A community is served by two identical companies providing taxi bookingservices. Each company owns two cabs, and both book rides at an average rateof eight per hour. The average duration of a ride is 12 minutes meaning each cabmakes 5 rides per hour. Calls for booking arrive according to a Poissondistribution, and the rides made is exponential. The two companies have beenbought by an investor and will be merged into one. Analyze the new investor'sproposal.The following is the queueing model of each company before and after they merge:Company CA = ? rides booked/hru = ? rides made/hrc = ? cabsCompany ACompany BA = 8 rides booked/hrµ = 5 rides made/hr2 cabsA = 8 rides booked/hrµ = 5 rides made/hr= 2 cabs%3D%3D%3DC =с 3%3D

Service rate is the rate at which the customers are being served in the organizational system by the…

Answered: The following is the queueing model of…

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/MA queueing system, the arrival rate is 3 customers per hour and the service rate is 5 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 your answers to 3 decimal places.) a. What is the utilization? Utilization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected waiting time (in hours) for the system (W)? Waiting time(in hours)
Customers arrive at Cochinito Bank according to a Poisson distribution, with a mean of 45 customers per hour. Transactions per customer take around 5 minutes and are distributed exponentially. The bank wants to use a single line and several boxes, similar to those used in airports and some dependencies. The manager is aware that customers may go to other banks if they perceive their waiting in line to be “excessive”. For this reason, the manager wants to limit the average wait time in the queue to no more than 30 seconds. How many boxes should the bank put into service?
In queueing theory, λ represents the mean arrival rate; for example, the number of peoplearriving at the service counter per hour. What does 1/λ represent?o Service rateo Interarrival timeo Service time None
What are several psychological alternatives to queue management, and why does a boss like to employ them?
An M/M/1 queueing system has that customers arrive to it at a rate of 5 per hour, i.e., its interarrival times between two consecutive arrivals follows an exponential distribution with parameter 5 per hour. This question will ask you to evaluate two options for designing the server in the system. Both options for the single server provide the same service for the customers in the queueing system but they cost different amounts to implement. In addition, the total costs of the queuing system are the implementation costs plus the customer costs. Currently, the customer costs are $100 per hour per customer in the queueing system. In comparing these options, it costs us $100 per hour per customer in the queueing system. (a) The first option for the server is one that has a service time that follows an exponential distribution with mean 10 minutes. Determine L, W, Lq, and Wq for this system. (b) The second option for the server is one that has a service time that follows an…
In a coffee shop, there are 4 baristas serving customers standing in a single queue. Customers arrive every 6 minutes on average, and one barista can serve an order in an average of 20 minutes. Customers’ arrivals tend to follow a Poisson distribution and service times tend to be negative exponential. The hourly salary of a barista is $10 per hour, but owner loses about $10 per hour of customer waiting for a barista to take an order. The average time (in hours) that customers must wait before a barista takes their orders. (please round your answer to THREE decimal places) ______ The hourly cost associated with patient waiting in the coffee shop. (please round your answer to ONE decimal place) ______ The total hourly cost in the coffee shop. (please round your answer to ONE decimal place)
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Customers arrive at a bank counter at an average rate of 3customers per hour.a) Suggest a suitable distribution to model the number ofcustomers arriving at the counter, X, per minute.b) State clearly any assumptions you have made by suggestingthis model.c) Using your model,I. Find the probability that no customer arrive in a givenminute.II. Find the probability that at most 4 customers arrive in agiven minute.III. In any given 4 minutes period, find ? such that?(? > ?) = 0.0487.IV. Check the answer of part I and part ii using RStudio.

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The following is the queueing model of each company before and after they merge: Company A A = 8 rides booked/hr µ = 5 rides made/hr c = 2 cabs Company B Company C A = 8 rides booked/hr + µ = 5 rides made/hr A = ? rides booked/hr u = ? rides made/hr c = ? cabs c = 2 cabs %3D