A note on queues with Bernoulli routing

A queuing system with K identical single-server queues in parallel is considered. Arrivals are characterized by a marked point process (τ_n, S_n), where τ_n and S_n denote the epoch and the service time of the nth arrival, respectively. The marked point process is assumed to be independent of the queuing system. Arrivals are routed to one of the K queues of i.i.d. Bernoulli random variables with parameter p=(p₁, p₂, . . ., p_K), where p is the routing vector. It is shown that various performance measures are minimized when p=(1/k, 1/k, . . ., 1/k)