An airline has N adjacent check-in desks at a particular airport, each of which can handle any customer from that airline. Arrivals of passengers at the check-in area are assumed to follow a Poisson process with rate q. The time taken to check-in a passenger is assumed to follow an exponential distribution with mean 1/a. Answer: The possible states are 0 to N desks in use with no passengers queuing, and N desks in use with 0, 1, 2, ….. passengers in the queue. When all desks are occupied and there are M passengers in the queue denote the state as N:M. State space is: {0, 1, 2, …., N - 1, N : 0, N : 1, N : 2, …..} I understand why the trans. rate from 1 to 0 is "a" (that's the parameter for the exp func.) but the ques is why do we multiply by the number of desks that are occupied, eg. 2a, Na. Thanks.
We multiply by the number of desks because the probability of someone leaving a desk increases the more desks that are currently taken.
confused part iv) kolmogorov foward eqtns in component form The 2nd answer gives d/dt Pr(t)=a(r+1)Pr+1(t)+qPr-1(t)-(ar+q)Pr(t) for r+1<=N However,taking say r=2, we can move as follows: 3-3-2 3-2-2 1-1-2 1-2-2 so im getting d/dt Pr(t)= a(r+1)Pr+1(t)+qPr-1(t)-2(ar+q)Pr(t) mine has a 2 before the last part while the examiners answer doesnt..........anyone explain where im going wrong?
I would do as (transition force in - transition force out) And get same result.... \( 3aP_3(t)+qP_1(t)-(2a+q)P_2(t) \) I can't understand how you did?
