Consider the La Crosse lock mentioned in Problem 15-1. Assume that the basic mod

Question

Consider the La Crosse lock mentioned in Problem 15-1. Assume that the basic model is a reasonable approximation of its operation. The new estimate of the mean interarrival time for the coming season is 60 minutes for barges, and on the average it takes 30 minutes to move a barge through the lock. Find: (a) The expected number in the system. (b) The expected number in the queue. (c) The expected waiting time. (d) The expected time in the queue. (e) The probability that the system is empty. (f ) The longest average service time for which the expected waiting time is less than 45 minutes. 15-15. Use the answers to Problem 15-14 to show that Little ’ s law holds.

Not sure if 15-1 is needed, but it is as follows:

Barges arrive at the La Crosse lock on the Mississippi River at an average rate of one every 2 hours. If

the interarrival time has an exponential distribution

Explanation / Answer

lambda = 1 /hr

mu = 1/ 0.5 = 2 /hr

utilization = r = 1/2 = 0.5

a) The expected number in the system

= r/(1-r) = 0.5/0.5 = 1

. (b) The expected number in the queue.

= r^2/(1-r) = 0.5

(c) The expected waiting time.

= L/lambda= 1/1 = 1 hour

(d) The expected time in the queue.

= Lq/ lambda = 0.5 hr

(e) The probability that the system is empty

= P0 = (1 - r) = 0.5

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.