Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephonecalls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hearsa waiting song until the first dispatchers becomes available. The telephone system will assign availabledispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poissondistribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spendswith a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes witheach caller.11. What percentage of time all dispatchers are idle?25.58%15.58%45.75%8.65%

Idle time percentage is the period when the representatives are not working or occupied with some…

Answered: Town Taxi uses three dispatchers to…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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What is the answer in this number 2?
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 2.0 per minute. In serving themselves, customers take about 25 seconds, exponentially distributed. (a) How long would you expect it to take to get a cup of coffee, including waiting time? (b) If the cafeteria installs an automatic vendor that dispenses a cup of coffee at a constant time of 25 seconds, how long would you expect it to take (in minutes) to get a cup of coffee, including waiting time?
(Please do not give solution in image format thanku) A single Automated Teller Machine (ATM) is located on the ground floor of a popular shopping mall. Service time at this machine is exponentially distributed. On average, the ATM machine can serve a customer in 3 minutes. Customer arrivals at the machine are Poisson distributed, with an average of 15 customers an hour. Relevant formulas to analyze this M/M/1 model are available in your textbook. What percent of the time is this machine idle? 25% 0% 75% 50% 100%
Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean oftwo hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day(assume Poisson). Determine the following: ( l) The average number of customers awaiting repairs (2) System utilization (3) The amount of time during an eight-hour day that the repairman is not out on a call (4) The probability of two or more customers in the system
Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places. What is the probability that the truck dock will be idle? What is the average number of trucks in the queue? truck(s) What is the average number of trucks in the system? truck(s) What is the average time a truck spends in the queue waiting for service? hour(s) What is the average time a truck spends in the system? hour(s) What is the probability that an arriving truck will have to wait? What is the probability that more than two trucks are waiting for service?
In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. What is the expected number of customers in the system (L)? (Round your answer to 3 decimal places.) What is the expected waiting time in the system (W)? (Express the waiting time in hours, round your answer to 3 decimal places.) What is the expected number of customers in the queue(Lq)? (Round your answer to 3 decimal places.) What is the expected waiting time in the queue(Wq)? (Express the waiting time in hours, round your answer to 3 decimal places.)
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 2
please answer in 30 mins.
Town Taxi uses three dispatchers to handle requests for service and to dispatch the cabs. The telephone calls that are made to Town Taxi use a common number. When all dispatchers are busy, the caller hears a waiting song until the first dispatchers becomes available. The telephone system will assign available dispatcher to the waiting callers according to FCFS. Assume that the arrival of calls follows a Poisson distribution, with an average of 35 calls per hour. Also assume that the time that each dispatcher spends with a customer follows Exponential distribution and each dispatcher takes an average of 3 minutes with each caller. 15.What is the average time in minutes that a customer spends in the system? 3.8 mins 7 mins 4.8 mins 8.9 mins
In a queueing system, customers arrive once every 6 minutes (standard deviation = 7) and services take 4 minutes (standard deviation = 4,6). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customers

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