In a single queue with random arrivals 60 an hour and random service times average 80...
In a single queue with random arrivals 60 an hour and random service times average 80 per hour. Find: (a) the average number of customers in the waiting line; (b) the average number of customers in the service system; (c) the average waiting time in line; (d) the average time spent in the system
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In a single queue with random arrivals 60 an hour and random
service times average 80...
1. A waiting line problem has an average of 80 arrivals per eight hour day. Suppose...
1. A waiting line problem has an average of 80 arrivals per eight hour day. Suppose there is a single server and the average service time is 8 minutes. The average service rate is a) 8 per minute. b) 8 minutes. c) 10 per day. d) 10 per hour. e) 24 per hour f) none of the above. 2. A waiting line problem has an average of 80 arrivals per hour. Suppose each server can serve one customer every 4...
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures....
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures. Customer Arrival Time Service Time (min) Time Customer Waits in Queue (min) Time Customer spends in System (min) Idle Time of Server (min) 04 0) Average Waiting Time (11) Probability of a customer to be waiting (i.e., number of waiting customers over total number of customers) (II) Probability of idle server (i.e., proportion of idle time over total running time) (iv) Average Service Time...
For the following problems compute (a) utilization, (b) average time a customer waits in the queue,...
For the following problems compute (a) utilization, (b) average time a customer waits in the queue, (c) average number of customers waiting in the queue, (d) average number of customers in service, (e) the average time a customer spends in the system. Problem 1. An average of 10 cars per hour (with variance 4) arrives at a single-server drive-in teller. Assume that the average service time for each customer is 5.5 minutes (with variance 5). Problem 2. Customers arrive to...
3. For a single-server, single-line, single-phase waiting line system, where l represents the mean arrival rate...
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...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all...
Star Car Wash estimates that dirty cars arrive at the rate of 15 per hour all day and at the wash line, the cars can be cleaned at the rate of one every 4 minutes. One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the: (a) average time a car spends in the service system. (b) average number of cars in line. (c) average time a...
Analysis of arrivals to a single pump gas station has shown that the times between arrivals...
Analysis of arrivals to a single pump gas station has shown that the times between arrivals can be depicted by negative exponential distribution with a mean of 10 minutes. Service times were observed to be distributed negative exponentially, as well, with a mean time of 6 minutes. What is the steady-state mean number of customers at the station and the steady-state mean number that are waiting?
Problem 8: 10 points Consider a queuing system M/M/1 with one server. Customer arrivals form a...
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
Please fill in all question marks!!!! Problem 15-25 (Algorithmic) Burger Dome sells hamburgers, cheeseburgers, French fries,...
Please fill in all question marks!!!! Problem 15-25 (Algorithmic) Burger Dome sells hamburgers, cheeseburgers, French fries, soft drinks, and milk shakes, as well as a limited number of specialty items and dessert selections. Although Burger Dome would like to serve each customer immediately, at times more customers arrive than can be handled by the Burger Dome food service staff. Thus, customers wait in line to place and receive their orders. Suppose that Burger Dome analyzed data on customer arrivals and...
SHOW ALL WORK! In a waiting line situation, arrivals occur at a rate of 2 per...
SHOW ALL WORK! In a waiting line situation, arrivals occur at a rate of 2 per minute, and the service times average 24 seconds. Assume the Poisson and exponential distributions. a. What is λ? What is μ? b. Find average number of units in the system. c. Find average time in the waiting line. d. Find probability that there is one person waiting. e. Find probability an arrival will have to wait.
Burger World is considering opening a drive-through window for customer service. Management estimates that customers will...
Burger World is considering opening a drive-through window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The server who will staff the drive-up window can service customers at the rate of one every three minutes. Assuming Poisson arrivals and exponential service, find: 40. Utilization of the teller A) 45% B) 55% C) 65% D) None of the above 41. Average number of customers in the waiting line A) 2.25 B) 5.22 C)...
1. A waiting line problem has an average of 80 arrivals per eight hour day. Suppose there is a single server and the average service time is 8 minutes. The average service rate is a) 8 per minute. b) 8 minutes. c) 10 per day. d) 10 per hour. e) 24 per hour f) none of the above. 2. A waiting line problem has an average of 80 arrivals per hour. Suppose each server can serve one customer every 4...
Problem 1 Given the data below for a single-server single-queue system, find the following performance measures. Customer Arrival Time Service Time (min) Time Customer Waits in Queue (min) Time Customer spends in System (min) Idle Time of Server (min) 04 0) Average Waiting Time (11) Probability of a customer to be waiting (i.e., number of waiting customers over total number of customers) (II) Probability of idle server (i.e., proportion of idle time over total running time) (iv) Average Service Time...
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
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