Customers arrive to a waterslide randomly (i.e., generic distribution) and slide down the waterslide according to...

 

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Customers arrive to a waterslide randomly (i.e., generic distribution) and slide down the waterslide according to a random time (i.e., generic distribution). The statistics are given in the sheet. h Variance (minute) 4 9 Service time Interarrival Time Mean (minute) 1/2 3/4 a. Calculate the number waiting in line, the number in system, time waiting in line, and time waiting in system. b. What if they had the same mean times but times were exponentially distributed? c. What if interarrival times were exponential, but the slide had a machine that pushed the customers down the slide so that it took exactly of a minute. d. The waterslide company experiences an increase in arrivals to 3 per minute. What is the new utilization? e. Assume that the arrival rate is now 3 per minute. The company noticed that the lines and wait times were getting extremely long and this was hurting the company's reputation so they decided to build a second slide. Assume exponential interarrivals and slide times. What would be the resulting effect on length of the line and waiting times? Customers arrive to a waterslide randomly (i.e., generic distribution) and slide down the waterslide according to a random time (i.e., generic distribution). The statistics are given in the sheet. h Variance (minute) 4 9 Service time Interarrival Time Mean (minute) 1/2 3/4 a. Calculate the number waiting in line, the number in system, time waiting in line, and time waiting in system. b. What if they had the same mean times but times were exponentially distributed? c. What if interarrival times were exponential, but the slide had a machine that pushed the customers down the slide so that it took exactly of a minute. d. The waterslide company experiences an increase in arrivals to 3 per minute. What is the new utilization? e. Assume that the arrival rate is now 3 per minute. The company noticed that the lines and wait times were getting extremely long and this was hurting the company's reputation so they decided to build a second slide. Assume exponential interarrivals and slide times. What would be the resulting effect on length of the line and waiting times?

Answer rating: 100% (QA)

To solve this problem we can use the MM1 queuing model where M stands for exponential distribution and 1 represents a single server Lets go through each part of the problem a Given data Mean service t... View the full answer