Equilibrium Results for a Pair of Coupled Discrete Time Queues

Steven Jaffe

The book Equilibrium Results for a Pair of Coupled Discrete Time Queues was written by author Steven Jaffe Here you can read free online of Equilibrium Results for a Pair of Coupled Discrete Time Queues book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is Equilibrium Results for a Pair of Coupled Discrete Time Queues a good or bad book?

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6), h is continuous across T \ {l}. Morera's theorem ensures that h is analytic in C" \ {l}, and (2. 5b) implies that the isolated singularity at 1 is a simple pole with residue (1 —p)/'(l). From these conditions we see that h(w) = ^^ + D where C = (1 - p)/!>'(l). Putting this in (2. 6) gives D = C/2, so we get Let Tp = ~^ be the conformal mapping from the interior of £ to D. Then (2. 8) g(x) = MV'(^))^^(l-p)V''(l) ^j^j^) The function V' is given explicitly by (Nehari [6]) (2. 9) V(a') = V^sn (... — sin-M ^-^x- 1 > "■ > . , -(!_ II TT \ p ) ) \p y p- where sn is the Jacobi elliptic function with nome q, K = K{q) and k — k(q). Using V'(l) = 1 and (sn'(;))^ = (l - sn-(r)) (l -yt=sn-(2)), we find that (2. 10) ^'(i).^(l_, )yi±^ Putting (2. 9) and (2. 10) into (2. 8) thus gives the explicit solution for g. From (2. 2) (2. 11) p(x, y)= ^^~^^^/^~^^ g(x)+9(y)) xy- r(x, y} (2. 12) = 2v/r p K{l-k) (x-l)(3/-l) V-(x)V. (y)-l V (V'(x) - l)(V'(y) - 1) xy-T{x, y) 3. Solution of the functional equation: Automorphy.

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