2 2 1 2 i v x 2 2 the variance is i i1 1 2 the

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Unformatted text preview: time is still exponential. Finally, G/G/1 means both inter-arrival time and service time are non-exponential (not necessarily the same distribution). More about this types of queues are left to courses such as CS 594 and CS 694. CS 522, v 0.94, d.medhi, W’99 24 20. An example of a non-exponential distribution: hyper-exponential The pdf for two-stage hyperexponential distribution (H2 ) is given by f x =  ,1 x +  ,2 x 1 1e 2 2e 1 The mean is 1 E X  = 2 + 1 2 2  0 and 1+ 2=1 : X ! 2 2 1 2 i ,  + : V X  = 2 2 The variance is i i=1 1 2 The distribution is considered to be balanced if: 1 1 = 2 2 : The squared co-efficient of variation (c2 ) is given by: c2 = (note: V X  E X  2 = E X 2  , 1: E X  2 E X 2 is the second moment). How about generating hyperexponential distribution? Given anced mean can be generated as follows: Calculate 1 and 2 as follows: 1= 1 2  1 , 2=1 and 1 and 2 as follows: r , c2 , 1 c2 + 1 c2 and , a hyperexponential with bal- ! 1 1 = 2 1  2 = 2 2 : CS 522, v 0.94, d.medhi, W’99 25 21. Considering M/M/1 and M/D/1 together In the figures below, we plot N and T for different values of Notice the difference as 1. for the systems M/M/1 and M/D/1. ! M/M/1 and M/D/1 Average number of customers in steady state mu = 0.1 10 8 6 4 2 0 0.1 0.2 0.3 0.4 0.5 0.6 utilization, ρ 0.7 N_mm1 0.8 0.9 N_md1 M/M/1 and M/D/1 µ = 0.1 Average Delay 120 100 80 60 40 20 0 0.1 0.2 0.3 0.4 0.5 utilization, ρ 0.6 0.7 T_mm1 CS 522, v 0.94, d.medhi, W’99 0.8 0.9 T_md1 26...
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