1. There is a Poisson queuing system with the average customer arrival rate of 3 customersper half of hour. This system starts working at 9:0 am. For this system, calculates:iv. The least number of servers needed in the system to ensure that each server would bebusy in 70 percent of time at most.

Queueing systems are basic mathematical models used to explain traffic bottlenecks. In general, a…

Answered: There is a Poisson queuing system with…

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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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. 12. What percentage of time only one dispatcher is busy? ° 56.27% 27.27% 45.35% 15.89%
Explain the concept of queue and queue theory or waiting line theory and its importance in business A bank has only one counter for its customers. Suppose that the customers to the bank arrive at random with exponential inter arrival time and their mean inter arrival time is 10 minutes. Suppose the counter takes on an average 15 minutes to serve the customer and this also follow an exponential distribution. What percentage of time the bank counter is busy? On the average, how many customers are in the system? On the average, how many customers are in the queue waiting for the service? How long a customer will take to be out of the service system after being served? How long a customer to wait before being served? What is the probability that there are at most three customers in the system?
Wesley is having a busy afternoon working at the Cool ice cream shop. He is the only employee working because his co-worker for this shift has called in sick. It is a hot summer day and a customer arrives every five minutes on average. Wesley takes an average of four minutes to serve a customer. Assume M/M/1 and FIFO queuing system and no limits on queue size. Select the best choice. a. Since his average service capacity is greater than the average customer demand, Wesley is never busy at the Cool ice cream place. b. Wesley is busy about 85% of the time at the Cool ice cream place. c. Wesley is busy about 25% of the time at the Cool ice cream place. d. Wesley is idle (i.e., not busy) about 20% of the time at the Cool ice cream place.
The world is in a pandemic situation with the outbreak of coronavirus (COVID -19). Due to this, there is a need for people to use face masks and hand sanitizers in order to maintain hygiene and to avoid the spread of this disease. Many companies that manufacture and pharmacies that sell face masks and hand sanitizers across the world are using this as an opportunity to increase the price of these products. They are also creating temporary shortage to create a panic among the people. Questions: a. If you own a company that manufactures face masks and hand sanitizers, explain five ethical principles your company can follow to help your country and society. (1.5 Marks) b. With the increasing number of COVID-19 cases globally every day, being a responsible citizen of this country, prepare five guidelines that all your employees must follow that will help Oman protect itself from such pandemic situations in the future. (2 Marks) c. Identify the unethical practices that such companies are…
Answer the following questions. Answers are listed at the end of this section.1. The queuing models assume that customers are served in what order?2. Consider two identical queuing systems except for the service time distribution. In the first system, the service time is random and Poisson distributed. The service time is constant in the second system. How would the waiting time differ in the two systems?3. What is the average utilization of the servers in a system that has three servers? On average, 15 customers arrive every 15 minutes. It takes a server exactly three minutes to wait on each customer.4. What is the expected waiting time for the system described in question 3?5. Firms that desire high service levels where customers have short wait times should target server utilization levels at no more than this percentage.
Below are the data of the gasoline station. Number of gas pumps = 1 Policy of the gasoline station is "If you want to wait, pay PhP45 per liter; if you do't want to wait, pay PhP55/liter." Service mean time (exponential distribution) = 5 minutes Arrival rate (Poisson distribution) = 10 per hour. Customers usually wait to buy gasoline. a) What is the probability (in decimal) that customer will wait? Answer in 4 decimal places.b) Determine the probability that the customer will not wait. Answer in 4 decimal places.c) How many customers are falling in line? Answer in integer value.d) Determine the expected price of gasoline per liter.
For the first three minutes of the day, the arrival rate at the book store is 23 customers per minute. The book store is capable of serving 21 customers per minute. Assume that the system is empty at the start and that no customer who arrives leaves without being served. (Round your answer to 2 decimal places.) What is the average wait time for customers during this time period (in minutes)? minute
[Queuing Theory - Operation research] The take-out counter at an ice-cream parlor is serviced by one attendant. Customers arrive according to a Poisson process, at a mean arrival rate of 30 per hour. They are serviced on a FCFS basis, and because of the quality of the ice cream, they are willing to wait if necessary. The service time per customer appears to be exponentially distributed, with a mean of 1.5 minutes. Determine the following: (a) probability that the system is idle (b) average number of customers in the system (c) amount of time a customer should expect to wait before service (d) probability that a customer will have to spend more than 15 minutes in the queue
In an M/MA queueing system, the arrival rate is 5 customers per hour and the service rate is 9 customers per hour. If the service process is automated (resulting in no varlation 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? Ubization b. What is the expected number of customers in the system (L)? Number of customers c. What is the expected walting time (in hours) for the system (W? Waiting timetin nours)
Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.c. How many customers are in the bakery on average?
Customers arrive randomly to an airport shoe-shine stand with only ONE attendant at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. Assume that service times are exponentially distributed and that the queuing system model is (M/M/1):(GD/infinity/infinity). Does this queuing system have a steady state? It cannot be determined. Yes none of the other choices No
Please do not give solution in image formate thanku. A new shopping mall is considering setting up an information desk manned by one employee. Based upon information obtained from similar information desks, it is believed that people will arrive at the desk at a rate of 20 per hour. It takes an average of 2 minutes to answer a question. It is assumed that the arrivals follow a Poisson distribution and answer times are exponentially distributed. Required: (g) Assume that the information desk employee earns $10 per hour. The cost of waiting time, in terms of customer unhappiness with the mall, is $12 per hour of time spent waiting in line. Find the total expected costs over an 8-hour day.

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There is a Poisson queuing system with the average customer arrival rate of 3 cus per half of hour. This system starts working at 9:0 am. For this system, calculates: iv. The least number of servers needed in the system to ensure that each server wo busy in 70 percent of time at most.