Pooled vs. Separate Queues

A facility has two identical servers. Customers arrive as a Poisson process and each needs one server for an exponentially distributed service time. Which queueing discipline should the facility use? Separate queues: each server has its own dedicated line; customers randomly pick a line on arrival and cannot switch. Pooled queue: a single shared line feeds whichever server becomes free first. It turns out that pooling the queues is always better, even though both systems have identical total arrival rate, identical per-server service rate, and identical utilization $\rho$. The pooled system consistently produces shorter mean wait times, often by a factor of two or more at moderate utilization. The reason is that separate queues waste servers’ idle time. In separate queues, one server may be idle while customers wait in the other line. Pooling eliminates this mismatch: a free server always serves the next waiting customer. Despite being provably worse, separate queues feel fairer…