Average number of customers in the line = LAMBDA^2 / MU(MU - LAMBDA)
LAMBDA = 10
MU = 20
CUSTOMERS IN LINE = 10^2 / (20 * (20 - 10)) = 0.5
QUESTION 5 0.5 In a single-server queuing system, 10 customers arrive per hour, and 20 customers...
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
For an infinite-source, single server system with an arrival rate of 15 customers per hour (Poisson) and service time of 2 minutes per customer (exponential), the average number waiting in line to be served is: a. 0.1 b. 0.133 c. 0.50 d.0.250
Problem 3: Assume that a single-server queueing system has a Poisson interarrival process with a rate of 10 customers per hour. Also, assume that the service time is exponential with at a rate of 12 customers per hour. Answer the following questions to 3 significant digits: a) What is the expected utilization of the server? b) What is the log-run time average of number of customers in the system? c) Using Little's law, use the answer from part (b) to calculate the average waiting...
3. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service rate, what is the formula for the average utilization of the system? a) l / m b) l / (m-l) c) l2 / m(m-l) d) 1 / (m-l) e) l / m(m-l) 4. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate of customers and m represents the mean service...
A single-server queuing system with an infinite calling population and a first-come, first-served queue discipline has the following arrival and service rates: ? = 36 customers per hour µ = 42 customers per hour Determine P0, P1, P2, L, Lq, W, Wq, and U. Note: Do hand calculations to answer this question. Show all details of your answer.
customers arrive at an average of 30 per hour. A single server in the store serves customers, taking 1.5 minutes on average to serve each customer. Inter-arrival times and service times follow the exponential distribution. What is the expected fraction of time that the server will be busy? On average, how many people will there be in the store? On average, how long will someone be in the store? What is the probability that there will be more than 2...
(Queuing Model) A single public health worker is inoculating children against measles at a local clinic. An average of 8 children per hour is expected to arrive according to a Markovian process. He serves the children at a rate of 10 per hour. Assume that the service process is also approximately a Markovian process. For the ‘inoculation system’, find: the utilization of the health worker. the average time spent by a child in the system. the average number of children...
Customers arrive at a service facility with one server according to a Poisson process with a rate of 5 per hour. The service time are i.i.d. exponential r.v.´s, and on the average, the server can serve 7 customers per hour. Suppose that the system is in the stationary regime. (a) What is the probability that at a particular time moment, there will be no queue? (b) What is the probability that a particular time moment, there will be more than...
QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour per server and arrival ratei - 45 customers per hour, on the verge, how long in minutes) does a customer wait in line round off to 2 decimal digits) QUESTION 10 A small branch bank has two teller, one for deposits and one fow withdrawals Cistomers arrivent arch teller's window with an average rate of 20 customers per hour. The total customer anivartes per...
Problem 8: 10 points Consider a queuing system M/M/1 with one server. Customer arrivals form a Poisson process with the intensity A 15 per hour. Service times are exponentially distributed with the expectation3 minutes Assume that the number of customers at t-0, has the stationary distribution. 1. Find the average queue length, (L) 2. What is the expected waiting time, (W), for a customer? 3. Determine the expected number of customers that have completed their services within the 8-hour shift