Question
2:A
service provider charges for his service on per minute basis and the customers
have to buy the service time in advance. 8 customers have bought the service
time as 12, 8, 5, 16, 10, 14, 7 and 5 minutes respectively. They arrive at the
service provider at different times. Their arrival time are 10, 18, 20, 23, 27, 40, 45 and 48 minutes after opening of the office.
a) Find
the average time customers spend in the system if First Come First Serve (FCFS)
sequencing rule is applied.
3 marks
b) What
will be the impact on this average time if the sequencing rule is changed to
Shortest Service Time First?
4 marks
c) Suppose
the service provider creates facilities for self-service 3 minutes of the
service time requirement. It means that a customer will require to be in queue
only for service time bought minus 3 minutes. For example, the customer who has
bought 16 minutes of service time will self-serve for 3 minutes and wait to be
served for remaining 13 minutes. What will be the impact of this change on the
average time customers remain at the service facility? Assume FCFS sequencing
rule for this part of the question. 3
marks
Answers can be viewed and downloaded from https://drive.google.com/file/d/0B6PHuk6I5SxbVmdLNTdyVzQ1czQ/view?usp=sharing.
Common mistakes and marking pattern:
ReplyDeletea) In some cases students have done calculation mistakes. For one independent calculation error there is no deduction in marks. Multiple errors have happened with conceptual mistakes getting 0 marks in that. Very few have just got the numbers without any explanation or any sign of calculation anywhere on the answer sheets. Answers were to be written with explanation as per the instruction. Hence 0 marks. Most of the students have answer this question right and got full marks.
b) No marks deduction for one independent calculation mistake. Some have kept the server idle even when customers are available in the system just because in the data some customer with lesser service time requirement is to come later. This is wrong. Whenever the server becomes free it will start serving the customer having minimum service time requirement available at that time. Making the server idle even when customers are waiting in the system is wrong. So 0 marks for such errors.
c) A very common mistake was that students reduced the service time by 3 minutes and did the calculations. The self-service too will happen after arrival only at the service facility. So 0 marks. In some rare cases, one mark has been given because of some good points in explanation. Some have done the calculation by reducing the service time and at the end added 3 minutes in the average. For them, the service completion time was wrong. Hence 1 mark only.