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- Buses arrive at the downtown bus stop and leave for themall stop. Past experience indicates that 20% of the time,the interval between buses is 20 minutes; 40% of the time,the interval is 40 minutes; and 40% of the time, the intervalis 2 hours. If I have just arrived at the downtown bus stop,how long, on the average, should I expect to wait for a bus?Game World, a video game arcade at Tanglewood Mall, has just installed a new virtual reality battle game. It requires exactly 2.7 minutes to play. Customers arrive, on average, every 2.9 minutes (Poisson distributed) to play the game. How long will the line of customers waiting to play the game be, and how long, on average, must a customer wait?5. Eat well is a small drive through fast food restaurant, staffed by an efficient employee John, is located in a super mall area. Customers arrive at the counter at an average of one every 15 minutes, and the customer arrival follows a Poisson distribution. John takes at most 10 minutes to process each food order. d) What percentage of time is John Idle?
- Eat Well is a tiny drive-through quick food restaurant in a shopping malltown, manned by an efficient employee named John. Customers arrive at the counter at a rate of one per 15 minutes on average, with a Poisson delivery for customer entry. Each food order takes John no more than ten minutes to process. a) How many customers are handled on average at any given time? b) The anticipated amount of clients that would be represented. c) Determine the average consumer wait time in the scheme. d) How much of the day is John Idle idle?A bike repair plant is trying to determine how long the average line for a repair process will be. If 13 bikes arrive each hour and must wait 5 minutes in the line, how long will the line be, on average?The check-out area of a grocery store has the average customer interarrival time = 2 minutes, the average processing time of each cashier = 6 minutes, and in total 4 cashiers. The average waiting time for each customer is 8 minutes. What is the average number of customers in the system (including waiting and using the service)? a 3 b 7 c 6 d 4
- In the library, students arrive randomly at the help desk, which is staffed by 4 employees (all of them answer inquiries from students). The time required for inquiry varies from student to student. Arrivals have been found to follow a Poisson process (i.e., exponentially distributed inter-arrival times), and the service times follow an exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 13 students per hour. What is the utilization of the help desk? Note: 1. Provide your answer as a percentage, but do not include the % mark. 2. Keep two decimal places. For example, if your result is 35.126%, enter 35.13.Car owners fill up when their tanks are exactly half full. At the present time, an average of 8.5 cars/hr arrive at a single-pump gas station. It takes an average of 3.68 minutes to service a car. Suppose that a gas shortage occurs and panic buying takes place. All car owners now purchase gas when their tanks are exactly 3/4 full. Since each car is putting less gas into the tank for each visit, the average service time has been reduced to 2.54 minutes. Assume that arrival and departure rates are both exponential. What is the difference in length of queue before and after the shortage scenario, in terms of vehicles? answer an absolute value, and in four decimal places.A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the um follow a Poisson distribution at the rate of three per minute. In serving themselves, customers take about 15 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee um? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used?
- The following data has been collected on the number of customers seen to arriveto a museum in a succession of 5-minute intervals: 5, 1, 3, 7, 5, 5, 6, 7, 5, 7, 4, 8, 1,5, 2, 3, and 5. Estimate the squared coefficient of variation of the arrival process. Ifthis data was known to come from a Poisson process, what would be your estimateof l, the rate of customer arrivals?Determining the Number of ServersIn the service department of the Glenn-Mark Auto Agency, mechanics requiring parts for auto repair or service present their request forms at the parts department counter. The parts clerk fills a request while the mechanic waits. Mechanics arrive in a random (Poisson) fashion at the rate of 40 per hour, and a clerk can fill requests at the rate of 20 per hour (exponential).If the cost for a parts clerk is $30 per hour and the cost for a mechanic is $60 per hour, determine the optimum number of clerks to staff the counter. (Because of the high arrival rate, an infinite source may be assumed.)A cafeteria serving line has a coffee urn from which customers serve themselves. Arrivals at the urn follow a Poisson distribution at the rate of 4.0 per minute. In serving themselves, customers take about 11 seconds, exponentially distributed. a. How many customers would you expect to see on the average at the coffee urn? b. How long would you expect it to take to get a cup of coffee? c. What percentage of time is the urn being used? d. What is the probability that three or more people are in the cafeteria? e. If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how many customers would you expect to see at the coffee urn (waiting and/or pouring coffee)? f.If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 11 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?