A virtual marketplace or service-providing system must ensure minimal task response times. Varying working rates among the human workers in the system can lead to longer delays for certain tasks. The waiting time in the queue is crucially affected by the queueing architecture used in the system, whether global or local. Studies generally favor global queue systems over local ones, assuming similar processing rates. However, system behavior changes when workers are heterogeneous. In this research, we used simulation to compare the waiting times of tasks assigned to three categories of processing rates in both architectures and with various routing policies in local queues. We found that when using random tie-breaking, there was a correlation between waiting time duration and the proportion of tie-breaking events. Performance is improved when controlling these events using scheduling awareness of the workers’ processing rates. The global queue outperforms local queues when the workers are homogeneous. However, the push mechanisms that control the assignment processes and heterogeneity-aware algorithms improve local queue system waiting times and load balance. It is better than global queues when tasks are assigned to medium and fast workers, but it also enables specific slow workers’ assignments.