In an M/MA queueing system, the arrival rate is 8 customers per hour and the service rate is 11 customers per hour. If the serviceprocess is automated (resulting in no variation in service times but the same service rate), what will be the resulting performancemeasurements? (Round your answers to 3 decimal places.)a. What is the utilization?Utilizationb. What is the expected number of customers in the system (L)?Number of customersc. What is the expected waiting time (in hours) for the system (W)?Waiting time(in hours)

Given data Arrival rate of clients (λ) = 8 customer per hour Service rate of clients (μ) = 11…

Answered: In an M/MA queueing system, the arrival…

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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In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?
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The manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?
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The bank manager is concerned with its waiting line system in his bank. Currently bank uses a single-server, single-line, single-phase system. Based on historical evidence, the average number of customers arriving per hour is C1 and is described by a Poisson distribution. The service rate is <=15 >11 customers per hour with the service times following an exponential distribution. The customers are come from an infinite population. The manager of the bank would like calculate the operational characteristics of the waiting line system that:(a) What is the average system utilization?(b) What is the average number of customers in the system? (c) What is the average number of customers waiting in line?(d) What is the average time a customer spends in the system?(e) What is the average time a customer spends waiting in line?
In an M/M/1 queueing system, the arrival rate is 7 customers per hour and the service rate is 12 customers per hour. Note: Round your answers to 3 decimal places. What is the probability that the server will be idle? What is the probability of having exactly 4 customers in the system? What is the probability of having 4 or fewer customers in the system?
In a queueing system, customers arrive once every 3 hours (standard deviation = 4) and services take 2 hours (standard devlation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average time a customer will spend in the system (in hours)? hours
In a queueing system, customers arrive once every 3 hours (standard devlation = 4) and services take 2 hours (standard deviation = 6.2). (Do not round intermediate calculations. Round your answer to three decimal places.) What is the average number of customers in the system? customers
In an M/M/1 queueing system, the arrival rate is 5 customers per hour and the service rate is 7 customers per hour. If the service process is automated (resulting in no variation in service times but the same service rate), what will be the resulting performance measurements? (Round all answers to three decimals.) What is the utilization? What is the expected number of customers in the system (L)? What is the expected waiting time (in hours) for the system (W)? What is the expected number of customers in the queue (Lq)? What is the expected waiting time (in hours) in the queue (Wq)?
At a border inspection station, vehicles arrive at the rate of 8 per hour in a Poisson distribution. For simplicity in this problem, assume that there is only one lane and one inspector, who can inspect vehicles at the rate of 11 per hour in an exponentially distributed fashion. a. What is the average length of the waiting line? b. What is the average time that a vehicle must wait to get through the system? c. What is the utilization of the inspector? d. What is the probability that when you arrive there will be three or more vehicles ahead of you?
Pasquist Water Company (PWC) operates a 24-hour facil-ity designed to efficiently fill water-hauling tanker trucks.Trucks arrive randomly to the facility and wait in line to ac-cess a wellhead pump. Since trucks vary in size and the filling operation is manually performed by the truck driver, the timeto fill a truck is also random.a. If the manager of PWC uses the multiple-server modelto calculate the operating characteristics of the facility’swaiting line, list three assumptions she must make regard-ing the behavior of waiting trucks and the truck arrivalprocess.b. Suppose an average of 336 trucks arrive each day, thereare four wellhead pumps, and each pump can serve anaverage of four trucks per hour.▪ What is the probability that exactly 10 trucks will arrivebetween 1:00 p.m. and 2:00 p.m. on any given day?▪ How likely is it that once a truck is in position at a well-head, the filling time will be less than 15 minutes?c. Contrast and comment on the performance differencesbetween:▪…
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