By Gordon F. Newell (auth.)
ISBN-10: 3540095527
ISBN-13: 9783540095521
ISBN-10: 3642464106
ISBN-13: 9783642464102
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Additional info for Approximate Behavior of Tandem Queues
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2) defines a well-posed problem. Since these equations describe f as a function of the initial state, independent of the history prior to time to' the dif- fusion approximation approximates the process (DO(t), " ' , Dn(t» by a Markov process (whether this is exactly true or not). f de- to to The above scribes the transition probabilities from (Yo' ••• , Yn) at time (x O' ••• , xn ) at time t which, along with the Markov property, gives a complete description of the stochastic behavior of the system.
1), if one boundary condition is satisfied, the other is automatically also satisfied. lb) with A(xo;t) some arbitrary positive function, which, however, is presumed to be slowly varying. lb). 4) in an attempt to obtain an equation for A(xo;t) , aA/ax O = O. 4) force is a constant. But, if A(xO;t) is a constant, we cannot satisfy the normalization condition +00 J -= dxO J cl 0 dt l g(xO' tl;t) 1 , (except for A = 0). lb) is approximately correct, but to obtain a second approximation, one must proceed differently from the above.
2). 4), to neglect with respect to ( f and ~ 1 - ~O + ~l ) a£ xO. 6). 1), if one boundary condition is satisfied, the other is automatically also satisfied. lb) with A(xo;t) some arbitrary positive function, which, however, is presumed to be slowly varying. lb). 4) in an attempt to obtain an equation for A(xo;t) , aA/ax O = O. 4) force is a constant. But, if A(xO;t) is a constant, we cannot satisfy the normalization condition +00 J -= dxO J cl 0 dt l g(xO' tl;t) 1 , (except for A = 0). lb) is approximately correct, but to obtain a second approximation, one must proceed differently from the above.
Approximate Behavior of Tandem Queues by Gordon F. Newell (auth.)
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