Arrival rate = λ = 45 per hour
Service rate = µ = 40 per hour
Traffic intensity = ρ = (λ/ µ) = (45/40) = 1.125
N = 2
Probability P0
P0 = (-0.125/(1-1.4238) = 0.0295
Effective Arrival rate = λeff = λ(1-PN) = λ(1-P0ρN)
λeff = 45 x [1 – (0.0295 x 1.125 ^2)] = 43.3198
please upvote for my answer. Thank you so much
QUESTIONS For MM: GD queuing system with 2 servers of service rate =40 customers per hour...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
Consider the M/M/1/GD/∞/∞ queuing system where λ and μ are the arrival and server rate, respectively. Suppose customers arrive according to a rate given by λ = 12 customers per hour and that service time is exponential with a mean equal to 3 minutes. Suppose the arrival rate is increased by 20%. Determine the change in the average number of customers in the system and the average time a customer spends in the system.
A queuing system with a Poisson arrival rate and exponential service time has a single queue, two servers, an average arrival rate of 60 customers per hour, and an average service time of 1.5 minutes per customer. Answer the following questions. Show ALL formulas and calculations used in your response. The manager is thinking of implementing additional queues to avoid an overloaded system. What is the minimum number of additional queues required? Explain. How many additional servers are required to...
Consider a simple queuing system in which customers arrive randomly such that the time between successive arrivals is exponentially distributed with a rate parameter l = 2.8 per minute. The service time, that is the time it takes to serve each customer is also Exponentially distributed with a rate parameter m = 3 per minute. Create a Matlab simulation to model the above queuing system by randomly sampling time between arrivals and service times from the Exponential Distribution. If a...
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...
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
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
Assume customers arrive at the average rate of 12 people per hour. There is one employee who can server one customer every 3 minutes on average. Assume that there is a variation in the demand and in the supply.Arrival time has a standard deviation of 1 min , and a standard deviation of 2 minutes for the service What is the average no. of customers in system (Ls) ?
A service facility has customers arriving at the rate of 8 customers per hour. The average time customers spend in the facility is 19 minutes. How many customers are in the facility on average?
Customers arrive at Rich Dunn's Styling Shop at a rate of 2 per hour, distributed in a Poisson fashion. Service times follow a negative exponential distribution, and Rich can perform an average of 5 haircuts per hour. customers (round your response to two decimal places). a) The average number of customers waiting for haircuts = customers (round your response to two decimal places). b) The average number of customers in the shop = c) The average time a customer waits...