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In A Commercial Bank, The Management Has Established That 20 Customers Arrive In The Banking Hall Per Hour While The Bank Serves A Customer In Two Minutes
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In a commercial bank, the management has established that 20 customers arrive in the banking hall per hour while the bank serves a customer in two minutes
( i ) What is the probability that a client will be waiting in the bank to be served
(ii) Assuming that all the customers who come at the banking hall are served by the cashiers only, what is the probability that the cashiers will be idle
(iii)what is the probability that 10 people will be waiting for service
( i ) What is the probability that a client will be waiting in the bank to be served
(ii) Assuming that all the customers who come at the banking hall are served by the cashiers only, what is the probability that the cashiers will be idle
(iii)what is the probability that 10 people will be waiting for service
Answers
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well hey crispino
yes this is a question on queuing theory
and you can say - yes it is !
and there are various models - the arriveal is gonna be Poisson with a mu of three I think
and you will be told if the service is constant ( 2 mins )
and you then construct the model from scratch OR
you read the course text and apply the formula they give you
you certainly dont have time: you have posted this in finance
and it should be science where a math modeller lurks ( Jim 360)
If you really ARE doing a banking course all they want you do to do is see that 20 customers in 60 mins gives an av or 3 ( so mu = 3 I think )
yes this is a question on queuing theory
and you can say - yes it is !
and there are various models - the arriveal is gonna be Poisson with a mu of three I think
and you will be told if the service is constant ( 2 mins )
and you then construct the model from scratch OR
you read the course text and apply the formula they give you
you certainly dont have time: you have posted this in finance
and it should be science where a math modeller lurks ( Jim 360)
If you really ARE doing a banking course all they want you do to do is see that 20 customers in 60 mins gives an av or 3 ( so mu = 3 I think )
Hi carp
You have taken the 'we are all dead in the long run' view which is true
BUT the first bit says twenny arrive in sixty and that 'says' the arrival is random ( in time ) but follow a poisson distribution
this is a single queue model ( unlike MacD's which you can also model )
and service isusually taken to be random and poisson as well
but here it seems constant
God I know so much about the construction of the model I should be able to do it
part 111 if it is 10 or more then you have to look at a table ( m=3), x>10
but the term that crispino doesnt have time to look at is
e to the minus 3 / factorial 10
and that is priddy small - about one in a million
this has even prompted me to go and look it up !
Crispino can you tell me which course you are doing ?
You have taken the 'we are all dead in the long run' view which is true
BUT the first bit says twenny arrive in sixty and that 'says' the arrival is random ( in time ) but follow a poisson distribution
this is a single queue model ( unlike MacD's which you can also model )
and service isusually taken to be random and poisson as well
but here it seems constant
God I know so much about the construction of the model I should be able to do it
part 111 if it is 10 or more then you have to look at a table ( m=3), x>10
but the term that crispino doesnt have time to look at is
e to the minus 3 / factorial 10
and that is priddy small - about one in a million
this has even prompted me to go and look it up !
Crispino can you tell me which course you are doing ?
Three scenarios to consider, Crispino:
1. The customers arrive conveniently at three minute intervals. None of them wait; the cashiers are idle for one minute in every three.
2. The customers arrive all at once. Assuming there is only one cashier (and you do not say), the first does not wait; the second waits two minutes; the third four minutes, etc. The cashiers are idle for the final twenty minutes.
3. The customers arrive at intervals somewhere between (1) and (2). That's where it gets tricky and that's where Peter's theory comes in.
1. The customers arrive conveniently at three minute intervals. None of them wait; the cashiers are idle for one minute in every three.
2. The customers arrive all at once. Assuming there is only one cashier (and you do not say), the first does not wait; the second waits two minutes; the third four minutes, etc. The cashiers are idle for the final twenty minutes.
3. The customers arrive at intervals somewhere between (1) and (2). That's where it gets tricky and that's where Peter's theory comes in.
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