Evaluation of loadsharing algorithms for heterogeneous distributed systems

The performance of loadsharing algorithms for heterogeneous distributed systems is investigated by simulation. The systems considered are networks of workstations (nodes) which differ in processing power. Two parameters are proposed for characterising system heterogeneity, namely the variance and skew of the distribution of processing power among the network nodes. A variety of networks are investigated, with the same number of nodes and total processing power, but with the processing power distributed differently among the nodes. Two loadsharing algorithms are evaluated, at overall system loadings of 50% and 90%, using job response time as the performance metric. Comparison is made with the ideal situation of ‘perfect sharing’, where it is assumed that the communication delays are zero and that complete knowledge is available about job lengths and the loading at the different nodes, so that an arriving job can be sent to the node where it will be completed in the shortest time. The algorithms studied are based on those already in use for homogeneous networks, but were adapted to take account of system heterogeneity. Both algorithms take into account the differences in the processing powers of the nodes in their location policies, but differ in the extent to which they ‘discriminate’ against the slower nodes. It is seen that the relative performance of the two is strongly influenced by the system utilisation and the distribution of processing power among the nodes.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.