Question

Queuing Theory

I have a question that I must determine if the service rate can be assumed to be exponential by this data. I am unsure how to show it follows an exponential distribution.

13.9 22.3 2.1 4.9 1.6 4.4 4.0 5.0 0.1 2.7 2.2 31.0 18.8 18.0 0.2 7.1 18.4 1.1 7.9 6.5 6.2 2.7 1.8 6.7 1.9 20.6 16.8 4.3 4.1 0.5

Answer 1

by using r software

and by using Q-Q plot

we can check whether given data is coming from exponential distribution or not.

r code-

Fitel Edit Packages Windows Help Untitled -R Editor rm (list ls)) d-c (13.9,22 3,2.1,4.9,1.6, 4.4,4.0 '5.0,0. 1,2.7,2.2,31.0,18 . 8, 18.0,0.2,7.1 ,18.4,1.1,7.9, 6.5, 6.2,2.7, 1.8 6.7,1 .9,20.6,16.8, 4.3,4-1, 0.5) d lam-1/mean (c) sample quantile pexp (c lam) theoretical quantile c(1/30, 2/30,3/30, 4/30, 5/30 6/30,7/30, 8730, 9/30, 10/30, 11/30,12/30, 13/30, 14/30 15/30,16/30,17/30, 18/30, 19/30,20/30,21/30,22/30, 23/30, 24/30,25/30,26/30,27/30, 28/30, 29/30,1) plot (theoretical quantile, sample quantile) abline (0,1)

r output-

rm (list=ls ( ) ) dc (13-9,22.3,2.,4.9,1.6,4.4,4.0 위 : ,5.0,0.1,2. 7,2.2,31.0,18.8,18·0,0.2,7.1 +,18.4,1.1,7.9,6.5, 6.2,2.7,1.8 +,6.7,1.9,20.6,16.8,4.3,4.1,0.5):d [11 13. 9 22.32.1 4.91.6 4.4 4.0 5.0 0.1 2.7 2.2 31.0 18.8 18.0 0.2 [161 7. 1 18.4 1.17.9 6. 5 6.2 2.7 1.8 6.7 1.9 20.6 16.8 4.3 4.1 0.5 0.20.51.1 1.6 1.8 1.9 2.1 2.2 2.72.74.0 4.14.3 4.4 .17.9 13.9 16.8 18.0 18.4 18.8 20.6 22.3 31.0 16] 4.9 5.06.2 6.56 > lam=1/mean mple quantile pexp (c, lam) P theoretical quantile/30,2/30,3/30,4/30, 5/30, 60, 8/30,9/30, 10/30, 11/30, 12/30, 13/30,14/30, 7/ /30,18/30,19/30,20/30,21/30, 22/30,23/30, 25/30, 2/30,27/30,28/30, 29/30,1) plot theoretical quantile, sample quantile)

R Graphics Device2 (ACTVE O Oo O o O o 0.0 0.2 0.4 0.6 0.8 theoretical quantile
here from graph

we observed that all points are lies nearly equal on line

thus,

we conclude that the given data coming from exponential distribution