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? Probet descrplion
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![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?
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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.1Consider 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 2Workers come to tool store room to enquire about special tools (required by them) for accomplishing a particular project assigned to them. The average time between two arrivals is 60 seconds and the arivals are assumed to be in Poisson distribution. The average service time (of the tool room attendant) is 40 seconds. Determine: (1) average queue length, (i) average length of non-empty queues, (ii) average number of workers in system including the worker being attended (iv) mean waiting time of an arrival, (v) average waiting time of an arrival who waits.
- Queuing Models1. 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.For each of the following queuing systems, indicate whether it is a single or multiple-server model, the queue discipline, and whether it’s calling population is infinite or finite. Hair salon Bank Laundromat Doctor’s office Advisor’s office Airport runway Service station Copy centre Team trainer Mainframe computer
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