Comment on ´Behaviour of circuit-switched multistage networks in presence of memory hot spot´ (and reply)

For original article see ibid., vol.25, p.833-4 (1989). Pombortsis and Halatsis have considered the behaviour of circuit switched multistage interconnection networks (MINs) in the presence of a memory hot spot. An iterative algorithm was derived to compute the bandwidth of an n-stage MIN (each stage consists of alpha ^n-1 crossbar switching elements (SEs) of size alpha * alpha ) under the hot spot nonuniform traffic. A closer look at the expressions for P_h¹ and P_nh¹ given in their letter reveals that each processor may independently generate at most two requests (one for the hot MM with probability rh and one for the uniform background with probability r(1-h)) in a network cycle. The number of requests received during a network cycle by an output link of a SE at each stage is one at most. The recursive formulas for P_hⁱ and P_nhⁱ when i>or=2 should have different forms from those for P_h¹ and P_nh¹. An alternative recursive algorithm to compute the bandwidths of MINs under the hot spot nonuniform traffic is presented.