Firing Line. ''Borges: South America's Titan'' - download pdf or read online

By Jorge Luis Borges, William F. Buckley, Jr.

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Additional info for Firing Line. ''Borges: South America's Titan''

Example text

Let ° 0< 51:'_1 < N en L'k_1 = , J-(n) k-I > 1 -in) 51:'_1 = 0, Jk _ 1 = 1 J{ + u(5 k) - or 0n Uk_1 = J'V , or 51:'_1 = N, Jk _ 1 - •I-in) k-I -in) ° =° > u(k). ) _(n)(. Ck (5) I)PX]x',o,(Ck-I(V, x', 0, 0) + Ck_1 (v, x', N s , 1)) x' L[PX]x',x(Ck-I(V,X',O,j) Ck(V,X,S,j) = (4) x' L[PX]x',xCk-I(V,X',s -1,j x' = 0, if s if s = 1, j = ° + Ck_I(V,X', Ns,j + 1)) + 1) if 2 <:; s <:; N s , 1 <:; j <:; K otherwise ° (6) 1 <:; j <:; K +1 where k :::: 1, n :::: 1, x,x' E X, v E V. f. f. of system state at the nth embedded point is given as c~n+I)(V',x,s,j) = LLav(v',k) c~n)(v,x,s,j), k v (7) ° + where k :::: 1, v, v' E V, x E X, 0<:; s <:; Ns and <:; j <:; K 1.

V-stream arrival in a slot is considered first for buffer allocation. Hence, we have CV == Co. Case 2: 'rx arrival policy. The system state seen by a V-stream arrival is after the X-stream cells of the same slot. () - ,) < + urSa)). l\ (9) + u(s) J K +u(s). I=K+u(s) 1=0 Some of the interesting performance measures of V-stream are found as follows: P[buffer occupancy P[cell loss] = j] = ~ [CV(V,X,O,j) + ~CV(V'X'S,j + 1)], ~ [ c"(v,x,O,K) P[delay = j slots] = j I:cV(v,x,s,1) ° fl. Ns + ~cV(v,x,s,A' + 1) ] ° (11) (12) ° + LcV(v,x,Ns,l) if j mod N" = if j m:~ Ns of- and N s :::; j < (K + l)Ns LcV(v,x,O,I-l) v,x 0:::; j:::; (13) otherwise when, s = (Ns - j) mod (Ns), 1= U/NsJ and delay is the time spent in the system.

In order to derive the pgf n(xl, x2, ... ), we let 1t(il> i2, ... I h ' h, ... ) denote the one-step transition probability that there are in (n ~ 1) sources in the nth slot of an on-period, given that there were h (l ~ 1) sources in the lth slot of an on-period in the previous slot. ) = LL ... ) (zO)k=1 hh Hence, we obtain the following equation for the pgf n(Xl, x2, ... ) : (28) 42 Part One ATM Multiplexing As can be expected intuitively, it is possible to show that the solution n(Xl' x2, ...

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Firing Line. ''Borges: South America's Titan'' by Jorge Luis Borges, William F. Buckley, Jr.


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