On a toll road, there are 3 lanes for drivers to pay their toll. Customer arrival times are random, with an exponential distribution. Service times are random, with a general distribution. What is the proper description for this queueing system? Proper description
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- On a toll road, there are 5 lanes for drivers to pay their toll. Customer arrival times are random, with a general independent distribution. Service times are constant, with a degenerate distribution. What is the proper description for this queueing system?On a toll road, there are 2 lanes for drivers to pay their toll. Customer arrival times are constant, with a degenerate distribution. Service times are random, with an exponential distribution. What is the proper description for this queueing system?What is the answer in this number 2?
- A self-service store employs one cashier at its counter. Nine customers 'arrive on an average every 5 minutes while the cashier can serve 10 customers in 5 minutes. Assuming Poisson distribution for arrival rate and exponential distribution for service time, find 1. Average number of customers in the system. 2. Average number of customers in the queue or average queue length. 3. Average time a customer spends in the system. 4. Average time a customer waits before being served. A.1In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. (Round your answers to 3 decimal places) a. What is the probability that the server will be idle? b. What is the probability of having exactly 4 customers in the system? c. What is the probability of having 4 or fewer customers in the system?How does an event improve the smooth queue management?
- 1. Customers arrive at a single-server queueing system according to a Poisson process at a mean rate of 30 per hour. If the server works continuously, the number of customers that can be served in an hour has a Poisson distribution with a mean of 50. Determine the proportion of time during which no one is waiting to be served.Consider a Poisson queue with random arrivals at the rate of 12 customers per hour and the following steady- state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and p, = 0 for n = 3,4,5, ... . What is the mean (or effective) arrival rate in customers per hour for this queuing system? Consider drawing a rate diagram to assist in your solution. O 10 12 O none of the other choices O 2Queuing Models
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