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They proposed an estimation for the mean cycle time in CQN with general service times. 12. n 1/, multiplied EŒT 2 by the estimated mean residual life time,31 given by 2EŒTi i . n • And the expected service time of the arriving job, EŒTi . The mean cycle time as the sum of the aforementioned components is given in Eq. 25). 27) 31 See Altiok (1996, p. 30). n 1/ is the probability that the server is occupied. As no blocking occurs, the probability that a job receives service equals the probability that the server is busy.
The Arrival Theorem is the short term for “Theorem of the distribution at arrival time”. By “distribution” the distribution of the number of customers at a station is meant. The theorem was proposed and proven for closed product-form networks by Reiser and Lavenberg (1980) and Sevcik and Mitrani (1981). The statement of the Arrival Theorem is that the probability mass function of the number of customers at a station—at the time-instant of the arrival of a customer—equals the probability mass function of the number of customers of the same network with one customer less in the system.
22) For the birth-death process, closed-form solutions exist, see Eqs. 24). kC1/ Marie’s method is an iterative procedure. First, the load-dependent service rates are initialized by the predefined processing rates (neglecting the coefficient of variation). g. the convolution algorithm) is applied to calculate the arrival rates i . The i are then employed to compute the i according to the specified service time distribution. The i serve as input for the product-form algorithm in order to update the i .