COMPUTER OUTPUT (RESULTS) HEAVEN SIGHT MARINA (ONE DOCK) QUEUE 1 : M / M / C Q U

Question

COMPUTER OUTPUT (RESULTS) HEAVEN SIGHT MARINA (ONE DOCK) QUEUE 1 : M / M / C Q U E U E S T A T I S T I C S Number of identical servers . . . . . . . . . 1 Mean arrival rate . . . . . . . . . . . . . . 8.0000 Mean service rate per server . . . . . . . . 10.0000 Mean server utilization (%) . . . . . . . . . 80.0000 Expected number of customers in queue . . . . 3.2000 Expected number of customers in system . . . 4.0000 Probability that a customer must wait . . . . 0.8000 Expected time in the queue . . . . . . . . . 0.4000 Expected time in the system . . . . . . . . . 0.5000 HEAVEN SIGHT MARINA QUEUE 1 : M / M / C PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 +----+----+----+----+----+----+----+----+----+----+ 0 0.2000|********** | Part (a) 1 0.1600|********---------- | 2 0.1280|******+----------------- | 3 0.1024|*****+------------------------ | 4 0.0819|****+----------------------------- | 5 0.0655|***+--------------------------------- | 6 0.0524|***------------------------------------- | 7 0.0419|**+--------------------------------------- | 8 0.0336|**----------------------------------------- | 9 0.0268|*+------------------------------------------- | 10 0.0215|*+-------------------------------------------- | 11 0.0172|*---------------------------------------------- | 12 0.0137|*---------------------------------------------- | 13 0.0110|*----------------------------------------------- | 14 0.0088|+----------------------------------------------- | 15 0.0070|+------------------------------------------------| 16 0.0056|+------------------------------------------------| OVER 0.0227|*+-----------------------------------------------| USE THE ABOVE COMPUTER OUTPUT TO RESPOND TO THE QUESTIONS IN THE SPACE BELOW a. What is the probability that no boats are in the system? ANSWER b. What is the average number of boats that will be waiting in the line for service? ANSWER Expected number of customers in queue . . . . c. What is the average time in minutes that the boat will be waiting in line for service? ANSWER Expected time in the queue . . . . . . d. What is the average time in minutes a boat will spend in the system? ANSWER Expected time in the system . . . . . . . . . e. If you were the manager of Heaven Sight Marina, would you be satisfied with the service level your system is providing? Why or why not? State your opinion as well as supporting reasons ANSWER

Explanation / Answer

a.

The probability that no boats are in the system = 1 - Probability that a customer must wait

= 1 - 0.8 = 0.2

b.

Average number of boats that will be waiting in the line for service

= Expected number of customers in queue = 3.2000

c.

Average time in minutes that the boat will be waiting in line for service

= Expected time in the queue = 0.4000

d.

Average time in minutes a boat will spend in the system

= Expected time in the system = 0.5000

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