Consider a memory system having address spaced at a distance of \(𝑚,𝑇\) =…

Given: m = spacing between addressed words (time interval between issuing consecutive requests or word-distance mapping), T = bank cycle time, n = number of banks.

Key idea: average throughput is limited either by how fast requests can be issued (interval m) or by how fast the banks collectively can supply data (combined interval T/n).

• Case 1 — Interleaving regime (successive addresses map to different banks, typically when the spacing is small relative to the number of banks): the memory can supply up to n words every T time units, i.e. an effective interval of T/n per word from the banks. However, the requester can only issue words every m time units. The achievable per-word interval is therefore determined by the slower of the two rates, so the time per word is whichever is larger: m or T/n.

• Case 2 — Bank reuse regime (addresses repeatedly hit the same bank, typically when spacing is large relative to number of banks): each new word requires waiting for that bank's next cycle, so the time per word is the full bank cycle T.

Therefore the average data access time per word in synchronous organization is:

For the interleaving case (m much smaller than n): time per word = either m or T/n (the larger one governs). For heavy bank reuse (m much larger than n): time per word = T.