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Waiting line model or queuing model

1. customer arrive at box office window, being manned by a singleindividual, according to a poisson input process with a mean rate of

20 per hour. The time required to serve a customer has an exponential

distribution with a mean of 90 seconds. Find the average waiting time

of customer.

2. Patients arrive at a clinic according to poisson distribution at the rateof 30 patients per hour. Examination time per patient is exponential

with mean rate of 40 per hour. Find the probability that an arriving

patient will not have to wait.

3. At a public telephone booth the arrivals are on the average 15 perhour. A call on an average takes 3 minutes, if there is just one phone.

i) what is the expected number of callers at the booth at any time?ii) For what proportion of time is the booth expected to be idle?4. In a cafeteria it was observed that there is only one bearer who takes

exactly 4 minutes to serve a cup of coffee once the order has been

placed with him. It the students arrive in a cafeteria at an average rate

of 10 per hour, how much time one is expected to spend waiting for

his turn to place the order.

5. Truck arrives at the truck dock of a whole sale concern in a poissonmanner at 8 per hour. Service time distribution is approximated by

exponential distribution with an average 5 minutes. Calculate

i) the number in waiting line, ii) the waiting time in the systemiii) the mean number in the system, iv) the problem of having 6

trucks in the system.

6. Problem arrive at a computing center in Poisson fashion with a meanarrival rate of 25 per hour. The average computing job requires 2

minutes of terminal time. Calculate

i) Average no. of problem waiting for the computer.ii) The percentage of times an arrival can walk right in without having

to wait.

7. A TV repairman finds that the time spent on his jobs has anexponential distribution with mean 30 minutes. If he repairs set in the

order in which they come in, and if the arrival of sets is approximately

Poisson with an average rate of 10 per 8 hour day, what is the

repairmans expected idle time each day? How many jobs are ahead

of the average set just brought in?

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8. Customer arrive at a sale counter manned by a single personaccording to Poisson process with a mean rate of 20 per hour. The

time required to serve a customer has an exponential distribution with

a mean of 100 seconds. Find the average waiting time of a customer.

9. In a bank there is only one window, a solitary employee performs allthe services required and the window remains continuously open from

7.00 am to 1.00 pm. It has been discovered that the average number of

clients is 54 during the day and that the average service time is 5

minutes per person. Calculate

i) the average number of clients in the system (including one beingserved)

ii) The average waiting time.10.At one man barbershop, it takes on the average one half hour to

service a customer and the customer arrive at an average rate of one

every forty five minutes. If a poisson exponential model is assumed

then find:

i) The average time a customer spends in the shopii) The expected number of customers in the queue at any given time.11.Telephone arrive at a booth following a poisson distribution with an

average time of 5 minutes between one arrival and the next. The time

taken for a telephone call is on an average 3 minutes and it follows an

exponential distribution. What is the probability that the booth is

busy? What is the average waiting time for a call before being

connected?

12.In a bank cheques are cashed by a single teller counter. Customerarrive at the counter in a Poisson fashion at an average rate of 30

customers per hour. The teller takes on an average one minute to cash

a cheque. The service time has been shown to be exponentially

distributed. Find the average number of customers in the waiting line

and find the average number of customers in the bank.