism is often combined with replication; high-availability systems use parallel data-update operations on redundant replicas, to enhance reliability, and grid systems use parallel computations for scalability. This work extends the replicated layered server model to systems with parallel execution paths. Different servers may be replicated to different degrees, with different relationships between them. The solution time is insensitive to the number of replicas of each replicated server, so systems with thousands or even millions of servers can be modelled efficiently.