Heavy Traffic/diffusion Approximation
When the server is heavily loaded (service rate of the queue is only just larger than arrival rate) the queue length process can be approximated by a reflected Brownian motion which converges to the same stationary distribution as the original queueing process.
Read more about this topic: Fork-join Queue, Stationary Distribution
Famous quotes containing the words heavy and/or traffic:
“Come to me, all you that are weary and are carrying heavy burdens, and I will give you rest. Take my yoke upon you, and learn from me; for I am gentle and humble in heart, and you will find rest for your souls. For my yoke is easy, and my burden is light.”
—Bible: New Testament, Matthew 11:28-30.
Jesus.
“Poems stirred
into paper coffee-cups, eaten
with petals on rye in the
sun—the cold shadows in back,
and the traffic grinding the
borders of spring ...”
—Denise Levertov (b. 1923)