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 vstem
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- 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…5. A small town with one hospital has two ambulances to supply ambulance service. Requests forambulances during non-holiday weekends average .45 per hour and tend to be Poisson-distributed.Travel and assistance time averages two hours per call and follows an exponential distribution.Find:a. System utilizationb. The average number of customers waitingc. The average time customers wait for an ambulanced. The probability that both ambulances will be busy when a call comes inPlease do not give solution in image formate thanku. λ= 4 customers per hour; μ = 5 customers per hour; M= 1 An average of 20 customers arrive at a service center each hour. There are two servers on duty, and each can process 12 customers per hour. a) What is the system utilization? b) What is the average waiting time for customers who actually have to wait? c) What is the average time customers wait in line for service?
- Fantasy Park has two service desks, one at each entrance of the park. Customers arrive at each service desk at an average of one every six minutes. The service rate at each service desk is four minutes per customer.2. There is a bank office with a single operator. The service time of each customer is exponentially distributed with the mean of 10 minutes. When a customer enters into the system, he notices that there are 3 customers in the bank. ii. What is the expected waiting time of the customer in the system?Customers in LineWestern National Bank is considering opening a drive-thru window for customer service. Management estimates that customers will arrive at the rate of 15 per hour. The teller who will staff the window can service customers at the rate of one every three minutes.Part 1 Assuming Poisson arrivals and exponential service, find1. Utilization of the teller.2. The average number in the waiting line.3. The average number in the system.4. The average waiting time in line.5. The average waiting time in the system, including service.
- Problem 15-31 (Algorithmic) Mid-West Publishing Company publishes college textbooks. The company operates an 800 telephone number whereby potential adopters can ask questions about forthcoming texts, request examination copies of texts, and place orders. Currently, two extension lines are used, with two representatives handling the telephone inquiries. Calls occurring when both extension lines are being used receive a busy signal; no waiting is allowed. Each representative can accommodate an average of 10 calls per hour. The arrival rate is 16 calls per hour.1. There is a Poisson queuing system with the average customer arrival rate of 3 customers per half of hour. This system starts working at 9:0 am. For this system, calculates: iv. The least number of servers needed in the system to ensure that each server would be busy in 70 percent of time at most.1.) M/M/2 Mean Arrival Rate: 20 customers/hour Mean Service Rate: 12 customers/hour Number of Servers: 2 On average, how many customers are in the line?
- n the ticket counter , customer arrivers in the queue according to Poisson process with 15 / hour mean rate . The total time taken to serve a customer has an exponential distribution with 150 seconds of mean . What is the average waiting time of a customer ( both in Queue and System ) ? Queue - 125Sec, System - 225Se Queue 250 Sec , System 325 Sec Queue 250 Sec , System 400 Sec Queue 225 Sec , System 125 SecPls 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 solution1. A single cashier handles customers that arrive at a bakery. About 34.8 customers come into the bakery per hour. It takes 73 seconds to serve each customer (standard time). 2. What is the utilization of the cashier?What is the probability there are no customers in line or at the cashier? 3. What is the probability there are less than 2 customers waiting? Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.