In Network of Queues, M/M/1 Can Outperform M/D/1

Let N be an open queueing network where the servers have generally distributed service times (with possibly different means) and the outside arrivals to the servers are Poisson. Define N_CF (respectively, N_EF) to be queueing network N where each server has a constant (respectively, exponentially distributed) service time with the same mean as the corresponding server in N, and the packets are served in a First-Come-First- Served order. It has long been conjectured that for all networks N, the average packet delay in N C,FCFE is upper bounded by the average packet delay in N E,FCFE. In this paper, we present a counter- example to this conjecture.

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