Question :
Customers arrive at
a service centre with a mean arrival rate (ʎ) of 20 per hour. Service facility
has been created to serve the customers at a mean rate (µ) of 25 per hour.
Assume that arrival and service completion both follow Poisson
distribution.
Probability that
there are n customers in the system is given by Pn = (ʎ/µ)*Pn-1.
Probability that
there is no customer in the system can be derived as P0 = 1- (ʎ/µ).
(i) What is the probability of the service
facility being idle?
(ii) What is the probability that there are
more than 4 customers in the system?
(iii) What should be the mean service rate to
make the probability of service facility being idle as 0.1?
(iv)
Will this change in service rate increase or
decrease the probability of having more than four customers in the system?
Write this answer in 2 sentences only. No need to give numerical values. Answer: Answer is discussed in the below video.
Marking pattern is given below.
ReplyDeletei) In this question you get either 0 or 1 mark. Verify your answer from the video and you know your marks.
ii) Probability of 0, 1, 2, 3 and 4 customers in the system were to be computed and the sum of these was to be subtracted from 1. Those who computed only the individual probabilities but could not find the probability of having more than 4 customers have been awarded just 1 mark. Right approaches with calculation errors have been given 2-3 marks. P5 or 1-P4 etc has been given 1.
iii) In this question, Correct answer – 2 marks, Correct approach but calculation error – 1 mark, and rest 0.
iv) Answer of this question depended on previous parts. If they are wrong then you get 0 here. Some students gave general statements instead of answering to the point. For correct statement but not answering the given question you get 1.