A distributed computing system manages execution of jobs and their associated tasks. A broker manages assignment of computing tasks from clients to available computing resources. Clients and available computing resources contact the broker by polling. To prevent “ringing,” the broker specifies wait times for the polling entities, and randomizes the wait times in a range around a desired target latency. That is, a pseudo-random number generator is used to select values within a range of the target value, to avoid the situation in which deterministic patterns in the polling and response times result in highly synchronized message traffic, which might otherwise overwhelm the broker and/or the communication network.