Low-Cost Allocator Implementations for Networks-on-Chip Routers

Table 2

Parameter list.

Parameter	Description
𝑅	The request matrix
𝑟^𝑘𝑙𝑚𝑛	The request from the 𝑛th VC at the 𝑚th input port to the 𝑙th VC at the 𝑘th output port. The value is 1 if the request is valid.
	Otherwise, the value is 0.
𝑟^𝑘𝑚𝑛	The request from the 𝑛th input VC at the 𝑚th input port to any VC at the 𝑘th output port. The value is 1 if the request is valid.
	Otherwise, the value is 0.
𝑟^𝑘𝑙	Whether there are valid requests to the 𝑙th VC of the 𝑘th output port. It is 0 when (∑^𝑝𝑖𝑚=1∑^𝑉𝑛=1𝑟^𝑘𝑙𝑚𝑛)=0. Otherwise, it is 1.
𝑟^𝑘	The number of simultaneously requested VCs at the 𝑘th output port (∑^𝑉𝑙=1𝑟^𝑘𝑙).
𝑟^𝑘𝑚	Whether there are valid requests from any VCs at the 𝑚th input port to any VC at the 𝑘th output port. It is 0 when ∑^𝑉𝑛=1𝑟^𝑘𝑚𝑛=0.
	Otherwise, it is 1.
𝑟𝑚	The number of output ports where a VC is requested by any VCs in the 𝑚th input port (∑^𝑝𝑜𝑘=1𝑟^𝑘𝑚).
𝑝𝑏1^𝑘	The probability that one VC at the 𝑘th output port is requested.
𝑝𝑏^𝑘	The probability that multi-VCs at the 𝑘th output port are concurrently requested.
𝑝𝑏1𝑚	The probability that VCs in the 𝑚th input port request VCs at one output ports.
𝑝𝑏𝑚	The probability that VCs in the 𝑚th input port request VCs at multi output ports.