Chapter 13, Problem 18QP

Queuing theory refers to the fundamental concepts of a phenomenon that we constantly experience, the concept of queues. These queues are in production processes, such as in banks, service providers, etc.Based on the concepts of Production Modeling and Simulation, do the following: a) Assuming that cars arrive at a toll, on average, every 0.5 minutes, and the toll has only one payment window, and both the time between arrivals and the time between calls follow an exponential distribution. The toll attendant takes an average of 0.3 minutes to collect. Calculate the system performance measures, ie the car arrival rate and the toll service rate.

Ray is planning to open a small car-wash operation for washing just one car at a time. He must decide how much additional space to provide for waiting cars. Ray estimates that customers would arrive according to a Poisson input process with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 2 minutes. Suppose that Ray makes an average $4 per served customers. Moreover, each car space rented for waiting costs $800 per month. Ray is planning to run the car-was for 200 hours every month. 2. How much space should Ray provide for the waiting cars in order to maximize his expected net profit? (By net profit, we mean profit from car-wash operations minus the rental cost)

On a toll road, there are 5 lanes for drivers to pay their toll. Customer arrival times are random, with a general independent distribution. Service times are constant, with a degenerate distribution. What is the proper description for this queueing system?

Neve Commercial Bank is the only bank in the town of​ York, Pennsylvania. On a typical​ Friday, an average of 12 customers per hour arrive at the bank to transact business. There is one teller at the​ bank, and the average time required to transact business is 4 minutes. It is assumed that service times may be described by the negative exponential distribution. A single line would be​ used, and the customer at the front of the line would go to the first available bank teller.  If a single teller is used, find: 1.      The average time in line 2.      The average number in the line 3.      The average time in the system 4.      The average number in the system 5.      The probability that the bank is empty 6.      CEO Benjamin Neve is considering a second teller (who would work at the same rate as the first) to reduce waiting time for customers.  A single line would be used, and the customer at the front of the line would go to the first available bank teller.  He assumes that this will…

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)?

A horologist (watchmaker) is typically able to service a mechanical watch in about 120 minutes (exponential distribution). Assuming an 8 hour work-day, the watchmaker averages 3 customers arriving at his shop every day following a poisson distribution. The watchmaker just purchased a new machine that will polish the dial and crystal reducing his service time by 20 minutes per watch. How much will the line for a watch waiting to be serviced be reduced by the watchmaker using this new machine, assuming no increase in customer demand? O 2.25 watches waiting for service O The number waiting to be serviced will be reduced by about 1.2 watches O The number waiting to be serviced will be reduced by about 0.4 watches The number waiting to be serviced will be reduced by about 1.45 watches

On a toll road, there are 2 lanes for drivers to pay their toll. Customer arrival times are constant, with a degenerate distribution. Service times are random, with an exponential distribution. What is the proper description for this queueing system?

Queuing Models

Please solve this in excel. Ray is planning to open a small car-wash operation for washing just one car at a time. He must decide how much additional space to provide for waiting cars. Ray estimates that customers would arrive according to a Poisson input process with a mean rate of 1 every 4 minutes, unless the waiting area is full, in which case the arriving customers would take their cars elsewhere. The time that can be attributed to washing one car has an exponential distribution with a mean of 2 minutes. Suppose that Ray makes an average $4 per served customers. Moreover, each car space rented for waiting costs $800 per month. Ray is planning to run the car-was for 200 hours every month. 2. How much space should Ray provide for the waiting cars in order to maximize his expected net profit? (By net profit, we mean profit from car-wash operations minus the rental cost)