In a recent paper, Lam and Lien described an algorithm called tree-convolution that can reduce the space and computation time required for evaluating sparse multiclass, product-form queueing networks. In this paper, we develop an exact algorithm based on mean value analysis (MVA) that is the counterpart of the tree-convolution algorithm. The order of reduction in storage and computation achieved by our new Tree-MVA algorithm compared to the standard MVA algorithm is the same order of reduction obtained by the tree-convolution algorithm over that of the standard convolution algorithm. Our Tree-MVA algorithm preserves the inherent simplicity of MVA based algorithms.

We describe a new technique for accessing a shared bus in a distributed computing environment. The load balancing bus accessing scheme can be modeled by a new station type that can be incorporated in a BCMP multiple class queueing network model of the distributed system. We show one simple means of implementing the load balancing scheme.

Consider a queueing system in which customers (or jobs) arrive to one of Q separate queues to await service from one of S identical servers (Figure 1). Once a job enters a queue it does not leave that queue until it has been selected for service. Any server can serve any job from any queue. A job selected for service cannot be preempted. In this paper we consider jobs to be in a single class; for the multiple class result see [AFSH81a]. We assume once a queue has been selected, job scheduling from that queue is fair. In particular, our results hold for first come first serve as well as random selection [SPIR79] and, for that matter, any fair nonpreemptive scheduling policy within a queue. We assume that arrivals to each queue follow a Poisson process with the mean arrival rate to queue q being λq. The S identical exponential servers are each processing work at a mean rate of μ.