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Consider a system of $n$ single-server queues where tasks arrive at eachserver in a distributed fashion. A graph is used to locally balance the load bydispatching every incoming task to one of the shortest queues in theneighborhood where the task appears. In order to globally balance the load, theneighborship relations are constantly renewed by resampling the graph at rate$\mu_n$ from some fixed random graph law. We derive the fluid limit of theoccupancy process as $n \to \infty$ and $\mu_n \to \infty$ when the resamplingprocedure is symmetric with respect to the servers. The maximum degree of thegraph may remain bounded as $n$ grows and the total number of arrivals betweenconsecutive resampling times may approach infinity. The fluid limit onlydepends on the random graph laws through their limiting degree distribution andcan be interpreted as a generalized power-of-$(d + 1)$ scheme where $d$ israndom and has the limiting degree distribution. We use the fluid limit toobtain valuable insights into the performance impact and optimal design ofsparse dynamic graphs with a bounded average degree. In particular, weestablish a phase transition in performance when the probability that a serveris isolated switches from zero to positive, and we show that performanceimproves as the degree distribution becomes more concentrated.

Load balancing with sparse dynamic random graphs