By Gordon F. Newell (auth.)
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Additional resources for Approximate Behavior of Tandem Queues
Stat. 28, 768-773 (1957). 3. J. R. Jackson, "Networks of Waiting Lines," Opns. Res. 5, 518-521 (1957). 4. D. J. Daley, ''Notes on Queueing Output Processes," Mathematical Methods of Queueing Theory, Lecture Notes in Economics and Mathematical Systems 1t98, Springer-Verlag, 1974. 5. G. F. Newell, 1971. 6. G. F. Newell, "Approximate Stochastic Behavior of n-server Service Systems with Large n," Lecture Notes in Economic and Mathematical Systems 1t87, Springer-Verlag, 1973. 7. D. R. Cox and H. D. Miller, The Theory of Stochastic Processes, J.
G~U)'k) • k O,l, ... , n . imposes conditions on the, as yet un- These conditions will, in fact. be used later as further g*(t l • ••• , t n ) boundary conditions in the One of the primary objectives in the analysis of stochastic properties of tandem queues is to evaluate the question is: min j • The most important practical to what extent do the finite storages librium service rate tion, ]1 ]1. J ? ]1 c. J reduce the equi- relative to that given by deterministic approxima- Unfortunately there does not appear to be any "short-cut" method of evaluating the tion of all the queues.
52 such that, for sufficiently large t, gt approaches some limiting form. 3b). 5) has been arranged so that both sides are derivatives with respect to £1. 2). 2). 8) + ~ 2110Cllil - flO + fll + exp(Clli l ) - 1 - Cl l \ exp(Cllc l ) - 1 [eXP(_Clli l ) Clg(xO'O ;t) ~--~----- Cl l axe This still does not describe an explicit solution for it only relates g(xO,i;t) to an as yet unknown function the probability density at zero queue. lb) and the second term gives a correction due to the drag at the boundaries.
Approximate Behavior of Tandem Queues by Gordon F. Newell (auth.)