HW #5 - 2 Μ= 60/10= 6 λ= 4 hours a)ρ= /μ 4/6= 66.67...

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Chris Martin BUAD 311 March 7, 2007 Homework #5 1. a) Exponential distribution is not a very good approximation for the time between consecutive bus arrivals because the busses are supposed to arrive according to a predetermined time. Exponential distribution, on the other hand, is good at measuring the expected time of arrival if it is otherwise unknown. As previously stated, however, the arrival time of the individual busses is set and may not fit the exponential model because it largely depends on peak and off-peak travel times, in other words, there is a very small degree of variability. b) Exponential distribution is a good measure for the time of arrivals at a bakery because there are no predetermined arrival times, and thus, there is room for a relatively large amount of variability.
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Unformatted text preview: 2. Μ= 60/10= 6 λ= 4 hours a)ρ= λ /μ 4/6= 66.67% idle = (1- ρ) = (1-.6667)= 33.33% b) (4/ 6)*60/2 = 20 minutes c) 16/ [6(6-4)]= 1.33 people d) P0= 1-.667= .333 P1= (1-.667)(.667)= .2222 1-(.333 + .222)= .444= 44.44% of the time 3. a) λ= 180 Μ= 3600/15= 240 ns= λ/ μ-λ= 180/ 240-180= 3 b. ts = 1 min c. ρ = 15% d. P0= 1-.75= .25 P1= .25x.75= .1875 P2= .25 ( .75x .75)= .140625 1-[ .25 + .1875 + .14065]= .4219 or 42.19% New A= 1.875 New B= .625 mins 4. a. Pw = 50.94% b. cost = $78.34 c. No, the decrease in waiting time due to another teller does not justify the additional cost of $79.46. d. Not applicable 5. λ= 240 ρ= .8 a. utilization rate= 80% b. the average number of peanut butter sandwiches on hand is .8...
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