Performance of rate-based pull and push strategies in heterogeneous networks

Response times in large distributed systems can be reduced by exchanging jobs between idle servers and servers with pending jobs. When a pull strategy is deployed the initiative to exchange jobs is taken by the idle servers, while servers with pending jobs initiate the exchange when a push strategy is implemented. In this paper the performance of a class of rate-based pull and push strategies for large heterogeneous networks is studied using a mean field model. These strategies have the advantage that the rate at which servers probe other servers to initiate a job exchange can be controlled, allowing a fair comparison between pull and push strategies. Based on two natural conjectures we derive a simple condition for the required probe rate to establish system stability when the system size becomes large and consists of two types of servers. In some specific cases we show that this condition coincides with the existence of a unique positive fixed point for which we also present an explicit expression. This fixed point is used to express the queue length distribution and mean response time in the system in explicit form. The accuracy of both the stability condition and mean queue lengths as predicted by the mean field model is validated using time-consuming simulation experiments. We end the paper with some numerical results that compare the performance of the rate-based pull and push strategies in a heterogeneous setting.