Please answer Queuing Problem # 9

8. 10. 11. An integrated petroleum company is considering expansion of its one unloading facility at its Singapore refinery. Due to random variations in weather, loading delays, and other factors, the interarrival times for ships arriving at the refinery to unload crude oil follow an exponential distribution with average pa = 1.4 days. Service time is also exponential with average 1.15: 0.7 days. Refer to problem 980. The company has under consideration a second unloading berth, which could be rented $1,500 per day. The service time for this berth would also be exponential, with the same mean service time as the company's own berth. For each day of a ship spent idle waiting, the company loses $4,000. a. If a second berth is rented, what would be the average time a ship would wait? b. What would be the average number of ships waiting? c. Is the benefit of reduced of time (in dollars} worth the rental cost for the second berth? Refer to the problem (8). An alternative way to improve unloading facilities is for the company to rent a high-speed unloading device. With the new device, the service time would have a distribution with us: 0.5 days and as 0.3 days. The daily rental cost of the new device is $1,500. a. If this new device is rented, what would be the average time a ship would wait?I b. What would be the average total time a ship would spend {waiting plus unloading}? c. What would be the average number of ships waiting? d. Is the benefit of reduced waiting time (in dollars) worth the rental cost for the new device? Refer to problem (9) and {10). An analyst for the company, after studying the costs and benefits of the two suggested modifications, suggests, "in each case, the benefit exceeds the cost, so let's install both the high-speed unloading device on our own berth and rent the second berth\". Unfortunately. There are no formulas in the chapter that are appropriate for a two-channel queue with differing means service times. Find a way to calculate an upper limit on potential savings from this approach and use this limit to comment on the analyst's suggestion