The Queue of service enterprise is designed for capacity 30 customers per hour and its effective capacity of 28 customers per hour. Calculate the design capacity utilization for this line if the actual output is 18
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- Refer to the following information and output. Number of Servers Arrival Rate Service Rate P(0), probability that there are no customers in the system Lq, average length of the queue W, average time in the system L, average number of customers in the system Wq, average time in the queue Utilization factor of the system What is the average number of customers in the queue? O 2.33 O .23 O .70 O 1.63 1.0 7.00 10.00 30% 1.63 0.33 2.33 0.23 70%During the early morning hours, customers arrive at a branch post office at an average rate of 45 per hour (Poisson), while clerks can handle transactions in an average time (exponential) of 4 minutes each. Find: (a) The average number of customers waiting for service if 5 clerks are used. (b) The minimum number of clerks needed to keep the average waiting time in the system to under 5 minutes. (c) If clerk cost is $40 per hour and customer waiting time represents a “cost” of $30 per hour, how many clerks can be justified on a cost basis? Please show work.Single server system has customer arrival rate of 60 customers per minute and a service rate of 75 customers per minute. Customer arrival pattern is finite and they won't leave till they are served. The Arrival and Service patterns, both are exponential distribution. Based on the above information calculate a. Server utilization% b. Average numbers of customers in line C. Average time per customer in Line d. Average numbers of customers in system e. Average time per customer in System
- no handwritten solution Question The management of a busy petrol station is concerned that customers are being lost because of long waiting times sometimes required at their petrol pump. Over a two weeks period a careful study has been taken of the arrival of cars and the length of time taken to serve customers at the petrol station. The tables below show the arrival rates and the service time distribution: Inter arrival time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <2 1 60 60 00 - 59 2 - <4 3 25 85 60 - 84 4 - <6 5 10 95 85 - 94 6 - <8 7 5 100 95 - 99 Service time (minutes) Inter arrival time Midpoint Percentage of customers Cumulative frequency Random number 0 - <4 2 20 20 00 – 19 4 - <6 5 30 50 20 – 49 6 - <8 7 20 70 50 - 69 8 - <10 9 15 85 70 – 84…1 What can you say about a queue that is E_k/ M/3/PR/200/∞Exercise 1 A supermarket is trying to decide how many cash registers to keep open. Suppose an average of 18 customers arrive each hour, and the average checkout time for a customers is 4 minutes. Interarrival times and service times are exponential, and the system may be modeled as an M/M/S/GD//0 queuing system. It costs $20 per hour to operate a cash register, and a cost of 25 cents is assessed for each minute the customer spends in the cash register area. How many registers should the store open?
- Twelve customers arrive every hour (Poisson distributed) at Andy Johnson's food truck when it parks outside the Orlando Courthouse from 11-2 p.m. on weekdays. It takes Andy a mean time of 4 minutes to fill each order (following a negative exponential distribution). The Waiting La λ Line Table is provided below and also we know that W₁ = Table: Average Number of Customer in Waiting Line P .10 .15 .20 .25 .30 .35 .40 .45 .50 .55 .30 .55 60 .65 .70 .75 .80 .85 .90 .95 1.0 1.2 1.4 1.6 1.8 2.0 Poisson Arrivals, Exponential Service Times Number of Service Channels, M 2 3 4 1 .0111 .0264 .0500 .0833 .1285 .1884 .2666 .3681 .5000 .6722 3000 .6722 .9000 1.2071 1.6333 2.2500 3.2000 4.8166 8.1000 18.0500 .0008 .0020 .0039 .0069 .0110 .0166 .0239 .0333 .0449 0333 .0449 .0593 .0767 .0976 .1227 .1523 .1873 2285 .2767 .3333 .6748 1.3449 2.8444 7.6734 .0019 .0030 .0043 0030 .0043 .0061 .0084 .0112 .0147 .0189 0239 .0300 .0371 .0454 .0904 .1778 .3128 .5320 .8888 .0031 .0041 .0053 .0067 .0158 .0324…Pls solve this question correctly in 10 min i will give u thumsup 1. Which of the following statements are true about for the M/D/3 queuing system? Arrival rate is Poison distributed. I- Service time is Exponentially distributed. Ill- Inter-arrival is Exponentially distributed. 1v- There are 3 servers, 2. 5. What is the optimal solution for max Z=×+2y, st., x+ y less than or equal tpo 40, 2x + 4y less thsn or equal to 60, x, y greater than or equal to 0? A) Unique optimal solution, Z° = 30 B) Alternate optimal solutions, z = 30 C) Unique optimal solution, Z*= 40 D) infeasible solutionDemand at the Krispy Kreme drive-through has jumped up with the new restrictions on inside dining. Customers are arriving according to a Poisson process, at an average of 5 minutes between customers. It takes 4 minutes to serve a car. There is only one drive through channel. Answer the following questions. a. What model best matches this situation? Model used: (time units) |(time units) arrival rate: per population: ("infinite" or a number) service rate: per servers: b. What is the average number cars in the drive-through, including the one being served? c. How long does it take, on average, for a customer to get the product? (time units) d. What is the probability that a customer will show up and not find anyone in the drive-through? e. What is the probability that there will be 3 or more cars in the drive through when a customer arrives? (don't count the customer who is arriving)
- C) A carpentry shop receives orders according to the Poisson distribution with a mean of 6/day. On average, a carpenter makes 2.2 orders per day, under the Poisson distribution. Currently there are 3 carpenters working (each carpenter makes an order from start to finish). The daily salary of the carpenter is $260. The daily waiting cost in the system for an order is $450. There is a proposal to expand the service by hiring 2 additional carpenters 1 What is the average waiting time per order in the carpentry shop currently? 2. What is the average number of orders in the current carpentry shop? 3. Break down the total daily cost for current carpentry using formula CTdaily = daily salary* (# workers) + waiting cost in the system* (\lambda) 4. What is the average waiting time per order at the proposed carpentry shop? 5. What is the average order quantity in extended carpentry? 6. Break down the total daily cost for extended carpentry using formula CTdaily = daily salary* (# workers) +…A and C mall is a busy centre for residents in East Legon and its surrounding community. Assume that 2 customers arrive every 12 minutes and 3 customers are served every 15 minutes and that currently, there is only one cashier. a) Determine the average waiting time in minutes before service begins. (b) Calculate the financial gain to A and C mall under option 1 and advice management on the option. (c) Calculate the financial gain to A and C mall under option 2, assuming the initial capital outlay is sunk cost and advice management on this option.At a one man barber shop, customers arrive according to poison distribution with a mean arrival rate of 5 per hour and hair cutting time was exponentially distributed with an average hair cutting time was exponentially distributed with an average hair cut taking 19 minutes. It is assumed that because of excellent reputation, customers were always willing to wait. Calculate the following a. Average number of customers in the shop and average numbers waiting for a haircut b .Percentage of time arrival can walk in right without having to wait c. The percentage of customers who have to wait before getting into the barber’s chair