EXAMPLE 6.55 Find the length of the queueing system in an (M/M/1):(4/FIFO) model, if=3 per hour and μ = 3 per hour.

Given data is Mean arrival rate (lambda) = 3 per hour Mean service rate (mu) = 3 per hour

Answered: EXAMPLE 6.55 Find the length of the…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 35P

See similar textbooks

Similar questions

An emergency room (ER) at a Prisma Health Hospital has 10 total beds it can hold patients, i.e., the capacity of the queueing system of this ER is 10. Patients arrive to the ER at a rate of 5 per hour. Therefore, we have that λn = 6 for n = 0, 1, . . . , 9 and λ10 = 0 for this queueing system. A patient is seen by an ER doctor as the ‘service’ of this queueing system. The amount of time required for an ER doctor to treat a patient is exponentially distributed with a mean of .4 hours. We seek the minimum number of ER doctors so that the expected time of a patient waiting to be seen (so the Wq) is less than or equal to 15 minutes (.25 hours). You should begin by analyzing s = 1 and show any calculations that were used to determine Wq for each number of servers that you considered until you meet the target metric.
The QRS Trucking Services, has one warehouse servicing its 4 clients within the area. The warehouse hasonly one loading harbor with 3 service crews. The manager has observed that there are certain timeswherein their delivery vans are waiting in the harbor to be loaded. Also, there are instances whereintheir three service crews are idle. Thinking about the situation of their business , the manager noticedthat it follows the Single-Channel Queueing Model.Analyzing the record book, he noticed that the customers’ arrival rate is 3 delivery vans per hour, and onthe average service rate is 5 delivery vans per hour. What advise can you give to the manager about theimplication of adding another service crew, or even two or more crews to increase and improve theservice rate of his loading harbor?If the manager adds one or more service crew(s), the loading harbor can still be considered as a single-channel system, because only one delivery truck ( the customer) can be served at any one time.…
A manufacturing cell has 4 operators (working independently in parallel) and a shared buffer space that can fit at most 6 incoming jobs. During a production period, jobs arrive to the cell with rate of 10 jobs per hour (Poisson arrival, i.e., exponential inter-arrival time). The average processing time of a job is 30 minutes (exponentially distributed service time). Answer the following questions using the analytical formulas learned in class. (a) Which queueing model should be used to model this problem? (b) What is the long-term average waiting time of a job in the buffer? (c) What is the probability that an arriving job cannot be admitted into the cell due to full occupancy? (d) If the desired the rejection probability is no more than 10% in this case, what would you suggest? Use calculations to justify your answer.
We are in a M/M/1/3 queueing system in which we wish to determine the cost of operating the system. Each customer in the queue costs us $100 per hour and each customer being served costs us $50 an hour. Customers arrive at a rate of 4 per hour and the server can serve customers at a rate of 5 per hour. The following table in the picture provides Pn values, W, and Wq:
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)?
MacBurger’s is attempting to determine how manyservers (or lines) should be available during the breakfastshift. During each hour, an average of 100 customers arriveat the restaurant. Each line or server can handle an averageof 50 customers per hour. A server costs $5 per hour, andthe cost of a customer waiting in line for 1 hour is $20.Assuming that an M/M/s/GD/∞/∞ model is applicable,determine the number of lines that minimizes the sum ofdelay and service costs.
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
. For the MyMy1 queueing model, why do the following results hold? (Hint: Remember that 1ym is the meanservice time. Then think how long a typical arrival must wait in the system or in the queue.) a. W 5 (L 1 1)ym b. WQ 5 Lym
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 D/D/1 queueing systems, the arrival rate and service rate are equal to 6 customers/hour and 12 customers/hour, respectively. What is the average queue length?
Using an M/M/1 queuing system as an example demonstrate how the event list in a simulation model would evolve over 5 discrete steps if the first part will arrive at time zero, the time between the next four arrivals are 3, 5, 6, and 4 minutes and that the machining times for the first five parts are 6, 4, 3, 5, and 4 minutes. The performance metrics of interest are the average queue length and the number of items processed.
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?

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS

EXAMPLE 6.55 Find the length of the queueing system in an (M/M/1): (4/FIFO) model, if λ = 3 per hour and = 3 per hour.