8. CASE STUDIES
22.214.171.124 Age-based output arbitration
Packet latency is divided into two components: queueing and router latency. The total delay ( T )ofa
packet through the network with H hops is the sum of the queueing and router delay.
= H Q(λ)
where t r is the per-hop router delay (which is
50 ns for the Seastar router). The queueing delay,
Q(λ) , is a function of the offered load ( λ ) and described by the latency-bandwidth characteristics of
the network. An approximation of Q(λ) is given by an M/D/1 queue model (Figure 8.8 ).
When there is very low offered load on the network, the Q(λ) delay is negligible. However, as traffic
intensity increases, and the network approaches saturation, the queueing delay will dominate the
total packet latency.
Figure 8.8: Offered load versus latency for an ideal M/D/1 queue model.
As traffic flows through the network it merges with newly injected packets and traffic from
other directions in the network (Figure 8.9 ). This merging of traffic from different sources causes
packets that have further to travel (more hops) to receive geometrically less bandwidth. For example,
consider the 8-ary 1-mesh in Figure 8.9 (a) where processors P0 thru P6 are sending to P7. The
switch allocates the output port by granting packets fairly among the input ports. With a round-
robin packet arbitration policy, the processor closest to the destination (P6 is only one hop away) will
get the most bandwidth — 1/2 of the available bandwidth. The processor two hops away, P5, will